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Appendix C Answers to Exercises

I Linear Equations and Lines
1 Variables, Expressions, Equations, and Inequalities
1.1 Variables and Evaluating Expressions
1.1.6 Exercises

Skills Practice

1.1.6.1.
1.1.6.1.a
Answer 1.
\(d\hbox{, }D\hbox{, }x\hbox{, or }y\)
Answer 2.
\({\text{feet}}\)
1.1.6.1.b
Answer 1.
\(w\hbox{, }W\hbox{, }x\hbox{, or }y\)
Answer 2.
\({\text{pounds}}\)
1.1.6.3.
Answer.
\(5\)
1.1.6.5.
Answer.
\(4\)
1.1.6.7.
Answer.
\(1\)
1.1.6.9.
Answer.
\(-9\)
1.1.6.11.
Answer.
\(11\)
1.1.6.13.
Answer.
\(66\)
1.1.6.15.
Answer.
\(-34\)
1.1.6.17.
1.1.6.17.a
Answer.
\(16\)
1.1.6.17.b
Answer.
\(81\)
1.1.6.19.
1.1.6.19.a
Answer.
\(-36\)
1.1.6.19.b
Answer.
\(-64\)
1.1.6.21.
1.1.6.21.a
Answer.
\(729\)
1.1.6.21.b
Answer.
\(-216\)
1.1.6.23.
1.1.6.23.a
Answer.
\(324\)
1.1.6.23.b
Answer.
\(108\)
1.1.6.25.
Answer.
\(60\)
1.1.6.27.
Answer.
\(33\)
1.1.6.29.
Answer.
\(4 {\textstyle\frac{1}{2}}\)
1.1.6.31.
Answer.
\(3\)
1.1.6.33.
Answer.
\(-4\)
1.1.6.35.
Answer.
\(-3\)
1.1.6.37.
Answer.
\(-90\)
1.1.6.39.
Answer.
\(-130\)
1.1.6.41.
Answer.
\(81\)
1.1.6.43.
Answer.
\(5832\)
1.1.6.45.
Answer.
\(15\)
1.1.6.47.
Answer.
\(-65\)
1.1.6.49.
Answer.
\(17\)
1.1.6.51.
Answer.
\(-75\)
1.1.6.53.
Answer.
\(-4\)
1.1.6.55.
Answer.
\(10\)

Applications

1.1.6.57.
Answer.
\(280\ {\rm degK}\)
1.1.6.59.
Answer.
\(174\ {\rm years}\)
1.1.6.61.
Answer.
\(204\ {\rm mi}\)
1.1.6.63.
Answer.
\(75600\ {\rm seconds}\)
1.1.6.65.
Answer.
\(37.4\ {\rm degF}\)
1.1.6.67.
Answer.
\(111\ {\rm bpm}\)
1.1.6.69.
Answer.
\(30.3\%\)
1.1.6.71.
Answer.
\(99\ {\rm ft}\)
1.1.6.73.
Answer.
\(129.766\ {\rm feet}\)
1.1.6.75.
Answer.
\(3.42208\ {\rm seconds}\)
1.1.6.77.
Answer.
\(32.2\%\)
1.1.6.79.
Answer.
\(26\)
1.1.6.81.
1.1.6.81.a
Answer.
\(4.4\ {\rm ft}\)
1.1.6.81.b
Answer.
\(5.2\ {\rm ft}\)
1.1.6.83.
Answer.
\(60x\)
1.1.6.85.
Answer.
\(1.8x\)
1.1.6.87.
Answer.
\(n+5\)
1.1.6.89.
Answer.
\(360+125n\)

1.2 Combining Like Terms
1.2.5 Exercises

Prerequisite/Review Skills

1.2.5.1.
Answer.
\({\frac{22}{17}}\)
1.2.5.3.
Answer.
\({\frac{4}{17}}\)
1.2.5.5.
Answer.
\({\frac{11}{8}}\)
1.2.5.7.
Answer.
\({\frac{1}{6}}\)
1.2.5.9.
Answer.
\({\frac{81}{11}}\)
1.2.5.11.
Answer.
\({\frac{3}{10}}\)
1.2.5.13.
Answer.
\({\frac{83}{182}}\)
1.2.5.15.
Answer.
\({\frac{1}{12}}\)
1.2.5.17.
Answer.
\({\frac{61}{63}}\)
1.2.5.19.
Answer.
\({\frac{13}{40}}\)
1.2.5.21.
Answer.
\({\frac{2}{3}}\)
1.2.5.23.
Answer.
\({\frac{1}{3}}\)
1.2.5.25.
Answer.
\({\frac{79}{60}}\)
1.2.5.27.
Answer.
\({\frac{58}{63}}\)
1.2.5.29.
Answer.
\({\frac{47}{126}}\)
1.2.5.31.
Answer.
\({\frac{2}{35}}\)

Skills Practice

1.2.5.33.
Answer.
\(-{\frac{1}{2}}u, t, 2.7D, 18b\)
1.2.5.35.
Answer.
\({\frac{3}{10}}J, -13k, 49J\)
1.2.5.37.
Answer.
\({\frac{1}{10}}, 77x^{5}, -x^{9}\)
1.2.5.39.
Answer.
\(5.5y^{8}, -y^{9}, y^{9}\)
1.2.5.41.
Answer.
\(18.2K\)
1.2.5.43.
Answer.
\(\frac{6}{5}X\)
1.2.5.45.
Answer.
\(8.1i-l\)
1.2.5.47.
Answer.
\(-10u+4u^{3}+\frac{8}{3}u^{4}\)
1.2.5.49.
Answer.
\(\frac{-31}{6}F+\frac{1}{2}R\)
1.2.5.51.
Answer.
\(34R+6.8g\)
1.2.5.53.
Answer.
\(\frac{49}{36}c^{2}-2c^{5}\)
1.2.5.55.
Answer.
\(0.6n^{4}+14.9n^{6}\)
1.2.5.57.
Answer.
\(-9z\)
1.2.5.59.
Answer.
\(-3.9K\)
1.2.5.61.
Answer.
\(\frac{11}{3}W+\frac{29}{10}H\)
1.2.5.63.
Answer.
\(-6.3h+10.5Y\)
1.2.5.65.
Answer.
\(-71.2t^{2}+1.3t^{6}\)
1.2.5.67.
Answer.
\(\frac{88}{21}E^{3}+\frac{2}{5}E^{5}\)

Applications

1.2.5.69.
Answer.
\(\frac{53}{12}Q+\frac{9}{4}U\)
1.2.5.71.
Answer.
\(6.9c+81.3k\)
1.2.5.73.
Answer.
\(\frac{37}{8}n+\frac{19}{6}z+2c\)
1.2.5.75. Office Lunch.
1.2.5.75.a
Answer.
\(14S+8B\)
1.2.5.75.b
Answer.
\(27S+18B\)
1.2.5.77. Sportsball.
1.2.5.77.a
Answer.
\(19P+36L+44S\)
1.2.5.77.b
Answer.
\(25P+60L+81S\)

1.3 Comparison Symbols and Notation for Intervals
1.3.4 Exercises

Prerequisite/Review Skills

1.3.4.1.
Answer.
\(2.2\)
1.3.4.3.
Answer.
\(7.25\)
1.3.4.5.
Answer.
\(4.875\)
1.3.4.7.
Answer.
\(0.05\)
1.3.4.9.
Answer.
\(3.33333\)
1.3.4.11.
Answer.
\(5.83333\)
1.3.4.13.
Answer.
\(1.54545\)
1.3.4.15.
Answer.
\(4.58333\)

Skills Practice

1.3.4.17.
Answer.
\(\text{False}\)
1.3.4.19.
Answer.
\(\text{False}\)
1.3.4.21.
Answer.
\(\text{False}\)
1.3.4.23.
Answer.
\(\text{True}\)
1.3.4.25.
Answer.
\(\text{True}\)
1.3.4.27.
Answer.
\({\verb!<!}\)
1.3.4.29.
Answer.
\({\verb!>!}\)
1.3.4.31.
Answer.
\({\verb!<!}\)
1.3.4.33.
Answer.
\({\text{=}}\)
1.3.4.35.
Answer.
\({\verb!<!}\)
1.3.4.37.
Answer.
\(9>6>0>-3>-6\)
1.3.4.39.
Answer.
\(8.9>1.8>-0.7>-4.9>-5.8\)
1.3.4.41.
Answer.
\({\frac{10}{7}}>{\frac{11}{8}}>{\frac{7}{6}}>{\frac{1}{2}}>{\frac{2}{9}}\)
1.3.4.43.
Answer.
\({\frac{8}{13}}>0.3>\sqrt{3}>\frac{\pi }{4}>5\)
1.3.4.45.
Answer 1.
\(\left\{x \mid x < -4\right\}\)
Answer 2.
\(\left(-\infty ,-4\right)\)
1.3.4.47.
Answer 1.
\(\left\{x \mid x\le -1\right\}\)
Answer 2.
\(\left(-\infty ,-1\right]\)
1.3.4.49.
Answer 1.
\(\left\{x \mid x\ge 3\right\}\)
Answer 2.
\(\left[3,\infty \right)\)
1.3.4.51.
Answer 1.
\(\left\{x \mid x > 6\right\}\)
Answer 2.
\(\left(6,\infty \right)\)
1.3.4.53.
Answer 1.
\(\left\{\text{interval}, \left[-6,\infty \right)\right\}\)
Answer 2.
\(\left[-6,\infty \right)\)
1.3.4.55.
Answer 1.
\(\left\{\text{interval}, \left(-\infty ,-2\right)\right\}\)
Answer 2.
\(\left(-\infty ,-2\right)\)
1.3.4.57.
Answer 1.
\(\left\{\text{interval}, \left(-\infty ,1\right]\right\}\)
Answer 2.
\(\left(-\infty ,1\right]\)
1.3.4.59.
Answer 1.
\(\left\{\text{interval}, \left(4,\infty \right)\right\}\)
Answer 2.
\(\left(4,\infty \right)\)
1.3.4.61.
Answer 1.
\(\left\{\text{interval}, \left[-7,\infty \right)\right\}\)
Answer 2.
\(\left\{x \mid x\ge -7\right\}\)
1.3.4.63.
Answer 1.
\(\left\{\text{interval}, \left(-4,\infty \right)\right\}\)
Answer 2.
\(\left\{x \mid x > -4\right\}\)
1.3.4.65.
Answer 1.
\(\left\{\text{interval}, \left(-\infty ,-1\right)\right\}\)
Answer 2.
\(\left\{x \mid x < -1\right\}\)
1.3.4.67.
Answer 1.
\(\left\{\text{interval}, \left(-\infty ,3\right]\right\}\)
Answer 2.
\(\left\{x \mid x\le 3\right\}\)

Applications

1.3.4.69.
Answer 1.
\(\left\{a \mid a\ge 21\right\}\)
Answer 2.
\(\left[21,\infty \right)\)
1.3.4.71.
Answer 1.
\(\left\{d \mid d\ge 5000\right\}\)
Answer 2.
\(\left[5000,\infty \right)\)
1.3.4.73.
Answer 1.
\(\left\{\mathrm{pH} \mid \mathrm{pH} < 7\right\}\)
Answer 2.
\(\left(-\infty ,7\right)\)

Challenge

1.3.4.75.
Answer 1.
\({\verb!<!}\)
Answer 2.
\({\verb!>!}\)
Answer 3.
\({\verb!<!}\)
Answer 4.
\({\verb!>!}\)

1.4 Equations, Inequalities, and Solutions
1.4.6 Exercises

Prerequisite/Review Skills

1.4.6.1.
Answer.
\(0\)
1.4.6.3.
Answer.
\({\frac{2}{9}}\)
1.4.6.5.
Answer.
\(45\)
1.4.6.7.
Answer.
\(67\)

Skills Practice

1.4.6.9.
Answer 1.
\(6\)
Answer 2.
\(\text{Yes, it is a solution.}\)
1.4.6.11.
Answer 1.
\(-57.4\)
Answer 2.
\(\text{No, it is not a solution.}\)
1.4.6.13.
Answer 1.
\({\frac{14}{3}}\)
Answer 2.
\(\text{Yes, it is a solution.}\)
1.4.6.15.
Answer 1.
\(-2\)
Answer 2.
\(3\)
Answer 3.
\(\text{No, it is not a solution.}\)
1.4.6.17.
Answer 1.
\({\frac{23}{5}}\)
Answer 2.
\({\frac{189}{40}}\)
Answer 3.
\(\text{No, it is not a solution.}\)
1.4.6.19.
Answer 1.
\(0\)
Answer 2.
\(\text{No, it is not a solution.}\)
1.4.6.21.
Answer 1.
\(42\)
Answer 2.
\(42\)
Answer 3.
\(\text{Yes, it is a solution.}\)
1.4.6.23.
Answer 1.
\(0\)
Answer 2.
\(\text{Yes, it is a solution.}\)
1.4.6.25.
Answer 1.
\(3\)
Answer 2.
\(6\)
Answer 3.
\(\text{No, it is not a solution.}\)
1.4.6.27.
Answer 1.
\(8\)
Answer 2.
\(8\)
Answer 3.
\(\text{Yes, it is a solution.}\)
1.4.6.29.
Answer 1.
\(32\)
Answer 2.
\(\text{No, it is not a solution.}\)
1.4.6.31.
Answer 1.
\(6\)
Answer 2.
\(14\)
Answer 3.
\(\text{No, it is not a solution.}\)
1.4.6.33.
Answer 1.
\({\frac{257}{56}}\)
Answer 2.
\({\frac{257}{56}}\)
Answer 3.
\(\text{Yes, it is a solution.}\)
1.4.6.35.
Answer 1.
\(18\)
Answer 2.
\(\text{No, it is not a solution.}\)
1.4.6.37.
Answer 1.
\(68.1\)
Answer 2.
\(\text{Yes, it is a solution.}\)
1.4.6.39.
Answer 1.
\({\frac{116}{45}}\)
Answer 2.
\(\text{No, it is not a solution.}\)
1.4.6.41.
Answer 1.
\(-18\)
Answer 2.
\(-18\)
Answer 3.
\(\text{Yes, it is a solution.}\)
1.4.6.43.
Answer 1.
\({\frac{38}{3}}\)
Answer 2.
\({\frac{38}{3}}\)
Answer 3.
\(\text{Yes, it is a solution.}\)
1.4.6.45.
Answer 1.
\(8\)
Answer 2.
\(\text{Yes, it is a solution.}\)
1.4.6.47.
Answer 1.
\(5\)
Answer 2.
\(5\)
Answer 3.
\(\text{Yes, it is a solution.}\)
1.4.6.49.
Answer 1.
\(0\)
Answer 2.
\(\text{Yes, it is a solution.}\)
1.4.6.51.
Answer 1.
\(6\)
Answer 2.
\(6\)
Answer 3.
\(\text{No, it is not a solution.}\)
1.4.6.53.
Answer 1.
\(8\)
Answer 2.
\(8\)
Answer 3.
\(\text{No, it is not a solution.}\)
1.4.6.55.
Answer 1.
\(15\)
Answer 2.
\(\text{No, it is not a solution.}\)
1.4.6.57.
Answer 1.
\(8.7\)
Answer 2.
\(8.7\)
Answer 3.
\(\text{No, it is not a solution.}\)
1.4.6.59.
Answer 1.
\({\frac{11}{3}}\)
Answer 2.
\({\frac{11}{3}}\)
Answer 3.
\(\text{Yes, it is a solution.}\)
1.4.6.61.
Answer.
\(\text{Choice 2, Choice 4, Choice 5}\)
1.4.6.63.
Answer.
\(\text{Choice 2, Choice 6}\)
1.4.6.65.
Answer.
\(\text{Choice 4, Choice 6}\)

Applications

1.4.6.67.
Answer 1.
\(55.56\)
Answer 2.
\(\text{Yes, it is a solution.}\)
1.4.6.69.
Answer 1.
\(696\)
Answer 2.
\(\text{Yes, it is a solution.}\)
1.4.6.71.
Answer 1.
\(22\)
Answer 2.
\(\text{Yes, it is a solution.}\)
1.4.6.73.
Answer 1.
\(1225\)
Answer 2.
\(1225\)
Answer 3.
\(\text{Yes, it is a solution.}\)
1.4.6.75.
Answer 1.
\(\frac{1}{294}\pi \)
Answer 2.
\(\text{Yes, it is a solution.}\)

1.5 Solving One-Step Equations
1.5.6 Exercises

Review and Warmup

1.5.6.1.
Answer.
\({\frac{10}{81}}\)
1.5.6.3.
Answer.
\({\frac{32}{81}}\)
1.5.6.5.
Answer.
\({\frac{63}{2}}\)
1.5.6.7.
Answer.
\({\frac{32}{7}}\)
1.5.6.9.
Answer.
\({\frac{23}{19}}\)
1.5.6.11.
Answer.
\({\frac{1}{3}}\)
1.5.6.13.
Answer.
\({\frac{31}{12}}\)
1.5.6.15.
Answer.
\({\frac{295}{234}}\)
1.5.6.17.
Answer.
\({\frac{69}{88}}\)
1.5.6.19.
Answer.
\({\frac{55}{36}}\)
1.5.6.21.
Answer.
\({\frac{5}{63}}\)

Skills Practice

1.5.6.23.
Answer.
\(\left\{-17\right\}\)
1.5.6.25.
Answer.
\(\left\{18\right\}\)
1.5.6.27.
Answer.
\(\left\{-9\right\}\)
1.5.6.29.
Answer.
\(\left\{168\right\}\)
1.5.6.31.
Answer.
\(\left\{-4\right\}\)
1.5.6.33.
Answer.
\(\left\{\frac{10}{11}\right\}\)
1.5.6.35.
Answer.
\(\left\{-3\right\}\)
1.5.6.37.
Answer.
\(\left\{162\right\}\)
1.5.6.39.
Answer.
\(\left\{\frac{31}{12}\right\}\)
1.5.6.41.
Answer.
\(\left\{\frac{-59}{28}\right\}\)
1.5.6.43.
Answer.
\(\left\{\frac{31}{6}\right\}\)
1.5.6.45.
Answer.
\(\left\{\frac{-21}{4}\right\}\)
1.5.6.47.
Answer.
\(\left\{\frac{4}{7}\right\}\)
1.5.6.49.
Answer.
\(\left\{\frac{-36}{35}\right\}\)
1.5.6.51.
Answer.
\(\left\{-18.1\right\}\)
1.5.6.53.
Answer.
\(\left\{-21.57\right\}\)
1.5.6.55.
Answer.
\(\left\{23.03\right\}\)
1.5.6.57.
Answer.
\(\left\{-28.08\right\}\)
1.5.6.59.
Answer.
\(\left\{-0.652174\right\}\)

Applications

1.5.6.61.
Answer 1.
\(74 = C+273\)
Answer 2.
\(-199\ {\rm degC}\)
1.5.6.63.
Answer 1.
\(8.625+N = 17.5\)
Answer 2.
\(8.875\ {\rm in}\)
1.5.6.65.
Answer 1.
\(s\cdot 0.8 = 7\)
Answer 2.
\(\$8.75\)
1.5.6.67.
Answer 1.
\(10\pi = \pi d\)
Answer 2.
\(10\ {\rm cm}\)
1.5.6.69.
Answer 1.
\(-449.44+5.3v+6 = 0\)
Answer 2.
\(83.6679\ {\textstyle\frac{\rm\mathstrut ft}{\rm\mathstrut s}}\)

Challenge

1.5.6.71.
Answer.
\(x+1=6\)

1.6 Solving One-Step Inequalities
1.6.4 Exercises

Skills Practice

1.6.4.1.
Answer 1.
\(\left\{\text{interval}, \left(-\infty ,-2\right]\right\}\)
Answer 2.
\(\left(-\infty ,-2\right]\)
Answer 3.
\(\left\{u \mid u\le -2\right\}\)
1.6.4.3.
Answer 1.
\(\left\{\text{interval}, \left(-\infty ,2\right)\right\}\)
Answer 2.
\(\left(-\infty ,2\right)\)
Answer 3.
\(\left\{E \mid E < 2\right\}\)
1.6.4.5.
Answer 1.
\(\left\{\text{interval}, \left(5,\infty \right)\right\}\)
Answer 2.
\(\left(5,\infty \right)\)
Answer 3.
\(\left\{Q \mid Q > 5\right\}\)
1.6.4.7.
Answer 1.
\(\left\{\text{interval}, \left[-4,\infty \right)\right\}\)
Answer 2.
\(\left[-4,\infty \right)\)
Answer 3.
\(\left\{c \mid c\ge -4\right\}\)
1.6.4.9.
Answer 1.
\(\left\{\text{interval}, \left(-\infty ,-8\right)\right\}\)
Answer 2.
\(\left(-\infty ,-8\right)\)
Answer 3.
\(\left\{n \mid n < -8\right\}\)
1.6.4.11.
Answer 1.
\(\left\{\text{interval}, \left(12,\infty \right)\right\}\)
Answer 2.
\(\left(12,\infty \right)\)
Answer 3.
\(\left\{z \mid z > 12\right\}\)
1.6.4.13.
Answer 1.
\(\left\{\text{interval}, \left(-\infty ,-5\right)\right\}\)
Answer 2.
\(\left(-\infty ,-5\right)\)
Answer 3.
\(\left\{K \mid K < -5\right\}\)
1.6.4.15.
Answer 1.
\(\left\{\text{interval}, \left(1,\infty \right)\right\}\)
Answer 2.
\(\left(1,\infty \right)\)
Answer 3.
\(\left\{X \mid X > -\left(-1\right)\right\}\)
1.6.4.17.
Answer 1.
\(\left\{\text{interval}, \left(-\infty ,4\right)\right\}\)
Answer 2.
\(\left(-\infty ,4\right)\)
Answer 3.
\(\left\{h \mid h < 4\right\}\)
1.6.4.19.
Answer 1.
\(\left\{\text{interval}, \left[-6,\infty \right)\right\}\)
Answer 2.
\(\left[-6,\infty \right)\)
Answer 3.
\(\left\{t \mid t\ge -6\right\}\)

1.7 Algebraic Properties and Simplifying Expressions
1.7.6 Exercises

Vocabulary

1.7.6.1.
Answer.
\(9\)
1.7.6.3.
Answer.
\(-{\frac{1}{5}}\)
1.7.6.5.
Answer.
\(0.4\)
1.7.6.7.
Answer.
\({\frac{8}{7}}\)
1.7.6.9.
Answer.
\(-{\frac{3}{2}}\)
1.7.6.11.
Answer.
\(0\)

Skills Practice

1.7.6.13.
Answer.
\(P+\left(21+t\right)\)
1.7.6.15.
Answer.
\(\left(E+E^{2}\right)+{\frac{1}{7}}\)
1.7.6.17.
Answer.
\(18\mathopen{}\left(Qu\right)\)
1.7.6.19.
Answer.
\(K+b\)
1.7.6.21.
Answer.
\(a+{\frac{5}{8}}m\)
1.7.6.23.
Answer.
\(qy+t\)
1.7.6.25.
Answer.
\(\left(J+3\right)\cdot 7\)
1.7.6.27.
Answer.
\(10\mathopen{}\left(2+W\right)\)
1.7.6.29.
Answer.
\(4h+4\cdot 9\)
1.7.6.31.
Answer.
\(6t-6\cdot 8\)
1.7.6.33.
Answer.
\(\frac{9}{5}D+\frac{9}{5}\frac{7}{2}\)
1.7.6.35.
Answer.
\(-P-\left(\frac{3}{5}\right)\)
1.7.6.37.
Answer.
\(13x\)
1.7.6.39.
Answer.
\(\frac{5}{9}x\)
1.7.6.41.
Answer.
\(17y+21\)
1.7.6.43.
Answer.
\(23J+6\)
1.7.6.45.
Answer.
\(35W+52\)
1.7.6.47.
Answer.
\(36g+\left(-21\right)\)
1.7.6.49.
Answer.
\(42s+73\)
1.7.6.51.
Answer.
\(-23D+38\)
1.7.6.53.
Answer.
\(60P+39\)
1.7.6.55.
Answer.
\(17b+22\)
1.7.6.57.
Answer.
\(\frac{146}{3}B+\frac{-56}{5}\)
1.7.6.59.
Answer.
\(26.06y+\left(-54.62\right)\)

Critical Thinking

1.7.6.61.
1.7.6.61.a
Answer.
\(\left(I+f\right)+l\)
1.7.6.61.b
Answer.
\(I+\left(f+l\right)\)

1.8 Modeling with Equations and Inequalities
1.8.6 Exercises

Review and Warmup

1.8.6.1.
1.8.6.1.a
Answer 1.
\(a\hbox{, }A\hbox{, }x\hbox{, }y\hbox{, or }z\)
Answer 2.
\({\verb!ft^2 or m^2!}\)
1.8.6.1.b
Answer 1.
\(a\hbox{, }A\hbox{, }x\hbox{, }y\hbox{, or }z\)
Answer 2.
\({\text{years or months}}\)
1.8.6.1.c
Answer 1.
\(t\hbox{, }T\hbox{, }x\hbox{, }y\hbox{, or }z\)
Answer 2.
\({\text{hours or minutes}}\)

Skills Practice

1.8.6.3.
Answer.
\(x+8\)
1.8.6.5.
Answer.
\(1+x\)
1.8.6.7.
Answer.
\(x-3\)
1.8.6.9.
Answer.
\(5-x\)
1.8.6.11.
Answer.
\(11x+14\)
1.8.6.13.
Answer.
\(14\mathopen{}\left(x+4\right)\)
1.8.6.15.
Answer.
\(8x-3\)
1.8.6.17.
Answer.
\(\frac{x}{12}-6\)
1.8.6.19.
Answer.
\({\frac{9}{4}}x\)
1.8.6.21.
Answer.
\(x-{\frac{12}{13}}x\)
1.8.6.23.
Answer.
\(11x+2\)
1.8.6.25.
Answer.
\(x-20 = 50\)
1.8.6.27.
Answer.
\(\frac{x}{8} = 5\)
1.8.6.29.
Answer.
\(x-38 = 34\)
1.8.6.31.
Answer.
\(\frac{x}{14} = 13\)
1.8.6.33.
Answer.
\(14x-3 = 5\)
1.8.6.35.
Answer.
\(6\mathopen{}\left(x+9\right) = 12\)
1.8.6.37.
Answer.
\(9x = 2x-13\)

Applications

1.8.6.39.
Answer.
\(510t = 360\)
1.8.6.41.
Answer.
\(100+56t = 282\)
1.8.6.43.
Answer.
\(6+0.25t = 10\)
1.8.6.45.
Answer.
\(389.5+4.12t = 780\)
1.8.6.47.
Answer.
\(57+28t = 212\)
1.8.6.49.
Answer.
\(425-27t = 250\)
1.8.6.51.
Answer.
\(100-7t = 30\)
1.8.6.53.
Answer.
\(90+13n = 350\)
1.8.6.55.
Answer.
\(S+0.024S = 57999\)
1.8.6.57.
Answer.
\(p+0.067p = 472\)
1.8.6.59.
Answer.
\(p-0.2p = 332\)
1.8.6.61.
Answer.
\(b+0.18b = 73.2\)
1.8.6.63.
Answer.
\(r+0.025r = 1360\)
1.8.6.65.
Answer.
\(80+8.3454V\le 1900\)
1.8.6.67.
Answer.
\(7.8-0.5t\ge 0.5\)
1.8.6.69.
Answer.
\(S+0.029S < 71385\)
1.8.6.71.
Answer.
\(b+0.2b\le 79.65\)

Challenge

1.8.6.73.
Answer.
\(\$10.62\)

1.9 Variables, Expressions, and Equations Chapter Review

Review Exercises for Chapter 1

Section 1: Variables and Evaluating Expressions
1.9.1.
1.9.1.a
Answer 1.
\(t\hbox{, }T\hbox{, }x\hbox{, or }y\)
Answer 2.
\({\text{hours or minutes}}\)
1.9.1.b
Answer 1.
\(a\hbox{, }A\hbox{, }s\hbox{, }S\hbox{, }x\hbox{, or }y\)
Answer 2.
\({\verb!ft^2 or m^2!}\)
1.9.3.
Answer.
\(-13\)
1.9.5.
1.9.5.a
Answer.
\(512\)
1.9.5.b
Answer.
\(-216\)
1.9.7.
Answer.
\(-5\)
1.9.9.
Answer.
\(-1\)
1.9.11.
Answer.
\(291\ {\rm mi}\)
1.9.13.
Answer.
\(70\ {\rm feet}\)
1.9.15.
Answer.
\(5280x\)
1.9.17.
Answer.
\(140+40n\)
Section 2: Combining Like Terms
1.9.19.
Answer.
\(\frac{7}{3}e\)
1.9.21.
Answer.
\(\frac{-32}{7}q\)
1.9.23.
Answer.
\(\frac{29}{30}B+\frac{4}{3}A\)
1.9.25.
1.9.25.a
Answer.
\(24p+19c\)
1.9.25.b
Answer.
\(40p+39c\)
Section 3: Comparison Symbols and Notation for Intervals
1.9.27.
Answer.
\(\text{False}\)
1.9.29.
Answer.
\({\verb!<!}\)
1.9.31.
Answer.
\(9.5>4.2>3.6>-4>-4.1\)
1.9.33.
Answer 1.
\(\left\{x \mid x > 2\right\}\)
Answer 2.
\(\left(2,\infty \right)\)
1.9.35.
Answer 1.
\(\left\{\text{interval}, \left(-\infty ,5\right)\right\}\)
Answer 2.
\(\left\{x \mid x < 5\right\}\)
1.9.37.
Answer 1.
\(\left\{\mathrm{pH} \mid \mathrm{pH} < 7\right\}\)
Answer 2.
\(\left(-\infty ,7\right)\)
Section 4: Equations, Inequalities, and Solutions
1.9.39.
Answer 1.
\(-58\)
Answer 2.
\(-52\)
Answer 3.
\(\text{No, it is not a solution.}\)
1.9.41.
Answer 1.
\(48\)
Answer 2.
\(\text{No, it is not a solution.}\)
1.9.43.
Answer 1.
\({\frac{11}{2}}\)
Answer 2.
\({\frac{13}{2}}\)
Answer 3.
\(\text{No, it is not a solution.}\)
1.9.45.
Answer 1.
\(51\)
Answer 2.
\(\text{Yes, it is a solution.}\)
1.9.47.
Answer 1.
\(730\)
Answer 2.
\(\text{Yes, it is a solution.}\)
1.9.49.
Answer 1.
\(49.8087\)
Answer 2.
\(\text{No, it is not a solution.}\)
Section 5: Solving One-Step Equations
1.9.51.
Answer.
\(\left\{-12\right\}\)
1.9.53.
Answer.
\(\left\{10.3\right\}\)
1.9.55.
Answer 1.
\(6.25+N = 17.5\)
Answer 2.
\(11.25\ {\rm in}\)
Section 6: Solving One-Step Inequalities
1.9.57.
Answer 1.
\(\left\{\text{interval}, \left[4,\infty \right)\right\}\)
Answer 2.
\(\left[4,\infty \right)\)
Answer 3.
\(\left\{p \mid p\ge 4\right\}\)
Section 7: Algebraic Properties and Simplifying Expressions
1.9.59.
Answer.
\(0\)
1.9.61.
Answer.
\(\left(L+10\right)\cdot 4\)
1.9.63.
Answer.
\(\frac{-22}{21}x\)
1.9.65.
Answer.
\(-2i+21\)
Section 8: Modeling with Equations and Inequalities
1.9.67.
Answer.
\(5+x\)
1.9.69.
Answer.
\(x-{\frac{9}{14}}x\)
1.9.71.
Answer.
\(3x-13 = 12\)
1.9.73.
Answer.
\(12-0.05d = 1\)
1.9.75.
Answer.
\(425-24t = 275\)
1.9.77.
Answer.
\(S+0.028S = 66466\)
1.9.79.
Answer.
\(7.7-0.7t\ge 0.4\)

2 Linear Equations and Inequalities
2.1 Solving Multistep Linear Equations
2.1.6 Exercises

Review and Warmup

2.1.6.1.
Answer.
\(\left\{-6\right\}\)
2.1.6.3.
Answer.
\(\left\{-17\right\}\)
2.1.6.5.
Answer.
\(\left\{\frac{2}{7}\right\}\)

Vocabulary

2.1.6.7.
2.1.6.7.a
Answer.
\(\text{solve}\)
2.1.6.7.b
Answer.
\(\text{simplified}\)
2.1.6.7.c
Answer.
\(\text{simplify}\)
2.1.6.7.d
Answer.
\(\text{evaluate}\)

Skills Practice

2.1.6.9.
Answer.
\(\left\{6\right\}\)
2.1.6.11.
Answer.
\(\left\{-7\right\}\)
2.1.6.13.
Answer.
\(\left\{-1\right\}\)
2.1.6.15.
Answer.
\(\left\{\frac{13}{6}\right\}\)
2.1.6.17.
Answer.
\(\left\{\frac{-5}{9}\right\}\)
2.1.6.19.
Answer.
\(\left\{\frac{-1}{2}\right\}\)
2.1.6.21.
Answer.
\(\left\{0.756757\right\}\)
2.1.6.23.
Answer.
\(\left\{0.366197\right\}\)
2.1.6.25.
Answer.
\(\left\{-0.6\right\}\)
2.1.6.27.
Answer.
\(\left\{2\right\}\)
2.1.6.29.
Answer.
\(\left\{7\right\}\)
2.1.6.31.
Answer.
\(\left\{-6\right\}\)
2.1.6.33.
Answer.
\(\left\{4\right\}\)
2.1.6.35.
Answer.
\(\left\{6\right\}\)
2.1.6.37.
Answer.
\(\left\{-8\right\}\)
2.1.6.39.
Answer.
\(\left\{\frac{-1}{4}\right\}\)
2.1.6.41.
Answer.
\(\left\{\frac{-3}{2}\right\}\)
2.1.6.43.
Answer.
\(\left\{\frac{67}{25}\right\}\)
2.1.6.45.
Answer.
\(\left\{\frac{-26}{31}\right\}\)
2.1.6.47.
Answer.
\(\left\{2\right\}\)
2.1.6.49.
Answer.
\(\left\{8\right\}\)
2.1.6.51.
Answer.
\(\left\{\frac{-25}{4}\right\}\)

Applications

2.1.6.53.
Answer.
\(4.25862\ {\rm hr}\)
2.1.6.55.
Answer.
\(12\ {\rm yr}\)
2.1.6.57.
Answer.
\(58.913\ {\rm weeks}\)
2.1.6.59.
Answer.
\(6.16\ {\rm min}\)
2.1.6.61.
Answer.
\(7.14286\ {\rm min}\)
2.1.6.63.
Answer.
\(8.88889\ {\rm days}\)
2.1.6.65.
Answer.
\(23\)
2.1.6.67.
Answer.
\(\$60{,}685.36\)
2.1.6.69.
Answer.
\(\$462.11\)
2.1.6.71.
Answer.
\(\$1{,}251.23\)

2.2 Solving Multistep Linear Inequalities
2.2.4 Exercises

Review and Warmup

2.2.4.1.
Answer 1.
\(\left\{\text{interval}, \left(-3,\infty \right)\right\}\)
Answer 2.
\(\left(-3,\infty \right)\)
Answer 3.
\(\left\{D \mid D > -3\right\}\)
2.2.4.3.
Answer 1.
\(\left\{\text{interval}, \left[8,\infty \right)\right\}\)
Answer 2.
\(\left[8,\infty \right)\)
Answer 3.
\(\left\{P \mid P\ge 8\right\}\)

Skills Practice

2.2.4.5.
Answer 1.
\(\left\{\text{interval}, \left(-\infty ,5\right]\right\}\)
Answer 2.
\(\left(-\infty ,5\right]\)
Answer 3.
\(\left\{b \mid b\le 5\right\}\)
2.2.4.7.
Answer 1.
\(\left\{\text{interval}, \left(-\infty ,-4\right]\right\}\)
Answer 2.
\(\left(-\infty ,-4\right]\)
Answer 3.
\(\left\{m \mid m\le -4\right\}\)
2.2.4.9.
Answer 1.
\(\left\{\text{interval}, \left[-1,\infty \right)\right\}\)
Answer 2.
\(\left[-1,\infty \right)\)
Answer 3.
\(\left\{y \mid y\ge -1\right\}\)
2.2.4.11.
Answer 1.
\(\left\{\text{interval}, \left[3,\infty \right)\right\}\)
Answer 2.
\(\left[3,\infty \right)\)
Answer 3.
\(\left\{J \mid J\ge 3\right\}\)
2.2.4.13.
Answer 1.
\(\left\{\text{interval}, \left(-\infty ,-6\right]\right\}\)
Answer 2.
\(\left(-\infty ,-6\right]\)
Answer 3.
\(\left\{V \mid V\le -6\right\}\)
2.2.4.15.
Answer 1.
\(\left\{\text{interval}, \left(-\infty ,-2\right)\right\}\)
Answer 2.
\(\left(-\infty ,-2\right)\)
Answer 3.
\(\left\{g \mid g < -2\right\}\)
2.2.4.17.
Answer 1.
\(\left\{\text{interval}, \left[2,\infty \right)\right\}\)
Answer 2.
\(\left[2,\infty \right)\)
Answer 3.
\(\left\{s \mid s\ge 2\right\}\)
2.2.4.19.
Answer 1.
\(\left\{\text{interval}, \left[6,\infty \right)\right\}\)
Answer 2.
\(\left[6,\infty \right)\)
Answer 3.
\(\left\{D \mid D\ge 6\right\}\)
2.2.4.21.
Answer 1.
\(\left\{\text{interval}, \left(-\infty ,-3\right)\right\}\)
Answer 2.
\(\left(-\infty ,-3\right)\)
Answer 3.
\(\left\{P \mid P < -3\right\}\)
2.2.4.23.
Answer 1.
\(\left\{\text{interval}, \left(-\infty ,1\right]\right\}\)
Answer 2.
\(\left(-\infty ,1\right]\)
Answer 3.
\(\left\{b \mid b\le 1\right\}\)
2.2.4.25.
Answer 1.
\(\left\{\text{interval}, \left[5,\infty \right)\right\}\)
Answer 2.
\(\left[5,\infty \right)\)
Answer 3.
\(\left\{l \mid l\ge 5\right\}\)
2.2.4.27.
Answer 1.
\(\left\{\text{interval}, \left(-\infty ,-4\right]\right\}\)
Answer 2.
\(\left(-\infty ,-4\right]\)
Answer 3.
\(\left\{x \mid x\le -4\right\}\)
2.2.4.29.
Answer 1.
\(\left\{\text{interval}, \left(-1,\infty \right)\right\}\)
Answer 2.
\(\left(-1,\infty \right)\)
Answer 3.
\(\left\{I \mid I > -1\right\}\)
2.2.4.31.
Answer 1.
\(\left\{\text{interval}, \left(4,\infty \right)\right\}\)
Answer 2.
\(\left(4,\infty \right)\)
Answer 3.
\(\left\{V \mid V > 4\right\}\)

Applications

2.2.4.33.
2.2.4.33.a
Answer.
\(15+2x\le 43\)
2.2.4.33.b
Answer.
\(14\ {\rm mi}\)
2.2.4.33.c
Answer.
\(\left[0,14\right]\)
2.2.4.35.
2.2.4.35.a
Answer.
\(47+24x\ge 212\)
2.2.4.35.b
Answer.
\(6.875\ {\rm min}\)
2.2.4.35.c
Answer.
\(\left[6.875,\infty \right)\)
2.2.4.37.
2.2.4.37.a
Answer.
\(x+0.08x < 94485\)
2.2.4.37.b
Answer.
\(87486\)
2.2.4.37.c
Answer.
\(\left[10000,87486\right)\)

2.3 Equations and Inequalities with Fractions
2.3.5 Exercises

Review and Warmup

2.3.5.1.
Answer.
\(44\)
2.3.5.3.
Answer.
\(630\)
2.3.5.5.
Answer.
\(210\)

Skills Practice

2.3.5.7.
Answer 1.
\(3\)
Answer 2.
\(\left\{\frac{1}{3}\right\}\)
2.3.5.9.
Answer 1.
\(12\)
Answer 2.
\(\left\{\frac{-125}{36}\right\}\)
2.3.5.11.
Answer 1.
\(5\)
Answer 2.
\(\left\{17\right\}\)
2.3.5.13.
Answer 1.
\(35\)
Answer 2.
\(\left\{\frac{-295}{28}\right\}\)
2.3.5.15.
Answer 1.
\(100\)
Answer 2.
\(\left\{\frac{-765}{4}\right\}\)
2.3.5.17.
Answer 1.
\(30\)
Answer 2.
\(\left\{2\right\}\)
2.3.5.19.
Answer 1.
\(4\)
Answer 2.
\(\left\{\frac{29}{15}\right\}\)
2.3.5.21.
Answer 1.
\(21\)
Answer 2.
\(\left\{\frac{-224}{165}\right\}\)
2.3.5.23.
Answer 1.
\(105\)
Answer 2.
\(\left\{\frac{-831}{395}\right\}\)
2.3.5.25.
Answer 1.
\(60\)
Answer 2.
\(\left\{\frac{325}{23}\right\}\)
2.3.5.27.
Answer 1.
\(11\)
Answer 2.
\(\left\{x \mid x\le \frac{29}{11}\right\}\)
Answer 3.
\(\left(-\infty ,{\frac{29}{11}}\right]\)
2.3.5.29.
Answer 1.
\(5\)
Answer 2.
\(\left\{x \mid x\ge \frac{-52}{11}\right\}\)
Answer 3.
\(\left[-{\frac{52}{11}},\infty \right)\)
2.3.5.31.
Answer 1.
\(60\)
Answer 2.
\(\left\{x \mid x > \frac{-284}{35}\right\}\)
Answer 3.
\(\left(-{\frac{284}{35}},\infty \right)\)
2.3.5.33.
Answer 1.
\(10\)
Answer 2.
\(\left\{x \mid x < \frac{1}{15}\right\}\)
Answer 3.
\(\left(-\infty ,{\frac{1}{15}}\right)\)
2.3.5.35.
Answer 1.
\(36\)
Answer 2.
\(\left\{x \mid x\le \frac{57}{194}\right\}\)
Answer 3.
\(\left(-\infty ,{\frac{57}{194}}\right]\)

Applications

2.3.5.37.
Answer.
\(15.2903\ {\rm s}\)
2.3.5.39.
Answer.
\(12\ {\rm yr}\)
2.3.5.41.
Answer.
\(82.5\)
2.3.5.43.
Answer.
\(50\ {\rm g}\)
2.3.5.45.
Answer.
\(\$86.13\)
2.3.5.47.
Answer.
\(129\)

Challenge

2.3.5.49.
Answer.
\(24\)

2.4 Special Solution Sets
2.4.4 Exercises

Notation

2.4.4.1.
Answer.
\(\text{no real solutions}\)

Skills Practice

2.4.4.3.
Answer.
\(\text{no real solutions}\)
2.4.4.5.
Answer.
\(\left(-\infty ,\infty \right)\hbox{ or }\text{infinitely many solutions}\)
2.4.4.7.
Answer.
\(\left(-\infty ,\infty \right)\hbox{ or }\text{infinitely many solutions}\)
2.4.4.9.
Answer.
\(\text{no real solutions}\)
2.4.4.11.
Answer.
\(\text{no real solutions}\)
2.4.4.13.
Answer.
\(\text{no real solutions}\)
2.4.4.15.
Answer.
\(\text{no real solutions}\)
2.4.4.17.
Answer.
\(\text{no real solutions}\)
2.4.4.19.
Answer.
\(\left(-\infty ,\infty \right)\hbox{ or }\text{infinitely many solutions}\)
2.4.4.21.
Answer.
\(\text{no real solutions}\)
2.4.4.23.
Answer.
\(\text{no real solutions}\)
2.4.4.25.
Answer.
\(\left(-\infty ,\infty \right)\hbox{ or }\text{infinitely many solutions}\)
2.4.4.27.
Answer.
\(\text{no real solutions}\)
2.4.4.29.
Answer.
\(\text{no real solutions}\)
2.4.4.31.
Answer.
\(\text{no real solutions}\)
2.4.4.33.
Answer.
\(\text{no real solutions}\)
2.4.4.35.
Answer.
\(\left(-\infty ,\infty \right)\hbox{ or }\text{infinitely many solutions}\)
2.4.4.37.
Answer.
\(\text{no real solutions}\)
2.4.4.39.
Answer.
\(\text{no real solutions}\)

Challenge

2.4.4.41.
Answer 1.
\(9x+42\)
Answer 2.
\(10\mathopen{}\left(x+4\right)\)

2.5 Isolating a Linear Variable
2.5.3 Exercises

Skills Practice

2.5.3.1.
2.5.3.1.a
Answer.
\(\left\{1\right\}\)
2.5.3.1.b
Answer.
\(G = x-X\)
2.5.3.3.
2.5.3.3.a
Answer.
\(\left\{12\right\}\)
2.5.3.3.b
Answer.
\(S = q+m\)
2.5.3.5.
2.5.3.5.a
Answer.
\(\left\{\frac{9}{7}\right\}\)
2.5.3.5.b
Answer.
\(e = \frac{h}{D}\)
2.5.3.7.
2.5.3.7.a
Answer.
\(\left\{24\right\}\)
2.5.3.7.b
Answer.
\(q = YS\)
2.5.3.9.
2.5.3.9.a
Answer.
\(\left\{\frac{1}{2}\right\}\)
2.5.3.9.b
Answer.
\(B = \frac{D-Q}{i}\)
2.5.3.11.
Answer.
\(L = G-y\)
2.5.3.13.
Answer.
\(Y = \frac{w-x}{M}\)
2.5.3.15.
Answer.
\(x = \frac{y-q}{e}\)
2.5.3.17.
Answer.
\(u = s\mathopen{}\left(r-g\right)\)

Applications

2.5.3.19.
Answer.
\(b = \frac{2A}{h}\)
2.5.3.21.
Answer.
\(m = \frac{y-b}{x}\)
2.5.3.23.
Answer.
\(r = \frac{c}{2\pi }\)
2.5.3.25.
Answer.
\(h = \frac{V}{\pi r^{2}}\)
2.5.3.27.
Answer.
\(y = 4x+4\)
2.5.3.29.
Answer.
\(y = -{\frac{3}{7}}x+3\)
2.5.3.31.
Answer.
\(y = x+{\frac{2}{9}}\)
2.5.3.33.
Answer.
\(y = -{\frac{7}{3}}x+{\frac{17}{33}}\)

2.6 Linear Equations and Inequalities Chapter Review

Review Exercises for Chapter 2

Section 1: Solving Multistep Linear Equations
2.6.1.
2.6.1.a
Answer.
\(\text{simplified}\)
2.6.1.b
Answer.
\(\text{evaluate}\)
2.6.1.c
Answer.
\(\text{solve}\)
2.6.1.d
Answer.
\(\text{simplify}\)
2.6.3.
Answer.
\(\left\{-0.0697674\right\}\)
2.6.5.
Answer.
\(\left\{1\right\}\)
2.6.7.
Answer.
\(\left\{\frac{-6}{7}\right\}\)
2.6.9.
Answer.
\({\frac{72}{11}}\ {\rm yr}\)
2.6.11.
Answer.
\(2.81818\ {\rm hr}\)
2.6.13.
Answer.
\(\$458.17\)
Section 2: Solving Multistep Linear Inequalities
2.6.15.
Answer 1.
\(\left\{\text{interval}, \left(-\infty ,-6\right)\right\}\)
Answer 2.
\(\left(-\infty ,-6\right)\)
Answer 3.
\(\left\{F \mid F < -6\right\}\)
2.6.17.
Answer 1.
\(\left\{\text{interval}, \left(-\infty ,-2\right]\right\}\)
Answer 2.
\(\left(-\infty ,-2\right]\)
Answer 3.
\(\left\{R \mid R\le -2\right\}\)
2.6.19.
Answer 1.
\(\left\{\text{interval}, \left[2,\infty \right)\right\}\)
Answer 2.
\(\left[2,\infty \right)\)
Answer 3.
\(\left\{d \mid d\ge 2\right\}\)
2.6.21.
2.6.21.a
Answer.
\(15+4x\le 95\)
2.6.21.b
Answer.
\(20\ {\rm mi}\)
2.6.21.c
Answer.
\(\left[0,20\right]\)
Section 3: Equations and Inequalities with Fractions
2.6.23.
Answer 1.
\(7\)
Answer 2.
\(\left\{\frac{-27}{49}\right\}\)
2.6.25.
Answer 1.
\(210\)
Answer 2.
\(\left\{1\right\}\)
2.6.27.
Answer 1.
\(7\)
Answer 2.
\(\left\{x \mid x\ge \frac{-61}{84}\right\}\)
Answer 3.
\(\left[-{\frac{61}{84}},\infty \right)\)
2.6.29.
Answer 1.
\(3\)
Answer 2.
\(\left\{x \mid x < 3\right\}\)
Answer 3.
\(\left(-\infty ,3\right)\)
2.6.31.
Answer.
\({\frac{72}{5}}\ {\rm yr}\)
2.6.33.
Answer.
\(\$94.62\)
Section 4: Special Solution Sets
2.6.35.
Answer.
\(\text{no real solutions}\)
2.6.37.
Answer.
\(\text{no real solutions}\)
2.6.39.
Answer.
\(\left(-\infty ,\infty \right)\hbox{ or }\text{infinitely many solutions}\)
2.6.41.
Answer.
\(\left(-\infty ,\infty \right)\hbox{ or }\text{infinitely many solutions}\)
Section 5: Isolating a Linear Variable
2.6.43.
Answer.
\(x = \frac{y-u}{p}\)
2.6.45.
Answer.
\(m = \frac{y-b}{x}\)
2.6.47.
Answer.
\(y = 8x-1\)

3 Graphing Lines
3.1 Cartesian Coordinates

Exercises

3.1.1.
Answer 1.
\(\left(1,2\right)\)
Answer 2.
\(\left(-1,-2\right)\)
Answer 3.
\(\left(0,4\right)\)
Answer 4.
\(\left(-3,0\right)\)
3.1.3.
Answer.
\(\left\{\text{point}, \left(0,-1\right)\right\}, \left\{\text{point}, \left(5,-3\right)\right\}, \left\{\text{point}, \left(1,-8\right)\right\}, \left\{\text{point}, \left(4,0\right)\right\}\)
3.1.5.
Answer.
\(\left\{\text{point}, \left(-5,0.666667\right)\right\}, \left\{\text{point}, \left(-3.66667,-2\right)\right\}\)
3.1.7.
Answer.
\(\left\{\text{point}, \left(-2.75,-4.25\right)\right\}, \left\{\text{point}, \left(0.75,2.25\right)\right\}\)
3.1.9.
Answer.
\(\left\{\text{point}, \left(149,108\right)\right\}, \left\{\text{point}, \left(176,115\right)\right\}\)
3.1.11.
Answer.
\(\left\{\text{fill}, \left(1,1\right)\right\}, \left\{\text{fill}, \left(-1,1\right)\right\}\)
3.1.13.
Answer.
\(\left\{\text{fill}, \left(1,1\right)\right\}, \left\{\text{fill}, \left(-1,-1\right)\right\}\)
3.1.15.
Answer 1.
\(\left(20,1\right)\)
Answer 2.
\(\left(20,1\right)\)
3.1.17.
Answer 1.
\(\text{III}\)
Answer 2.
\(\text{IV}\)
Answer 3.
\(\text{I}\)
Answer 4.
\(\text{IV}\)
3.1.19.
Answer 1.
\(\text{III}\)
Answer 2.
\(\text{IV}\)
Answer 3.
\(\text{I}\)
Answer 4.
\(\text{IV}\)

3.2 Graphing Equations

Exercises

Skills Practice
3.2.1.
Answer.
\(\text{Choice 1, Choice 3}\)
3.2.3.
Answer.
\(\text{Choice 3, Choice 4}\)
3.2.5.
Answer.
\(\text{Choice 1, Choice 3}\)
3.2.7.
Answer.
\(\text{Choice 1, Choice 2}\)
3.2.9.
Answer 1.
\(1;\,\left(-2,1\right);\,-1;\,\left(-1,-1\right);\,-3;\,\left(0,-3\right);\,-5;\,\left(1,-5\right);\,-7;\,\left(2,-7\right)\)
Answer 2.
\(\left\{\text{point}, \left(-2,1\right)\right\}, \left\{\text{point}, \left(-1,-1\right)\right\}, \left\{\text{point}, \left(0,-3\right)\right\}, \left\{\text{point}, \left(1,-5\right)\right\}, \left\{\text{point}, \left(2,-7\right)\right\}, \left\{\text{line}, \text{solid}, \left(-2,1\right), \left(-1,-1\right)\right\}\)
3.2.11.
Answer 1.
\(7;\,\left(-6,7\right);\,3;\,\left(-3,3\right);\,-1;\,\left(0,-1\right);\,-5;\,\left(3,-5\right);\,-9;\,\left(6,-9\right)\)
Answer 2.
\(\left\{\text{point}, \left(-6,7\right)\right\}, \left\{\text{point}, \left(-3,3\right)\right\}, \left\{\text{point}, \left(0,-1\right)\right\}, \left\{\text{point}, \left(3,-5\right)\right\}, \left\{\text{point}, \left(6,-9\right)\right\}, \left\{\text{line}, \text{solid}, \left(-6,7\right), \left(-3,3\right)\right\}\)
3.2.13.
Answer 1.
\(1;\,\left(-2,1\right);\,-4;\,\left(-1,-4\right);\,-7;\,\left(0,-7\right);\,-8;\,\left(1,-8\right);\,-7;\,\left(2,-7\right)\)
Answer 2.
\(\left\{\text{point}, \left(-2,1\right)\right\}, \left\{\text{point}, \left(-1,-4\right)\right\}, \left\{\text{point}, \left(0,-7\right)\right\}, \left\{\text{point}, \left(1,-8\right)\right\}, \left\{\text{point}, \left(2,-7\right)\right\}, \left\{\text{quadratic}, \text{solid}, \left(-2,1\right), \left(-1,-4\right), \left(0,-7\right)\right\}\)
3.2.15.
Answer 1.
\(-2;\,\left(-2,-2\right);\,1;\,\left(-1,1\right);\,0;\,\left(0,0\right);\,1;\,\left(1,1\right);\,10;\,\left(2,10\right)\)
Answer 2.
\(\left\{\text{point}, \left(-2,-2\right)\right\}, \left\{\text{point}, \left(-1,1\right)\right\}, \left\{\text{point}, \left(0,0\right)\right\}, \left\{\text{point}, \left(1,1\right)\right\}, \left\{\text{point}, \left(2,10\right)\right\}, \left\{\text{cubic}, \text{solid}, \left(-2,-2\right), \left(-1,1\right), \left(0,0\right), \left(1,1\right)\right\}\)
3.2.17.
Answer.
\(\text{Choice 1, Choice 2, Choice 4}\)
Applications
3.2.19.
Answer.
\(\left\{\text{line}, \text{solid}, \left(0,900\right), \left(1,925\right)\right\}\)
3.2.21.
Answer.
\(\left\{\text{line}, \text{solid}, \left(40,100\right), \left(90,110\right)\right\}\)

3.3 Exploring Two-Variable Data and Rate of Change
3.3.5 Exercises

Skills Practice

3.3.5.1.
Answer.
\(y = 4x\)
3.3.5.3.
Answer.
\(y = x+4\)
3.3.5.5.
Answer.
\(y = x-3\)
3.3.5.7.
Answer.
\(y = \sqrt{x}\)
3.3.5.9.
Answer.
\(y = x^{2}\)
3.3.5.11.
Answer.
\(y = \frac{1}{x}\)
3.3.5.13.
Answer.
\({\frac{9}{13}}\)
3.3.5.15.
Answer.
\(9.125\)
3.3.5.17.
Answer.
\({\frac{153}{28}}\)
3.3.5.19.
Answer.
\(-1\)
3.3.5.21.
Answer.
\(-{\frac{5}{3}}\)
3.3.5.23.
Answer.
\({\frac{16}{35}}\)
3.3.5.25.
Answer.
\({\frac{4}{3}}\)
3.3.5.27.
Answer.
\({\frac{767}{40}}\)
3.3.5.29.
Answer.
\(\text{yes}\)
3.3.5.31.
Answer.
\(\text{yes}\)
3.3.5.33.
Answer.
\(\text{no}\)
3.3.5.35.
Answer.
\(\text{no}\)
3.3.5.37.
Answer.
\(\text{yes}\)
3.3.5.39.
Answer.
\(\text{yes}\)

3.4 Slope
3.4.5 Exercises

Skills Practice

3.4.5.1.
Answer.
\(7\)
3.4.5.3.
Answer.
\(-1\)
3.4.5.5.
Answer.
\({\frac{1}{3}}\)
3.4.5.7.
Answer.
\(-{\frac{1}{4}}\)
3.4.5.9.
Answer.
\({\frac{9}{4}}\)
3.4.5.11.
Answer.
\(-3.24\)
3.4.5.13.
Answer.
\(0\)
3.4.5.15.
Answer.
\({\frac{501}{670}}\)
3.4.5.17.
Answer.
\(-{\frac{245}{8}}\)
3.4.5.19.
Answer.
\(7\)
3.4.5.21.
Answer.
\(3\)
3.4.5.23.
Answer.
\({\frac{3}{10}}\)
3.4.5.25.
Answer.
\(0\)
3.4.5.27.
Answer.
\(1\)
3.4.5.29.
Answer.
\(1.12046\)
3.4.5.31.
Answer.
\({\frac{12}{5}}\)
3.4.5.33.
Answer.
\({\frac{17}{11}}\)
3.4.5.35.
Answer.
\(1.91935\)
3.4.5.37.
Answer.
\(\left\{\text{line}, \text{solid}, \left(-3,-1\right), \left(0,3\right)\right\}\)
3.4.5.39.
Answer.
\(\left\{\text{line}, \text{solid}, \left(1,-2\right), \left(4,-4\right)\right\}\)
3.4.5.41.
Answer.
\(\left\{\text{line}, \text{solid}, \left(-8,-8\right), \left(-5,-7\right)\right\}, \left\{\text{line}, \text{solid}, \left(-7,-8\right), \left(-4,-7\right)\right\}, \left\{\text{line}, \text{solid}, \left(-6,-8\right), \left(-3,-7\right)\right\}, \left\{\text{line}, \text{solid}, \left(-5,-8\right), \left(-2,-7\right)\right\}, \left\{\text{line}, \text{solid}, \left(-4,-8\right), \left(-1,-7\right)\right\}, \left\{\text{line}, \text{solid}, \left(-3,-8\right), \left(0,-7\right)\right\}, \left\{\text{line}, \text{solid}, \left(-2,-8\right), \left(1,-7\right)\right\}, \left\{\text{line}, \text{solid}, \left(-1,-8\right), \left(2,-7\right)\right\}, \left\{\text{line}, \text{solid}, \left(0,-8\right), \left(3,-7\right)\right\}, \left\{\text{line}, \text{solid}, \left(1,-8\right), \left(4,-7\right)\right\}, \left\{\text{line}, \text{solid}, \left(2,-8\right), \left(5,-7\right)\right\}, \left\{\text{line}, \text{solid}, \left(3,-8\right), \left(6,-7\right)\right\}, \left\{\text{line}, \text{solid}, \left(4,-8\right), \left(7,-7\right)\right\}, \left\{\text{line}, \text{solid}, \left(5,-8\right), \left(8,-7\right)\right\}, \left\{\text{line}, \text{solid}, \left(-8,-7\right), \left(-5,-6\right)\right\}, \left\{\text{line}, \text{solid}, \left(-8,-6\right), \left(-5,-5\right)\right\}, \left\{\text{line}, \text{solid}, \left(-8,-5\right), \left(-5,-4\right)\right\}, \left\{\text{line}, \text{solid}, \left(-8,-4\right), \left(-5,-3\right)\right\}, \left\{\text{line}, \text{solid}, \left(-8,-3\right), \left(-5,-2\right)\right\}, \left\{\text{line}, \text{solid}, \left(-8,-2\right), \left(-5,-1\right)\right\}, \left\{\text{line}, \text{solid}, \left(-8,-1\right), \left(-5,0\right)\right\}, \left\{\text{line}, \text{solid}, \left(-8,0\right), \left(-5,1\right)\right\}, \left\{\text{line}, \text{solid}, \left(-8,1\right), \left(-5,2\right)\right\}, \left\{\text{line}, \text{solid}, \left(-8,2\right), \left(-5,3\right)\right\}, \left\{\text{line}, \text{solid}, \left(-8,3\right), \left(-5,4\right)\right\}, \left\{\text{line}, \text{solid}, \left(-8,4\right), \left(-5,5\right)\right\}, \left\{\text{line}, \text{solid}, \left(-8,5\right), \left(-5,6\right)\right\}, \left\{\text{line}, \text{solid}, \left(-8,6\right), \left(-5,7\right)\right\}, \left\{\text{line}, \text{solid}, \left(-8,7\right), \left(-5,8\right)\right\}, \left\{\text{line}, \text{solid}, \left(-7,-7\right), \left(-4,-6\right)\right\}, \left\{\text{line}, \text{solid}, \left(-7,-6\right), \left(-4,-5\right)\right\}, \left\{\text{line}, \text{solid}, \left(-7,-5\right), \left(-4,-4\right)\right\}, \left\{\text{line}, \text{solid}, \left(-7,-4\right), \left(-4,-3\right)\right\}, \left\{\text{line}, \text{solid}, \left(-7,-3\right), \left(-4,-2\right)\right\}, \left\{\text{line}, \text{solid}, \left(-7,-2\right), \left(-4,-1\right)\right\}, \left\{\text{line}, \text{solid}, \left(-7,-1\right), \left(-4,0\right)\right\}, \left\{\text{line}, \text{solid}, \left(-7,0\right), \left(-4,1\right)\right\}, \left\{\text{line}, \text{solid}, \left(-7,1\right), \left(-4,2\right)\right\}, \left\{\text{line}, \text{solid}, \left(-7,2\right), \left(-4,3\right)\right\}, \left\{\text{line}, \text{solid}, \left(-7,3\right), \left(-4,4\right)\right\}, \left\{\text{line}, \text{solid}, \left(-7,4\right), \left(-4,5\right)\right\}, \left\{\text{line}, \text{solid}, \left(-7,5\right), \left(-4,6\right)\right\}, \left\{\text{line}, \text{solid}, \left(-7,6\right), \left(-4,7\right)\right\}, \left\{\text{line}, \text{solid}, \left(-7,7\right), \left(-4,8\right)\right\}, \left\{\text{line}, \text{solid}, \left(-6,-7\right), \left(-3,-6\right)\right\}, \left\{\text{line}, \text{solid}, \left(-6,-6\right), \left(-3,-5\right)\right\}, \left\{\text{line}, \text{solid}, \left(-6,-5\right), \left(-3,-4\right)\right\}, \left\{\text{line}, \text{solid}, \left(-6,-4\right), \left(-3,-3\right)\right\}, \left\{\text{line}, \text{solid}, \left(-6,-3\right), \left(-3,-2\right)\right\}, \left\{\text{line}, \text{solid}, \left(-6,-2\right), \left(-3,-1\right)\right\}, \left\{\text{line}, \text{solid}, \left(-6,-1\right), \left(-3,0\right)\right\}, \left\{\text{line}, \text{solid}, \left(-6,0\right), \left(-3,1\right)\right\}, \left\{\text{line}, \text{solid}, \left(-6,1\right), \left(-3,2\right)\right\}, \left\{\text{line}, \text{solid}, \left(-6,2\right), \left(-3,3\right)\right\}, \left\{\text{line}, \text{solid}, \left(-6,3\right), \left(-3,4\right)\right\}, \left\{\text{line}, \text{solid}, \left(-6,4\right), \left(-3,5\right)\right\}, \left\{\text{line}, \text{solid}, \left(-6,5\right), \left(-3,6\right)\right\}, \left\{\text{line}, \text{solid}, \left(-6,6\right), \left(-3,7\right)\right\}, \left\{\text{line}, \text{solid}, \left(-6,7\right), \left(-3,8\right)\right\}\)
3.4.5.43.
Answer.
\(\left\{\text{line}, \text{solid}, \left(-8,-13\right), \left(-6,-18\right)\right\}, \left\{\text{line}, \text{solid}, \left(-8,-12\right), \left(-6,-17\right)\right\}, \left\{\text{line}, \text{solid}, \left(-8,-11\right), \left(-6,-16\right)\right\}, \left\{\text{line}, \text{solid}, \left(-8,-10\right), \left(-6,-15\right)\right\}, \left\{\text{line}, \text{solid}, \left(-8,-9\right), \left(-6,-14\right)\right\}, \left\{\text{line}, \text{solid}, \left(-8,-8\right), \left(-6,-13\right)\right\}, \left\{\text{line}, \text{solid}, \left(-8,-7\right), \left(-6,-12\right)\right\}, \left\{\text{line}, \text{solid}, \left(-8,-6\right), \left(-6,-11\right)\right\}, \left\{\text{line}, \text{solid}, \left(-8,-5\right), \left(-6,-10\right)\right\}, \left\{\text{line}, \text{solid}, \left(-8,-4\right), \left(-6,-9\right)\right\}, \left\{\text{line}, \text{solid}, \left(-8,-3\right), \left(-6,-8\right)\right\}, \left\{\text{line}, \text{solid}, \left(-8,-2\right), \left(-6,-7\right)\right\}, \left\{\text{line}, \text{solid}, \left(-8,-1\right), \left(-6,-6\right)\right\}, \left\{\text{line}, \text{solid}, \left(-8,0\right), \left(-6,-5\right)\right\}, \left\{\text{line}, \text{solid}, \left(-8,1\right), \left(-6,-4\right)\right\}, \left\{\text{line}, \text{solid}, \left(-8,2\right), \left(-6,-3\right)\right\}, \left\{\text{line}, \text{solid}, \left(-8,3\right), \left(-6,-2\right)\right\}, \left\{\text{line}, \text{solid}, \left(-8,4\right), \left(-6,-1\right)\right\}, \left\{\text{line}, \text{solid}, \left(-8,5\right), \left(-6,0\right)\right\}, \left\{\text{line}, \text{solid}, \left(-8,6\right), \left(-6,1\right)\right\}, \left\{\text{line}, \text{solid}, \left(-8,7\right), \left(-6,2\right)\right\}, \left\{\text{line}, \text{solid}, \left(-8,8\right), \left(-6,3\right)\right\}, \left\{\text{line}, \text{solid}, \left(-8,9\right), \left(-6,4\right)\right\}, \left\{\text{line}, \text{solid}, \left(-8,10\right), \left(-6,5\right)\right\}, \left\{\text{line}, \text{solid}, \left(-8,11\right), \left(-6,6\right)\right\}, \left\{\text{line}, \text{solid}, \left(-8,12\right), \left(-6,7\right)\right\}, \left\{\text{line}, \text{solid}, \left(-8,13\right), \left(-6,8\right)\right\}, \left\{\text{line}, \text{solid}, \left(-7,-13\right), \left(-5,-18\right)\right\}, \left\{\text{line}, \text{solid}, \left(-7,-12\right), \left(-5,-17\right)\right\}, \left\{\text{line}, \text{solid}, \left(-7,-11\right), \left(-5,-16\right)\right\}, \left\{\text{line}, \text{solid}, \left(-7,-10\right), \left(-5,-15\right)\right\}, \left\{\text{line}, \text{solid}, \left(-7,-9\right), \left(-5,-14\right)\right\}, \left\{\text{line}, \text{solid}, \left(-7,-8\right), \left(-5,-13\right)\right\}, \left\{\text{line}, \text{solid}, \left(-7,-7\right), \left(-5,-12\right)\right\}, \left\{\text{line}, \text{solid}, \left(-7,-6\right), \left(-5,-11\right)\right\}, \left\{\text{line}, \text{solid}, \left(-7,-5\right), \left(-5,-10\right)\right\}, \left\{\text{line}, \text{solid}, \left(-7,-4\right), \left(-5,-9\right)\right\}, \left\{\text{line}, \text{solid}, \left(-7,-3\right), \left(-5,-8\right)\right\}, \left\{\text{line}, \text{solid}, \left(-7,-2\right), \left(-5,-7\right)\right\}, \left\{\text{line}, \text{solid}, \left(-7,-1\right), \left(-5,-6\right)\right\}, \left\{\text{line}, \text{solid}, \left(-7,0\right), \left(-5,-5\right)\right\}, \left\{\text{line}, \text{solid}, \left(-7,1\right), \left(-5,-4\right)\right\}, \left\{\text{line}, \text{solid}, \left(-7,2\right), \left(-5,-3\right)\right\}, \left\{\text{line}, \text{solid}, \left(-7,3\right), \left(-5,-2\right)\right\}, \left\{\text{line}, \text{solid}, \left(-7,4\right), \left(-5,-1\right)\right\}, \left\{\text{line}, \text{solid}, \left(-7,5\right), \left(-5,0\right)\right\}, \left\{\text{line}, \text{solid}, \left(-7,6\right), \left(-5,1\right)\right\}, \left\{\text{line}, \text{solid}, \left(-7,7\right), \left(-5,2\right)\right\}, \left\{\text{line}, \text{solid}, \left(-7,8\right), \left(-5,3\right)\right\}, \left\{\text{line}, \text{solid}, \left(-7,9\right), \left(-5,4\right)\right\}, \left\{\text{line}, \text{solid}, \left(-7,10\right), \left(-5,5\right)\right\}, \left\{\text{line}, \text{solid}, \left(-7,11\right), \left(-5,6\right)\right\}, \left\{\text{line}, \text{solid}, \left(-7,12\right), \left(-5,7\right)\right\}, \left\{\text{line}, \text{solid}, \left(-7,13\right), \left(-5,8\right)\right\}\)

Applications

3.4.5.45.
Answer 1.
\(375\ {\textstyle\frac{\rm\mathstrut ft}{\rm\mathstrut h}}\)
Answer 2.
\(125\ {\textstyle\frac{\rm\mathstrut ft}{\rm\mathstrut h}}\)
Answer 3.
\(0\ {\textstyle\frac{\rm\mathstrut ft}{\rm\mathstrut h}}\)
Answer 4.
\(-500\ {\textstyle\frac{\rm\mathstrut ft}{\rm\mathstrut h}}\)
3.4.5.47.
Answer.
\(-8\ {\textstyle\frac{\rm\mathstrut ml}{\rm\mathstrut min}}\)

Challenge

3.4.5.49.
Answer.
\(\text{True}\)

3.5 Slope-Intercept Form
3.5.7 Exercises

Skills Practice

3.5.7.1.
Answer 1.
\(2\)
Answer 2.
\(\left(0,7\right)\)
3.5.7.3.
Answer 1.
\(-7\)
Answer 2.
\(\left(0,-2\right)\)
3.5.7.5.
Answer 1.
\(1\)
Answer 2.
\(\left(0,1\right)\)
3.5.7.7.
Answer 1.
\(-1\)
Answer 2.
\(\left(0,5\right)\)
3.5.7.9.
Answer 1.
\({\frac{8}{5}}\)
Answer 2.
\(\left(0,9\right)\)
3.5.7.11.
Answer 1.
\(-6.2\)
Answer 2.
\(\left(0,-6\right)\)
3.5.7.13.
Answer 1.
\(5\)
Answer 2.
\(\left(0,6\right)\)
3.5.7.15.
Answer 1.
\(-7\)
Answer 2.
\(\left(0,8\right)\)
3.5.7.17.
Answer.
\(y = 2x+3\)
3.5.7.19.
Answer.
\(y = {\frac{1}{4}}x-4\)
3.5.7.21.
Answer.
\(y = x-2\)
3.5.7.23.
Answer.
\(y = x+4\)
3.5.7.25.
Answer.
\(y = {\frac{1}{3}}x+2\)
3.5.7.27.
Answer.
\(y = {\frac{5}{4}}x\)
3.5.7.29.
Answer.
\(\left\{\text{line}, \text{solid}, \left(0,5\right), \left(1,7\right)\right\}\)
3.5.7.31.
Answer.
\(\left\{\text{line}, \text{solid}, \left(0,2\right), \left(1,-1\right)\right\}\)
3.5.7.33.
Answer.
\(\left\{\text{line}, \text{solid}, \left(0,-3\right), \left(-4,-2\right)\right\}\)
3.5.7.35.
Answer.
\(\left\{\text{line}, \text{solid}, \left(0,-4\right), \left(5,-3\right)\right\}\)
3.5.7.37.
Answer.
\(\left\{\text{line}, \text{solid}, \left(0,0\right), \left(9,2\right)\right\}\)
3.5.7.39.
Answer.
\(\left\{\text{line}, \text{solid}, \left(0,-1\right), \left(7,3\right)\right\}\)
3.5.7.41.
Answer.
\(\left\{\text{line}, \text{solid}, \left(0,1\right), \left(1,2\right)\right\}\)
3.5.7.43.
Answer.
\(\left\{\text{line}, \text{solid}, \left(0,5\right), \left(1,4\right)\right\}\)
3.5.7.45.
Answer.
\(\left\{\text{line}, \text{solid}, \left(0,-2\right), \left(7,-11\right)\right\}\)
3.5.7.47.
Answer.
\(\left\{\text{line}, \text{solid}, \left(0,2\right), \left(10,-4\right)\right\}\)
3.5.7.49.
Answer.
\(y = 9x-2\)
3.5.7.51.
Answer.
\(y = -3x+3\)
3.5.7.53.
Answer.
\(y = 6x+7\)
3.5.7.55.
Answer.
\(y = {\frac{8}{7}}x-8\)
3.5.7.57.
Answer.
\(y = -{\frac{3}{4}}x-4\)
3.5.7.59.
Answer.
\(y = {\frac{14}{19}}x+62\)
3.5.7.61.
Answer.
\(y = 4.5x+4.4\)

Applications

3.5.7.63.
Answer.
\(14\)
3.5.7.65.
Answer.
\(360\)
3.5.7.67.
Answer.
\(45\)
3.5.7.69.
Answer 1.
\(y = 0.06x+19\)
Answer 2.
\(\$29.20\)
Answer 3.
\(490\)
3.5.7.71.
Answer 1.
\(y = 0.27x+13.2\)
Answer 2.
\(21.03\)
Answer 3.
\(59\)
3.5.7.73.
Answer 1.
\(y = -22000x+831000\)
Answer 2.
\(\$611{,}000\)
Answer 3.
\(2037\)
3.5.7.75.
Answer 1.
\(y = -8.9x+382.7\)
Answer 2.
\(62.3\)
Answer 3.
\(43\)

3.6 Point-Slope Form
3.6.5 Exercises

Skills Practice

3.6.5.1.
Answer 1.
\(2\)
Answer 2.
\(\left(6,5\right)\)
3.6.5.3.
Answer 1.
\(-4\)
Answer 2.
\(\left(-8,3\right)\)
3.6.5.5.
Answer 1.
\(6\)
Answer 2.
\(\left(-2,-3\right)\)
3.6.5.7.
Answer 1.
\(7\)
Answer 2.
\(\left(4,-9\right)\)
3.6.5.9.
Answer.
\(y = 9\mathopen{}\left(x-6\right)+7\)
3.6.5.11.
Answer.
\(y = 3\mathopen{}\left(x+9\right)-6\)
3.6.5.13.
Answer.
\(y = -1.7\mathopen{}\left(x-5\right)-8\)
3.6.5.15.
Answer.
\(y = 6\mathopen{}\left(x-7\right)+3\hbox{ or }y = 6\mathopen{}\left(x-4\right)-15\)
3.6.5.17.
Answer.
\(y = -7\mathopen{}\left(x-8\right)-9\hbox{ or }y = -7\mathopen{}\left(x-4\right)+19\)
3.6.5.19.
Answer.
\(y = \frac{-3}{7}\mathopen{}\left(x+8\right)-5\hbox{ or }y = \frac{-3}{7}\mathopen{}\left(x+57\right)+16\)
3.6.5.21.
Answer.
\(y = \frac{7}{5}\mathopen{}\left(x+4\right)+1\hbox{ or }y = \frac{7}{5}\mathopen{}\left(x-6\right)+15\)
3.6.5.23.
Answer.
\(y = 6x-43\)
3.6.5.25.
Answer.
\(y = -7x-9\)
3.6.5.27.
Answer.
\(y = \frac{2}{7}x+\frac{10}{7}\)
3.6.5.29.
Answer.
\(y = -5.7x+\left(-37.81\right)\)
3.6.5.31.
Answer.
\(y = \frac{8}{7}\mathopen{}\left(x+4\right)-2\hbox{ or }y = \frac{8}{7}\mathopen{}\left(x-3\right)+6\)
3.6.5.33.
Answer.
\(y = \frac{-5}{8}\mathopen{}\left(x+2\right)+3\hbox{ or }y = \frac{-5}{8}\mathopen{}\left(x-6\right)-2\)
3.6.5.35.
Answer.
\(y = 20\mathopen{}\left(x-2\right)+300\hbox{ or }y = 20\mathopen{}\left(x-7\right)+400\)
3.6.5.37.
Answer.
\(y = \frac{-57}{4}\mathopen{}\left(x-1\right)+297\hbox{ or }y = \frac{-57}{4}\mathopen{}\left(x-9\right)+183\)
3.6.5.39.
Answer.
\(\left\{\text{line}, \text{solid}, \left(3,2\right), \left(4,6\right)\right\}\)
3.6.5.41.
Answer.
\(\left\{\text{line}, \text{solid}, \left(3,-4\right), \left(4,-2\right)\right\}\)
3.6.5.43.
Answer.
\(\left\{\text{line}, \text{solid}, \left(-8,-9\right), \left(-3,-2\right)\right\}\)
3.6.5.45.
Answer.
\(\left\{\text{line}, \text{solid}, \left(-3,8\right), \left(2,6\right)\right\}\)
3.6.5.47.
Answer.
\(\left\{\text{line}, \text{solid}, \left(3,4\right), \left(13,12\right)\right\}\)

Applications

3.6.5.49.
Answer 1.
\(y = 0.04\mathopen{}\left(x-240\right)+26.6\)
Answer 2.
\(\$25.00\)
Answer 3.
\(430\)
3.6.5.51.
Answer 1.
\(y = 0.22\mathopen{}\left(x-11\right)+13.92\)
Answer 2.
\(18.1\)
Answer 3.
\(52\)
3.6.5.53.
Answer 1.
\(y = -45000\mathopen{}\left(x-2\right)+658000\hbox{ or }y = -45000\mathopen{}\left(x-7\right)+433000\)
Answer 2.
\(\$253{,}000\)
Answer 3.
\(2016\)
3.6.5.55.
Answer 1.
\(y = -7.1\mathopen{}\left(x-10\right)+213\hbox{ or }y = -7.1\mathopen{}\left(x-12\right)+198.8\)
Answer 2.
\(7.1\)
Answer 3.
\(40\)

3.7 Standard Form
3.7.5 Exercises

Review and Warmup

3.7.5.1.
Answer.
\(y = -9x+11\)
3.7.5.3.
Answer.
\(y = -x+9\)
3.7.5.5.
Answer.
\(y = -{\frac{66}{23}}x+{\frac{206}{23}}\)

Skills Practice

3.7.5.7.
Answer 1.
\(\left(4,0\right)\)
Answer 2.
\(\left(0,8\right)\)
Answer 3.
\(-{\frac{1}{2}}\)
3.7.5.9.
Answer 1.
\(\left(5,0\right)\)
Answer 2.
\(\left(0,-3\right)\)
Answer 3.
\({\frac{5}{3}}\)
3.7.5.11.
Answer 1.
\(\left({\frac{5}{7}},0\right)\)
Answer 2.
\(\left(0,{\frac{5}{6}}\right)\)
Answer 3.
\(-{\frac{6}{7}}\)
3.7.5.13.
Answer 1.
\(\left({\frac{49}{47}},0\right)\)
Answer 2.
\(\left(0,-{\frac{49}{40}}\right)\)
Answer 3.
\({\frac{40}{47}}\)
3.7.5.15.
Answer 1.
\(\left(24,0\right)\)
Answer 2.
\(\left(0,{\frac{40}{3}}\right)\)
Answer 3.
\(-{\frac{9}{5}}\)
3.7.5.17.
Answer 1.
\(\left(-1.27273,0\right)\)
Answer 2.
\(\left(0,0.875\right)\)
Answer 3.
\(1.45455\)
3.7.5.19.
Answer.
\(6x-y=-3\)
3.7.5.21.
Answer.
\(8x-9y=27\)
3.7.5.23.
Answer.
\(\left\{\text{line}, \text{solid}, \left(2,0\right), \left(0,5\right)\right\}, \left\{\text{point}, \left(2,0\right)\right\}, \left\{\text{point}, \left(0,5\right)\right\}\)
3.7.5.25.
Answer.
\(\left\{\text{line}, \text{solid}, \left(-4,0\right), \left(0,7\right)\right\}, \left\{\text{point}, \left(-4,0\right)\right\}, \left\{\text{point}, \left(0,7\right)\right\}\)
3.7.5.27.
Answer.
\(\left\{\text{line}, \text{solid}, \left(-5,0\right), \left(0,-9\right)\right\}, \left\{\text{point}, \left(-5,0\right)\right\}, \left\{\text{point}, \left(0,-9\right)\right\}\)

Applications

3.7.5.29.
Answer.
\(0.6x+0.15y=99.6\)
3.7.5.31.
Answer.
\(4.93x+2.25y=4.66\)

Challenge

3.7.5.33.
3.7.5.33.a
Answer 1.
\(13\)
Answer 2.
\(2\)
Answer 3.
\(3\)
3.7.5.33.b
Answer 1.
\(2\)
Answer 2.
\(13\)
Answer 3.
\(3\)

3.8 Geometry of Lines
3.8.5 Exercises

Review and Warmup

3.8.5.1.
Answer.
\(y = 8\mathopen{}\left(x-7\right)+6\hbox{ or }y = 8\mathopen{}\left(x-3\right)-26\)
3.8.5.3.
Answer.
\(y = \frac{-5}{7}\mathopen{}\left(x+9\right)-8\hbox{ or }y = \frac{-5}{7}\mathopen{}\left(x-19\right)-28\)
3.8.5.5.
Answer.
\(\text{Choice 1, Choice 4}\)
3.8.5.7.
Answer.
\(\text{Choice 2, Choice 4}\)

Skills Practice

3.8.5.9.
Answer 1.
\(4;\,-2;\,\left(4,-2\right);\,4;\,-1;\,\left(4,-1\right);\,4;\,0;\,\left(4,0\right);\,4;\,1;\,\left(4,1\right);\,4;\,2;\,\left(4,2\right)\)
Answer 2.
\(\left\{\text{line}, \text{solid}, \left(4,-2\right), \left(4,-1\right)\right\}\)
3.8.5.11.
Answer 1.
\(-2;\,8;\,\left(-2,8\right);\,-1;\,8;\,\left(-1,8\right);\,0;\,8;\,\left(0,8\right);\,1;\,8;\,\left(1,8\right);\,2;\,8;\,\left(2,8\right)\)
Answer 2.
\(\left\{\text{line}, \text{solid}, \left(-2,8\right), \left(-1,8\right)\right\}\)
3.8.5.13.
Answer.
\(y = -5\)
3.8.5.15.
Answer.
\(x = -2\)
3.8.5.17.
Answer.
\(x = 2\)
3.8.5.19.
Answer.
\(y = 6\)
3.8.5.21.
Answer 1.
\(\text{NONE}\)
Answer 2.
\(\left(0,-9\right)\)
3.8.5.23.
Answer 1.
\(\left(-5,0\right)\)
Answer 2.
\(\text{NONE}\)
3.8.5.25.
Answer.
\(\text{distinct and parallel}\)
3.8.5.27.
Answer.
\(\text{perpendicular}\)
3.8.5.29.
Answer.
\(\text{none of the above}\)
3.8.5.31.
Answer.
\(\text{same line}\)
3.8.5.33.
Answer 1.
\(y-0.75x = -6.25\)
Answer 2.
\(\left\{\text{line}, \text{solid}, \left(7,-1\right), \left(-5,-10\right)\right\}\)
3.8.5.35.
Answer 1.
\(0.444444x+y = 1.66667\)
Answer 2.
\(\left\{\text{line}, \text{solid}, \left(6,-1\right), \left(24,-9\right)\right\}\)
3.8.5.37.
Answer 1.
\(x = 7\)
Answer 2.
\(\left\{\text{line}, \text{solid}, \left(7,8\right), \left(7,4\right)\right\}\)
3.8.5.39.
Answer 1.
\(y = -8\)
Answer 2.
\(\left\{\text{line}, \text{solid}, \left(4,-8\right), \left(5,-8\right)\right\}\)

3.9 Strategies for Graphing Lines
3.9.5 Exercises

3.9.5.1.

Answer 1.
\(3;\,\left(-2,3\right);\,2;\,\left(-1,2\right);\,1;\,\left(0,1\right);\,0;\,\left(1,0\right);\,-1;\,\left(2,-1\right)\)
Answer 2.
\(\left\{\text{point}, \left(-2,3\right)\right\}, \left\{\text{point}, \left(-1,2\right)\right\}, \left\{\text{point}, \left(0,1\right)\right\}, \left\{\text{point}, \left(1,0\right)\right\}, \left\{\text{point}, \left(2,-1\right)\right\}, \left\{\text{line}, \text{solid}, \left(-2,3\right), \left(-1,2\right)\right\}\)

3.9.5.3.

Answer 1.
\(8;\,\left(-8,8\right);\,5;\,\left(-4,5\right);\,2;\,\left(0,2\right);\,-1;\,\left(4,-1\right);\,-4;\,\left(8,-4\right)\)
Answer 2.
\(\left\{\text{point}, \left(-8,8\right)\right\}, \left\{\text{point}, \left(-4,5\right)\right\}, \left\{\text{point}, \left(0,2\right)\right\}, \left\{\text{point}, \left(4,-1\right)\right\}, \left\{\text{point}, \left(8,-4\right)\right\}, \left\{\text{line}, \text{solid}, \left(-8,8\right), \left(-4,5\right)\right\}\)

3.9.5.5.

Answer 1.
\(6;\,-2;\,\left(6,-2\right);\,6;\,-1;\,\left(6,-1\right);\,6;\,0;\,\left(6,0\right);\,6;\,1;\,\left(6,1\right);\,6;\,2;\,\left(6,2\right)\)
Answer 2.
\(\left\{\text{line}, \text{solid}, \left(6,-2\right), \left(6,-1\right)\right\}\)

3.9.5.7.

Answer 1.
\(-2;\,-9;\,\left(-2,-9\right);\,-1;\,-9;\,\left(-1,-9\right);\,0;\,-9;\,\left(0,-9\right);\,1;\,-9;\,\left(1,-9\right);\,2;\,-9;\,\left(2,-9\right)\)
Answer 2.
\(\left\{\text{line}, \text{solid}, \left(-2,-9\right), \left(-1,-9\right)\right\}\)

3.9.5.9.

Answer.
\(\left\{\text{line}, \text{solid}, \left(3,0\right), \left(0,7\right)\right\}, \left\{\text{point}, \left(3,0\right)\right\}, \left\{\text{point}, \left(0,7\right)\right\}\)

3.9.5.11.

Answer.
\(\left\{\text{line}, \text{solid}, \left(5,0\right), \left(0,-9\right)\right\}, \left\{\text{point}, \left(5,0\right)\right\}, \left\{\text{point}, \left(0,-9\right)\right\}\)

3.9.5.13.

Answer.
\(\left\{\text{line}, \text{solid}, \left(-7,0\right), \left(0,-4\right)\right\}, \left\{\text{point}, \left(-7,0\right)\right\}, \left\{\text{point}, \left(0,-4\right)\right\}\)

3.9.5.15.

Answer.
\(\left\{\text{line}, \text{solid}, \left(0,-3\right), \left(1,2\right)\right\}\)

3.9.5.17.

Answer.
\(\left\{\text{line}, \text{solid}, \left(0,-5\right), \left(1,-7\right)\right\}\)

3.9.5.19.

Answer.
\(\left\{\text{line}, \text{solid}, \left(0,2\right), \left(-3,3\right)\right\}\)

3.9.5.21.

Answer.
\(\left\{\text{line}, \text{solid}, \left(0,3\right), \left(4,4\right)\right\}\)

3.9.5.23.

Answer.
\(\left\{\text{line}, \text{solid}, \left(0,4\right), \left(3,12\right)\right\}\)

3.9.5.25.

Answer.
\(\left\{\text{line}, \text{solid}, \left(0,-9\right), \left(1,-8\right)\right\}\)

3.9.5.27.

Answer.
\(\left\{\text{line}, \text{solid}, \left(0,-1\right), \left(8,-4\right)\right\}\)

3.9.5.29.

Answer.
\(\left\{\text{line}, \text{solid}, \left(3,5\right), \left(4,9\right)\right\}\)

3.9.5.31.

Answer.
\(\left\{\text{line}, \text{solid}, \left(4,-2\right), \left(5,1\right)\right\}\)

3.9.5.33.

Answer.
\(\left\{\text{line}, \text{solid}, \left(-8,-3\right), \left(-3,0\right)\right\}\)

3.9.5.35.

Answer.
\(\left\{\text{line}, \text{solid}, \left(-8,4\right), \left(-5,-4\right)\right\}\)

3.9.5.37.

Answer.
\(\left\{\text{line}, \text{solid}, \left(-9,8\right), \left(1,5\right)\right\}\)

3.9.5.39.

Answer.
\(\left\{\text{line}, \text{solid}, \left(0,-2\right), \left(1,2\right)\right\}\)

3.9.5.41.

Answer.
\(\left\{\text{line}, \text{solid}, \left(0,1\right), \left(3,-7\right)\right\}\)

3.9.5.43.

Answer.
\(\left\{\text{line}, \text{solid}, \left(-8,-2\right), \left(-5,0\right)\right\}\)

3.9.5.45.

Answer.
\(\left\{\text{line}, \text{solid}, \left(3,0\right), \left(0,4\right)\right\}, \left\{\text{point}, \left(3,0\right)\right\}, \left\{\text{point}, \left(0,4\right)\right\}\)

3.9.5.47.

Answer.
\(\left\{\text{line}, \text{solid}, \left(-1,-2\right), \left(-1,-1\right)\right\}\)

3.9.5.49.

Answer.
\(\left\{\text{line}, \text{solid}, \left(-2,3\right), \left(-1,3\right)\right\}\)

3.10 Graphing Lines Chapter Review

Review Exercises for Chapter 3

Section 1: Cartesian Coordinates
3.10.1.
Answer 1.
\(\left(1,0\right)\)
Answer 2.
\(\left(3,-1\right)\)
Answer 3.
\(\left(0,-2\right)\)
Answer 4.
\(\left(-3,-4\right)\)
3.10.3.
Answer.
\(\left\{\text{point}, \left(0,3\right)\right\}, \left\{\text{point}, \left(-8,0\right)\right\}, \left\{\text{point}, \left(2,-6\right)\right\}, \left\{\text{point}, \left(6,-1\right)\right\}\)
3.10.5.
Answer.
\(\left\{\text{fill}, \left(1,1\right)\right\}, \left\{\text{fill}, \left(1,-1\right)\right\}\)
3.10.7.
Answer 1.
\(\text{III}\)
Answer 2.
\(\text{IV}\)
Answer 3.
\(\text{IV}\)
Answer 4.
\(\text{I}\)
Section 2: Graphing Equations
3.10.9.
Answer.
\(\text{Choice 1, Choice 2}\)
3.10.11.
Answer 1.
\(-13;\,\left(-2,-13\right);\,-2;\,\left(-1,-2\right);\,1;\,\left(0,1\right);\,2;\,\left(1,2\right);\,7;\,\left(2,7\right)\)
Answer 2.
\(\left\{\text{point}, \left(-2,-13\right)\right\}, \left\{\text{point}, \left(-1,-2\right)\right\}, \left\{\text{point}, \left(0,1\right)\right\}, \left\{\text{point}, \left(1,2\right)\right\}, \left\{\text{point}, \left(2,7\right)\right\}, \left\{\text{cubic}, \text{solid}, \left(-2,-13\right), \left(-1,-2\right), \left(0,1\right), \left(1,2\right)\right\}\)
Section 3: Exploring Two-Variable Data and Rate of Change
3.10.13.
Answer.
\(y = 6x\)
3.10.15.
Answer.
\(y = x^{2}\)
3.10.17.
Answer.
\(-{\frac{9}{50}}\)
3.10.19.
Answer.
\({\frac{3}{2}}\)
3.10.21.
Answer.
\(\text{yes}\)
Section 4: Slope
3.10.23.
Answer.
\({\frac{8}{9}}\)
3.10.25.
Answer.
\({\frac{400}{231}}\)
3.10.27.
Answer.
\(0.872449\)
3.10.29.
Answer.
\(\left\{\text{line}, \text{solid}, \left(-8,-8\right), \left(-5,-4\right)\right\}, \left\{\text{line}, \text{solid}, \left(-8,-7\right), \left(-5,-3\right)\right\}, \left\{\text{line}, \text{solid}, \left(-8,-6\right), \left(-5,-2\right)\right\}, \left\{\text{line}, \text{solid}, \left(-8,-5\right), \left(-5,-1\right)\right\}, \left\{\text{line}, \text{solid}, \left(-7,-8\right), \left(-4,-4\right)\right\}, \left\{\text{line}, \text{solid}, \left(-7,-7\right), \left(-4,-3\right)\right\}, \left\{\text{line}, \text{solid}, \left(-7,-6\right), \left(-4,-2\right)\right\}, \left\{\text{line}, \text{solid}, \left(-7,-5\right), \left(-4,-1\right)\right\}, \left\{\text{line}, \text{solid}, \left(-6,-8\right), \left(-3,-4\right)\right\}, \left\{\text{line}, \text{solid}, \left(-6,-7\right), \left(-3,-3\right)\right\}, \left\{\text{line}, \text{solid}, \left(-6,-6\right), \left(-3,-2\right)\right\}, \left\{\text{line}, \text{solid}, \left(-6,-5\right), \left(-3,-1\right)\right\}, \left\{\text{line}, \text{solid}, \left(-5,-8\right), \left(-2,-4\right)\right\}, \left\{\text{line}, \text{solid}, \left(-5,-7\right), \left(-2,-3\right)\right\}, \left\{\text{line}, \text{solid}, \left(-5,-6\right), \left(-2,-2\right)\right\}, \left\{\text{line}, \text{solid}, \left(-5,-5\right), \left(-2,-1\right)\right\}, \left\{\text{line}, \text{solid}, \left(-4,-8\right), \left(-1,-4\right)\right\}, \left\{\text{line}, \text{solid}, \left(-4,-7\right), \left(-1,-3\right)\right\}, \left\{\text{line}, \text{solid}, \left(-4,-6\right), \left(-1,-2\right)\right\}, \left\{\text{line}, \text{solid}, \left(-4,-5\right), \left(-1,-1\right)\right\}, \left\{\text{line}, \text{solid}, \left(-3,-8\right), \left(0,-4\right)\right\}, \left\{\text{line}, \text{solid}, \left(-3,-7\right), \left(0,-3\right)\right\}, \left\{\text{line}, \text{solid}, \left(-3,-6\right), \left(0,-2\right)\right\}, \left\{\text{line}, \text{solid}, \left(-3,-5\right), \left(0,-1\right)\right\}, \left\{\text{line}, \text{solid}, \left(-2,-8\right), \left(1,-4\right)\right\}, \left\{\text{line}, \text{solid}, \left(-2,-7\right), \left(1,-3\right)\right\}, \left\{\text{line}, \text{solid}, \left(-2,-6\right), \left(1,-2\right)\right\}, \left\{\text{line}, \text{solid}, \left(-2,-5\right), \left(1,-1\right)\right\}, \left\{\text{line}, \text{solid}, \left(-1,-8\right), \left(2,-4\right)\right\}, \left\{\text{line}, \text{solid}, \left(-1,-7\right), \left(2,-3\right)\right\}, \left\{\text{line}, \text{solid}, \left(-1,-6\right), \left(2,-2\right)\right\}, \left\{\text{line}, \text{solid}, \left(-1,-5\right), \left(2,-1\right)\right\}, \left\{\text{line}, \text{solid}, \left(0,-8\right), \left(3,-4\right)\right\}, \left\{\text{line}, \text{solid}, \left(0,-7\right), \left(3,-3\right)\right\}, \left\{\text{line}, \text{solid}, \left(0,-6\right), \left(3,-2\right)\right\}, \left\{\text{line}, \text{solid}, \left(0,-5\right), \left(3,-1\right)\right\}, \left\{\text{line}, \text{solid}, \left(1,-8\right), \left(4,-4\right)\right\}, \left\{\text{line}, \text{solid}, \left(1,-7\right), \left(4,-3\right)\right\}, \left\{\text{line}, \text{solid}, \left(1,-6\right), \left(4,-2\right)\right\}, \left\{\text{line}, \text{solid}, \left(1,-5\right), \left(4,-1\right)\right\}, \left\{\text{line}, \text{solid}, \left(2,-8\right), \left(5,-4\right)\right\}, \left\{\text{line}, \text{solid}, \left(2,-7\right), \left(5,-3\right)\right\}, \left\{\text{line}, \text{solid}, \left(2,-6\right), \left(5,-2\right)\right\}, \left\{\text{line}, \text{solid}, \left(2,-5\right), \left(5,-1\right)\right\}, \left\{\text{line}, \text{solid}, \left(3,-8\right), \left(6,-4\right)\right\}, \left\{\text{line}, \text{solid}, \left(3,-7\right), \left(6,-3\right)\right\}, \left\{\text{line}, \text{solid}, \left(3,-6\right), \left(6,-2\right)\right\}, \left\{\text{line}, \text{solid}, \left(3,-5\right), \left(6,-1\right)\right\}, \left\{\text{line}, \text{solid}, \left(4,-8\right), \left(7,-4\right)\right\}, \left\{\text{line}, \text{solid}, \left(4,-7\right), \left(7,-3\right)\right\}, \left\{\text{line}, \text{solid}, \left(4,-6\right), \left(7,-2\right)\right\}, \left\{\text{line}, \text{solid}, \left(4,-5\right), \left(7,-1\right)\right\}, \left\{\text{line}, \text{solid}, \left(5,-8\right), \left(8,-4\right)\right\}, \left\{\text{line}, \text{solid}, \left(5,-7\right), \left(8,-3\right)\right\}, \left\{\text{line}, \text{solid}, \left(5,-6\right), \left(8,-2\right)\right\}, \left\{\text{line}, \text{solid}, \left(5,-5\right), \left(8,-1\right)\right\}, \left\{\text{line}, \text{solid}, \left(-8,-4\right), \left(-5,0\right)\right\}, \left\{\text{line}, \text{solid}, \left(-8,-3\right), \left(-5,1\right)\right\}, \left\{\text{line}, \text{solid}, \left(-8,-2\right), \left(-5,2\right)\right\}, \left\{\text{line}, \text{solid}, \left(-8,-1\right), \left(-5,3\right)\right\}, \left\{\text{line}, \text{solid}, \left(-8,0\right), \left(-5,4\right)\right\}, \left\{\text{line}, \text{solid}, \left(-8,1\right), \left(-5,5\right)\right\}, \left\{\text{line}, \text{solid}, \left(-8,2\right), \left(-5,6\right)\right\}, \left\{\text{line}, \text{solid}, \left(-8,3\right), \left(-5,7\right)\right\}, \left\{\text{line}, \text{solid}, \left(-8,4\right), \left(-5,8\right)\right\}, \left\{\text{line}, \text{solid}, \left(-7,-4\right), \left(-4,0\right)\right\}, \left\{\text{line}, \text{solid}, \left(-7,-3\right), \left(-4,1\right)\right\}, \left\{\text{line}, \text{solid}, \left(-7,-2\right), \left(-4,2\right)\right\}, \left\{\text{line}, \text{solid}, \left(-7,-1\right), \left(-4,3\right)\right\}, \left\{\text{line}, \text{solid}, \left(-7,0\right), \left(-4,4\right)\right\}, \left\{\text{line}, \text{solid}, \left(-7,1\right), \left(-4,5\right)\right\}, \left\{\text{line}, \text{solid}, \left(-7,2\right), \left(-4,6\right)\right\}, \left\{\text{line}, \text{solid}, \left(-7,3\right), \left(-4,7\right)\right\}, \left\{\text{line}, \text{solid}, \left(-7,4\right), \left(-4,8\right)\right\}, \left\{\text{line}, \text{solid}, \left(-6,-4\right), \left(-3,0\right)\right\}, \left\{\text{line}, \text{solid}, \left(-6,-3\right), \left(-3,1\right)\right\}, \left\{\text{line}, \text{solid}, \left(-6,-2\right), \left(-3,2\right)\right\}, \left\{\text{line}, \text{solid}, \left(-6,-1\right), \left(-3,3\right)\right\}, \left\{\text{line}, \text{solid}, \left(-6,0\right), \left(-3,4\right)\right\}, \left\{\text{line}, \text{solid}, \left(-6,1\right), \left(-3,5\right)\right\}, \left\{\text{line}, \text{solid}, \left(-6,2\right), \left(-3,6\right)\right\}, \left\{\text{line}, \text{solid}, \left(-6,3\right), \left(-3,7\right)\right\}, \left\{\text{line}, \text{solid}, \left(-6,4\right), \left(-3,8\right)\right\}\)
3.10.31.
Answer.
\(-6.66667\ {\textstyle\frac{\rm\mathstrut ml}{\rm\mathstrut min}}\)
Section 5: Slope-Intercept Form
3.10.33.
Answer 1.
\({\frac{6}{5}}\)
Answer 2.
\(\left(0,-8\right)\)
3.10.35.
Answer.
\(y = x-2\)
3.10.37.
Answer.
\(\left\{\text{line}, \text{solid}, \left(0,-2\right), \left(-4,-1\right)\right\}\)
3.10.39.
Answer.
\(\left\{\text{line}, \text{solid}, \left(0,1\right), \left(9,-6\right)\right\}\)
3.10.41.
Answer.
\(y = -{\frac{8}{7}}x+9\)
3.10.43.
Answer.
\(15\)
3.10.45.
Answer 1.
\(y = -5x+220\)
Answer 2.
\(60\)
Answer 3.
\(44\)
Section 6: Point-Slope Form
3.10.47.
Answer 1.
\(7\)
Answer 2.
\(\left(8,9\right)\)
3.10.49.
Answer.
\(y = 8\mathopen{}\left(x-2\right)+7\)
3.10.51.
Answer.
\(y = 2\mathopen{}\left(x-5\right)+7\hbox{ or }y = 2\mathopen{}\left(x-6\right)+9\)
3.10.53.
Answer.
\(y = -4x-23\)
3.10.55.
Answer.
\(y = \frac{-5}{3}\mathopen{}\left(x+1\right)+7\hbox{, }y = \frac{-5}{3}\mathopen{}\left(x-2\right)+2\hbox{, or }y = \frac{-5}{3}\mathopen{}\left(x-5\right)-3\)
3.10.57.
Answer.
\(\left\{\text{line}, \text{solid}, \left(4,2\right), \left(5,5\right)\right\}\)
3.10.59.
Answer 1.
\(y = -49000\mathopen{}\left(x-4\right)+636000\)
Answer 2.
\(\$391{,}000\)
Answer 3.
\(2016\)
3.10.61.
Answer 1.
\(y = 0.13\mathopen{}\left(x-14\right)+19.92\hbox{ or }y = 0.13\mathopen{}\left(x-19\right)+20.57\)
Answer 2.
\(22\)
Answer 3.
\(56\)
Section 7: Standard Form
3.10.63.
Answer 1.
\(\left(2.28571,0\right)\)
Answer 2.
\(\left(0,-1.54839\right)\)
Answer 3.
\(1.47619\)
3.10.65.
Answer.
\(7x+5y=-5\)
3.10.67.
Answer.
\(\left\{\text{line}, \text{solid}, \left(-8,0\right), \left(0,-7\right)\right\}, \left\{\text{point}, \left(-8,0\right)\right\}, \left\{\text{point}, \left(0,-7\right)\right\}\)
Section 8: Geometry of Lines
3.10.69.
Answer 1.
\(-2;\,-8;\,\left(-2,-8\right);\,-1;\,-8;\,\left(-1,-8\right);\,0;\,-8;\,\left(0,-8\right);\,1;\,-8;\,\left(1,-8\right);\,2;\,-8;\,\left(2,-8\right)\)
Answer 2.
\(\left\{\text{line}, \text{solid}, \left(-2,-8\right), \left(-1,-8\right)\right\}\)
3.10.71.
Answer 1.
\(\text{NONE}\)
Answer 2.
\(\left(0,-4\right)\)
3.10.73.
Answer.
\(\text{none of the above}\)

4 Systems of Two Linear Equations
4.1 Solving a System by Graphing
4.1.5 Exercises

Review

4.1.5.1.
Answer.
\(\text{Choice 2, Choice 4, Choice 6}\)

Skills Practice

4.1.5.3.
Answer.
\(\text{Yes, it is a solution.}\)
4.1.5.5.
Answer.
\(\text{No, it is not a solution.}\)
4.1.5.7.
Answer.
\(\text{No, it is not a solution.}\)
4.1.5.9.
Answer.
\(\left(-2,4\right)\)
4.1.5.11.
Answer.
\(\left(1,-4\right)\)
4.1.5.13.
Answer.
\(\text{no solutions}\)
4.1.5.15.
Answer 1.
\(\text{One}\)
Answer 2.
\(\text{None of the above}\)
4.1.5.17.
Answer 1.
\(\text{Infinitely many}\)
Answer 2.
\(\text{Dependent}\)
4.1.5.19.
Answer 1.
\(\text{Zero}\)
Answer 2.
\(\text{Inconsistent}\)
4.1.5.21.
Answer 1.
\(\left\{\text{line}, \text{solid}, \left(0,7\right), \left(4,2\right)\right\}, \left\{\text{line}, \text{solid}, \left(0,-3\right), \left(4,2\right)\right\}\)
Answer 2.
\(\left(4,2\right)\)
4.1.5.23.
Answer 1.
\(\left\{\text{line}, \text{solid}, \left(3,-2\right), \left(8,6\right)\right\}, \left\{\text{line}, \text{solid}, \left(6,9\right), \left(8,6\right)\right\}\)
Answer 2.
\(\left(8,6\right)\)
4.1.5.25.
Answer 1.
\(\left\{\text{line}, \text{solid}, \left(-1,-4\right), \left(2,-9\right)\right\}, \left\{\text{line}, \text{solid}, \left(6,7\right), \left(9,2\right)\right\}\)
Answer 2.
\(\text{no solutions}\)
4.1.5.27.
Answer 1.
\(\left\{\text{line}, \text{solid}, \left(-2,0\right), \left(0,1\right)\right\}, \left\{\text{line}, \text{solid}, \left(-8,0\right), \left(0,-2\right)\right\}\)
Answer 2.
\(\left(-4,-1\right)\)
4.1.5.29.
Answer 1.
\(\left\{\text{line}, \text{solid}, \left(2,0\right), \left(0,4\right)\right\}, \left\{\text{line}, \text{solid}, -16, \left(0,-6\right)\right\}\)
Answer 2.
\(\text{no solutions}\)
4.1.5.31.
Answer 1.
\(\left\{\text{line}, \text{solid}, \left(4,0\right), \left(0,-4\right)\right\}, \left\{\text{line}, \text{solid}, \left(4,-1\right), \left(0,-5\right)\right\}\)
Answer 2.
\(\text{no solutions}\)
4.1.5.33.
Answer 1.
\(\left\{\text{line}, \text{solid}, \left(-5,0\right), \left(0,1\right)\right\}, \left\{\text{line}, \text{solid}, \left(-8,-4\right), \left(5,2\right)\right\}\)
Answer 2.
\(\left(5,2\right)\)
4.1.5.35.
Answer 1.
\(\left\{\text{line}, \text{solid}, \left(3,0\right), \left(0,-1\right)\right\}\)
Answer 2.
\(\text{infinitely many solutions}\)
4.1.5.37.
Answer 1.
\(\left\{\text{line}, \text{solid}, \left(0,1\right), \left(1,9\right)\right\}, \left\{\text{line}, \text{solid}, \left(9,-4\right), \left(19,-1\right)\right\}\)
Answer 2.
\(\text{infinitely many solutions}\)
4.1.5.39.
Answer 1.
\(\left\{\text{line}, \text{solid}, \left(0,-2\right), \left(4,-3\right)\right\}\)
Answer 2.
\(\left(4,-3\right)\)

Applications

4.1.5.41.
4.1.5.41.a
Answer 1.
\(3x+2y = 54\)
Answer 2.
\(x+y = 24\)
4.1.5.41.b
Answer.
\(\left\{\text{line}, \text{solid}, \left(0,27\right), \left(18,0\right)\right\}, \left\{\text{line}, \text{solid}, \left(0,24\right), \left(24,0\right)\right\}\)
4.1.5.41.c
Answer 1.
\(6\)
Answer 2.
\(18\)
4.1.5.43.
4.1.5.43.a
Answer 1.
\(d = 3t\)
Answer 2.
\(d = 110+\left(-8\right)t\)
4.1.5.43.b
Answer.
\(\left\{\text{line}, \text{solid}, \left(0,0\right), \left(1,3\right)\right\}, \left\{\text{line}, \text{solid}, \left(0,110\right), \left(1,102\right)\right\}\)
4.1.5.43.c
Answer 1.
\(10\ {\rm s}\)
Answer 2.
\(30\ {\rm m}\)

4.2 Substitution
4.2.5 Exercises

Skills Practice

4.2.5.1.
Answer.
\(E = 4, D = -5\)
4.2.5.3.
Answer.
\(Q = 1, V = 3\)
4.2.5.5.
Answer.
\(c = -2, k = -6\)
4.2.5.7.
Answer.
\(n = -4, A = 2\)
4.2.5.9.
Answer.
\(z = -7, P = 7\)
4.2.5.11.
Answer.
\(\text{no solutions}\)
4.2.5.13.
Answer.
\(\text{infinitely many solutions}\)
4.2.5.15.
Answer.
\(h = 1, K = -3\)
4.2.5.17.
Answer.
\(\text{no solutions}\)
4.2.5.19.
Answer.
\(E = -4, r = -5\)
4.2.5.21.
Answer.
\(Q = -{\frac{11}{4}}, F = -{\frac{87}{4}}\)
4.2.5.23.
Answer.
\(\text{infinitely many solutions}\)
4.2.5.25.
Answer.
\(m = {\frac{13}{5}}, l = {\frac{51}{5}}\)
4.2.5.27.
Answer.
\(y = {\frac{64}{5}}, C = {\frac{83}{5}}\)
4.2.5.29.
Answer.
\(J = -{\frac{19}{9}}, S = -{\frac{34}{9}}\)
4.2.5.31.
Answer.
\(W = -{\frac{12}{5}}, h = -8\)
4.2.5.33.
Answer.
\(h = 1, y = 4\)
4.2.5.35.
Answer.
\(t = -1.11765, N = -4.44118\)
4.2.5.37.
Answer.
\(E = -0.250609, d = -1.18558\)
4.2.5.39.
Answer.
\(P = {\frac{26}{15}}, t = {\frac{19}{9}}\)
4.2.5.41.
Answer.
\(b = 15, I = {\frac{27}{5}}\)
4.2.5.43.
Answer.
\(m = -{\frac{1}{2}}, Z = -{\frac{3}{10}}\)
4.2.5.45.
Answer.
\(\text{no solutions}\)
4.2.5.47.
Answer.
\(J = {\frac{135}{4}}, D = -{\frac{15}{2}}\)
4.2.5.49.
Answer 1.
\(W = -36, T = {\frac{122}{3}}\)
Answer 2.
\(16\)
4.2.5.51.
Answer.
\(\text{infinitely many solutions}\)

Applications

4.2.5.53.
Answer 1.
\(L = 4W-8\)
Answer 2.
\(2L+2W = 139\)
Answer 3.
\(54\ {\rm ft}\)
Answer 4.
\(15.5\ {\rm ft}\)
4.2.5.55.
Answer 1.
\(B = 36.95+4.25D\)
Answer 2.
\(B = 45.95+3.2D\)
Answer 3.
\(8.57143\ {\rm GB}\)
Answer 4.
\(\$73.38\)
4.2.5.57.
Answer 1.
\(M+S = 29\)
Answer 2.
\(2M+8S = 100\)
Answer 3.
\(22\)
Answer 4.
\(7\)
4.2.5.59.
Answer 1.
\(x+y = 3900\)
Answer 2.
\(0.015x-0.07y = -212.5\)
Answer 3.
\(\$1{,}100\)
Answer 4.
\(\$2{,}800\)
4.2.5.61.
Answer 1.
\(x+y = 555\)
Answer 2.
\(0.1x+0.18y = 69.93\)
Answer 3.
\(375\ {\rm ml}\)
Answer 4.
\(180\ {\rm ml}\)

4.3 Elimination
4.3.5 Exercises

Skills Practice

4.3.5.1.
Answer.
\(I = -2, r = 1\)
4.3.5.3.
Answer.
\(V = -4, G = 6\)
4.3.5.5.
Answer.
\(g = -7, X = -2\)
4.3.5.7.
Answer.
\(s = 6, m = 4\)
4.3.5.9.
Answer.
\(\text{no solutions}\)
4.3.5.11.
Answer.
\(P = 1, S = 4\)
4.3.5.13.
Answer.
\(b = {\frac{7}{3}}, j = 1\)
4.3.5.15.
Answer.
\(l = -{\frac{32}{3}}, y = {\frac{34}{3}}\)
4.3.5.17.
Answer.
\(x = 17.6111, N = -2.27778\)
4.3.5.19.
Answer.
\(I = {\frac{17}{12}}, e = {\frac{9}{8}}\)
4.3.5.21.
Answer.
\(\text{infinitely many solutions}\)
4.3.5.23.
Answer.
\(\text{no solutions}\)
4.3.5.25.
Answer.
\(s = -2, Z = 5\)
4.3.5.27.
Answer.
\(C = -4, p = -3\)
4.3.5.29.
Answer.
\(N = -7, E = 4\)
4.3.5.31.
Answer.
\(\text{infinitely many solutions}\)

Applications

4.3.5.33.
Answer 1.
\(M+S = 36\)
Answer 2.
\(2M+6S = 100\)
Answer 3.
\(29\)
Answer 4.
\(7\)
4.3.5.35.
Answer 1.
\(x+y = 4700\)
Answer 2.
\(0.02x+0.055y = 223.5\)
Answer 3.
\(\$1{,}000\)
Answer 4.
\(\$3{,}700\)

Challenge

4.3.5.37.
Answer.
\(3\)

4.4 Systems of Two Linear Equations Chapter Review

Review Exercises for Chapter 4

Section 1: Solving a System by Graphing
4.4.1.
Answer.
\(\text{Yes, it is a solution.}\)
4.4.3.
Answer.
\(\text{no solutions}\)
4.4.5.
Answer 1.
\(\text{Infinitely many}\)
Answer 2.
\(\text{Dependent}\)
4.4.7.
Answer 1.
\(\left\{\text{line}, \text{solid}, \left(-1,0\right), \left(0,-3\right)\right\}, \left\{\text{line}, \text{solid}, \left(-8,1\right), \left(-4,9\right)\right\}\)
Answer 2.
\(\left(-4,9\right)\)
4.4.9.
4.4.9.a
Answer 1.
\(d = 3t\)
Answer 2.
\(d = 150+\left(-12\right)t\)
4.4.9.b
Answer.
\(\left\{\text{line}, \text{solid}, \left(0,0\right), \left(1,3\right)\right\}, \left\{\text{line}, \text{solid}, \left(0,150\right), \left(1,138\right)\right\}\)
4.4.9.c
Answer 1.
\(10\ {\rm s}\)
Answer 2.
\(30\ {\rm m}\)
Section 2: Substitution
4.4.11.
Answer.
\(T = 4, R = 7\)
4.4.13.
Answer.
\(\text{infinitely many solutions}\)
4.4.15.
Answer.
\(r = 0.0714286, z = -0.2\)
4.4.17.
Answer.
\(C = -2, N = {\frac{29}{14}}\)
4.4.19.
Answer 1.
\(R = 96000-4500t\)
Answer 2.
\(R = 41000+2000t\)
Answer 3.
\(8.46154\ {\rm months}\)
Answer 4.
\(\$0\)
4.4.21.
Answer 1.
\(P+C = 1\)
Answer 2.
\(1.6P+5.76C = 3\)
Answer 3.
\(0.663462\ {\rm lb}\)
Answer 4.
\(0.336538\ {\rm lb}\)
Section 3: Elimination
4.4.23.
Answer.
\(k = 4, J = 2\)
4.4.25.
Answer.
\(\text{no solutions}\)
4.4.27.
Answer 1.
\(x+y = 4200\)
Answer 2.
\(0.015x+0.05y = 157.5\)
Answer 3.
\(\$1{,}500\)
Answer 4.
\(\$2{,}700\)

II Preparation for STEM
5 Exponents and Polynomials
5.1 Adding and Subtracting Polynomials
5.1.5 Exercises

Review and Warmup

5.1.5.1.
Answer.
\(13V, -85d, -7.4v\)
5.1.5.3.
Answer.
\(-83x^{9}, {\frac{1}{6}}x^{7}, -x^{2}\)
5.1.5.5.
Answer.
\(40.3C\)
5.1.5.7.
Answer.
\(64.3N^{4}+6.6N^{6}\)

Vocabulary

5.1.5.9.
Answer 1.
\(\text{binomial}\)
Answer 2.
\(4\)
Answer 3.
\(9t^{4}\)
Answer 4.
\(9\)
5.1.5.11.
Answer 1.
\(\text{monomial}\)
Answer 2.
\(3\)
Answer 3.
\(6y^{3}\)
Answer 4.
\(6\)
5.1.5.13.
Answer 1.
\(\text{trinomial}\)
Answer 2.
\(5\)
Answer 3.
\(-83.2z^{5}\)
Answer 4.
\(-83.2\)
5.1.5.15.
Answer 1.
\(\text{binomial}\)
Answer 2.
\(9\)
Answer 3.
\(3z^{9}\)
Answer 4.
\(3\)
5.1.5.17.
Answer 1.
\(\text{trinomial}\)
Answer 2.
\(13\)
Answer 3.
\({\frac{3}{8}}y^{8}t^{5}\)
Answer 4.
\({\frac{3}{8}}\)

Simplifying Polynomials

5.1.5.19.
Answer.
\(-8\)
5.1.5.21.
Answer.
\(5y^{9}-10y^{4}\)
5.1.5.23.
Answer.
\(-r^{4}+3r^{3}-7\)
5.1.5.25.
Answer.
\(-0.458333t-0.587302\)
5.1.5.27.
Answer.
\(1.65278t^{2}+2.25t+0.777778\)
5.1.5.29.
Answer.
\(-1.77143x^{5}+0.375x^{7}-0.166667x^{9}\)
5.1.5.31.
Answer.
\(4y^{5}-3y^{6}+y\)
5.1.5.33.
Answer.
\(1.4r^{8}+0.7r^{4}-7.3r^{5}+1.7r^{9}\)
5.1.5.35.
Answer.
\(-17t-10\)
5.1.5.37.
Answer.
\(x^{4}-2x\)
5.1.5.39.
Answer.
\(16y^{9}+y^{7}+3\)
5.1.5.41.
Answer.
\(-2.4r-0.8\)
5.1.5.43.
Answer.
\(-2.16667t^{3}+2.10714t^{2}+2.21429\)
5.1.5.45.
Answer.
\(-1.33333t^{2}-1.25t^{5}+0.5t^{9}\)
5.1.5.47.
Answer.
\(-2x^{9}-4x^{3}+9x^{6}\)
5.1.5.49.
Answer.
\(-11.4y^{3}+9y+12.8y^{2}-3.2y^{7}\)
5.1.5.51.
Answer.
\(11r-3z\)
5.1.5.53.
Answer.
\(-2t^{7}r^{6}-6tr^{3}\)
5.1.5.55.
Answer.
\(2x^{6}-7x^{4}y^{6}+17y^{3}\)
5.1.5.57.
Answer.
\(-2.14286y+0.0416667z\)
5.1.5.59.
Answer.
\(1.55556z^{3}t^{5}-1.375zt^{8}-4.9t^{7}\)
5.1.5.61.
Answer.
\(-2.2r^{2}x^{3}+0.444444r^{3}x^{8}+1.5r^{8}x^{7}\)
5.1.5.63.
Answer.
\(-t^{9}y^{3}-5t^{2}y^{2}+6t^{5}y^{6}\)
5.1.5.65.
Answer.
\(10.5x^{7}r^{4}+4.7x^{6}r^{3}+0.5x^{4}-0.3x^{2}r^{5}\)

Evaluating Polynomials

5.1.5.67.
Answer 1.
\({\frac{65}{12}}\)
Answer 2.
\({\frac{49}{10}}\)
Answer 3.
\({\frac{19}{4}}\)
5.1.5.69.
Answer 1.
\(24\)
Answer 2.
\(47\)
Answer 3.
\(117\)
5.1.5.71.
Answer 1.
\(-223\)
Answer 2.
\(-35\)
Answer 3.
\(-53\)
5.1.5.73.
Answer 1.
\(9.44\)
Answer 2.
\(10.21\)
Answer 3.
\(7.36\)
5.1.5.75.
Answer 1.
\(-{\frac{1}{2}}\)
Answer 2.
\(-{\frac{5}{2}}\)
Answer 3.
\(5\)
5.1.5.77.
Answer 1.
\(-40\)
Answer 2.
\(-88\)
Answer 3.
\(-4\)

Applications

5.1.5.79.
Answer.
\(1.84467\times 10^{19}\ {\rm ft}\)
5.1.5.81.
Answer.
\(483636\)
5.1.5.83.
Answer.
\(554659\)
5.1.5.85.
Answer.
\(1.6x^{2}+0.18x+282\)
5.1.5.87.
Answer.
\(0.007x^{2}+0.93x+240\)

5.2 Introduction to Exponent Rules
5.2.4 Exercises

Review and Warmup

5.2.4.1.
5.2.4.1.a
Answer.
\(4\)
5.2.4.1.b
Answer.
\(16\)
5.2.4.1.c
Answer.
\(-3125\)
5.2.4.1.d
Answer.
\(-16\)
5.2.4.3.
5.2.4.3.a
Answer.
\({\frac{16}{625}}\)
5.2.4.3.b
Answer.
\({\frac{16}{25}}\)
5.2.4.3.c
Answer.
\(-{\frac{243}{3125}}\)
5.2.4.3.d
Answer.
\(-{\frac{16}{625}}\)
5.2.4.5.
5.2.4.5.a
Answer.
\(1158.56\)
5.2.4.5.b
Answer.
\(3.61\)
5.2.4.5.c
Answer.
\(-12.167\)
5.2.4.5.d
Answer.
\(-17.64\)

Skills Practice

5.2.4.7.
Answer.
\(8^{4}\)
5.2.4.9.
Answer.
\(2^{10}\)
5.2.4.11.
Answer.
\(g^{12}\)
5.2.4.13.
Answer.
\(m^{15}\)
5.2.4.15.
Answer.
\(7^{45}\)
5.2.4.17.
Answer.
\(y^{56}\)
5.2.4.19.
Answer.
\(8e^{3}\)
5.2.4.21.
Answer.
\(27j^{3}h^{3}\)
5.2.4.23.
Answer.
\(16q^{4}\)
5.2.4.25.
Answer.
\(18w^{0}\)
5.2.4.27.
Answer.
\(625b^{36}\)
5.2.4.29.
Answer.
\(168g^{18}\)
5.2.4.31.
Answer.
\(-125m^{27}\)
5.2.4.33.
Answer.
\(\frac{t^{0}}{15}\)
5.2.4.35.
Answer.
\(\frac{y^{0}}{256}\)
5.2.4.37.
Answer.
\(d^{2}+d\)
5.2.4.39.
Answer.
\(i^{3}+i^{2}\)
5.2.4.41.
Answer.
\(q^{12}+q^{7}\)
5.2.4.43.
5.2.4.43.a
Answer.
\(2w\)
5.2.4.43.b
Answer.
\(w^{2}\)
5.2.4.45.
5.2.4.45.a
Answer.
\(2b^{9}\)
5.2.4.45.b
Answer.
\(b^{18}\)
5.2.4.47.
5.2.4.47.a
Answer.
\(g^{4}+g^{3}\)
5.2.4.47.b
Answer.
\(g^{7}\)
5.2.4.49.
5.2.4.49.a
Answer.
\(2m^{6}+m^{2}\)
5.2.4.49.b
Answer.
\(m^{14}\)
5.2.4.51.
5.2.4.51.a
Answer.
\(14t^{9}\)
5.2.4.51.b
Answer.
\(45t^{18}\)
5.2.4.53.
Answer.
\(192y^{14}\)
5.2.4.55.
Answer.
\(128d^{17}n^{23}\)
5.2.4.57.
Answer.
\(-42i^{11}\)
5.2.4.59.
Answer.
\(-51p^{4}\)
5.2.4.61.
Answer.
\(2076w^{23}\)

Challenge

5.2.4.63.
5.2.4.63.a
Answer.
\(1\)
5.2.4.63.b
Answer.
\(94\)
5.2.4.63.c
Answer.
\(499\)
5.2.4.65.
Answer 1.
\(-11x;\,-10x\)
Answer 2.
\(-5x^{20};\,-6x^{20}\)
Answer 3.
\(7;\,x^{35};\,x^{10}\)

5.3 Dividing by a Monomial
5.3.4 Exercises

Skills Practice

5.3.4.1.
Answer.
\(m^{2}\)
5.3.4.3.
Answer.
\(t^{6}\)
5.3.4.5.
Answer.
\(8y^{6}\)
5.3.4.7.
Answer.
\(3d^{2}\)
5.3.4.9.
Answer.
\(0.142857i^{3}\)
5.3.4.11.
Answer.
\(0.888889t\)
5.3.4.13.
Answer.
\(182^{216}\)
5.3.4.15.
Answer.
\(42^{68}\cdot 68^{53}\)
5.3.4.17.
Answer.
\(g^{5}v^{2}\)
5.3.4.19.
Answer.
\(\frac{2}{7}a^{2}y^{7}\)
5.3.4.21.
Answer.
\(5i^{9}+9i^{5}\)
5.3.4.23.
Answer.
\(7v^{9}+6v^{5}\)
5.3.4.25.
Answer.
\(-7f^{9}+9f^{5}+2f^{7}\)
5.3.4.27.
Answer.
\(-5x^{5}+\left(-3\right)x^{9}+5x^{6}\)
5.3.4.29.
Answer.
\(6d^{8}-3d^{5}\)
5.3.4.31.
Answer.
\(9p^{5}w^{5}+2p^{4}w^{9}\)

Applications

5.3.4.33.
Answer.
\(2x^{4}+10x^{2}+6x\)
5.3.4.35.
Answer.
\(16\)

5.4 Multiplying Polynomials
5.4.5 Exercises

Review and Warmup

5.4.5.1.
Answer.
\(t^{9}\)
5.4.5.3.
Answer.
\(9y^{2}\)
5.4.5.5.
Answer.
\(14d^{0}\)

Skills Practice

5.4.5.7.
Answer.
\(-3x^{2}-9x\)
5.4.5.9.
Answer.
\(56x^{2}+49x\)
5.4.5.11.
Answer.
\(6x^{3}+48x^{2}\)
5.4.5.13.
Answer.
\(-20x^{4}+50x^{3}\)
5.4.5.15.
Answer.
\(-24x^{4}+20x^{3}+16x^{2}\)
5.4.5.17.
Answer.
\(12x^{25}y^{3}-36x^{11}y^{19}\)
5.4.5.19.
Answer.
\(-72a^{21}b^{33}-48a^{29}b^{27}\)
5.4.5.21.
Answer.
\(-80a^{17}+60a^{20}b^{5}-90a^{10}b^{8}\)
5.4.5.23.
Answer.
\(x^{2}+11x+30\)
5.4.5.25.
Answer.
\(9y^{2}+76y+32\)
5.4.5.27.
Answer.
\(r^{2}-7r-8\)
5.4.5.29.
Answer.
\(t^{2}-17t+70\)
5.4.5.31.
Answer.
\(5x^{2}+29x+36\)
5.4.5.33.
Answer.
\(8x^{2}-26x+21\)
5.4.5.35.
Answer.
\(4y^{2}-9y+5\)
5.4.5.37.
Answer.
\(7r^{2}+15r-18\)
5.4.5.39.
Answer.
\(12t^{3}-16t^{2}-42t+56\)
5.4.5.41.
Answer.
\(3x^{5}+9x^{3}+x^{2}+3\)
5.4.5.43.
Answer.
\(20y^{4}-46y^{2}+18\)
5.4.5.45.
Answer.
\(a^{2}-ab-56b^{2}\)
5.4.5.47.
Answer.
\(9a^{2}+20ab-21b^{2}\)
5.4.5.49.
Answer.
\(10a^{2}-31ab+15b^{2}\)
5.4.5.51.
Answer.
\(32a^{2}b^{2}+16ab-6\)
5.4.5.53.
Answer.
\(2y^{2}+2y-180\)
5.4.5.55.
Answer.
\(-2r^{2}-12r+32\)
5.4.5.57.
Answer.
\(t^{3}+8t^{2}+15t\)
5.4.5.59.
Answer.
\(5x^{3}-15x^{2}-20x\)
5.4.5.61.
Answer.
\(-9y^{2}+12y+45\)
5.4.5.63.
Answer.
\(-20x^{4}+26x^{3}+8x^{2}-20x+6\)
5.4.5.65.
Answer.
\(5x^{3}-23x^{2}+10x+8\)
5.4.5.67.
Answer.
\(x^{4}+2x^{3}-17x^{2}-12x+20\)
5.4.5.69.
Answer.
\(a^{3}+4a^{2}b-41ab^{2}+36b^{3}\)
5.4.5.71.
Answer.
\(a^{2}+2ab+b^{2}-36\)

Applications

5.4.5.73.
Answer.
\(2w^{2}-7w\)
5.4.5.75.
Answer.
\(2b^{2}+5b\)
5.4.5.77.
Answer.
\(h^{2}+5h\)
5.4.5.79.
Answer.
\(x^{2}+5x-50\)
5.4.5.81.
Answer.
\(-24x^{2}+344x+1760\)

Challenge

5.4.5.83.
Answer 1.
\(-7xy;\,-4xy\)
Answer 2.
\(-5x^{20}y^{9};\,-10x^{20}y^{9}\)
Answer 3.
\(x^{40};\,x^{10};\,y^{50};\,y^{30};\,13\)

5.5 Special Cases of Multiplying Polynomials
5.5.5 Exercises

Review and Warmup

5.5.5.1.
Answer.
\(16k^{2}\)
5.5.5.3.
Answer.
\(625r^{20}\)
5.5.5.5.
Answer.
\(625x^{36}\)

Skills Practice

5.5.5.7.
Answer.
\(x^{2}+10x+25\)
5.5.5.9.
Answer.
\(64y^{2}+64y+16\)
5.5.5.11.
Answer.
\(r^{2}-20r+100\)
5.5.5.13.
Answer.
\(25t^{2}-100t+100\)
5.5.5.15.
Answer.
\(49t^{4}-28t^{2}+4\)
5.5.5.17.
Answer.
\(x^{16}+26x^{8}+169\)
5.5.5.19.
Answer.
\(25a^{2}+40ab+16b^{2}\)
5.5.5.21.
Answer.
\(49a^{2}b^{2}-98ab+49\)
5.5.5.23.
Answer.
\(x^{4}+18x^{2}y^{2}+81y^{4}\)
5.5.5.25.
Answer.
\(x^{2}-64\)
5.5.5.27.
Answer.
\(16y^{2}-64\)
5.5.5.29.
Answer.
\(64-64r^{2}\)
5.5.5.31.
Answer.
\(t^{14}-121\)
5.5.5.33.
Answer.
\(16t^{8}-9\)
5.5.5.35.
Answer.
\(1-121x^{14}\)
5.5.5.37.
Answer.
\(25x^{2}-4y^{2}\)
5.5.5.39.
Answer.
\(a^{2}b^{2}-49\)
5.5.5.41.
Answer.
\(4t^{2}-36\)
5.5.5.43.
Answer.
\(108x^{2}-12\)
5.5.5.45.
Answer.
\(4y^{2}+24y+36\)
5.5.5.47.
Answer.
\(108r^{2}+108r+27\)
5.5.5.49.
Answer.
\(x^{4}-64y^{4}\)
5.5.5.51.
Answer.
\(100x^{4}-9y^{16}\)
5.5.5.53.
Answer.
\(9x^{12}y^{4}-36y^{16}\)
5.5.5.55.
Answer.
\(y^{3}+15y^{2}+75y+125\)
5.5.5.57.
Answer.
\(r^{3}-6r^{2}+12r-8\)
5.5.5.59.
Answer.
\(27t^{3}+162t^{2}+324t+216\)
5.5.5.61.
Answer.
\(125x^{3}-450x^{2}+540x-216\)
5.5.5.63.
5.5.5.63.a
Answer.
\(\text{False}\)
5.5.5.63.b
Answer.
\(\text{False}\)
5.5.5.63.c
Answer.
\(\text{True}\)

5.6 More Exponent Rules
5.6.7 Exercises

Review and Warmup

5.6.7.1.
5.6.7.1.a
Answer.
\(16\)
5.6.7.1.b
Answer.
\(625\)
5.6.7.1.c
Answer.
\(-3125\)
5.6.7.1.d
Answer.
\(-4\)
5.6.7.3.
5.6.7.3.a
Answer.
\({\frac{4}{25}}\)
5.6.7.3.b
Answer.
\({\frac{625}{256}}\)
5.6.7.3.c
Answer.
\(-{\frac{1}{243}}\)
5.6.7.3.d
Answer.
\(-{\frac{4}{25}}\)

Skills Practice

5.6.7.5.
Answer.
\(t^{31}\)
5.6.7.7.
Answer.
\(r^{33}\)
5.6.7.9.
Answer.
\(64y^{6}\)
5.6.7.11.
Answer.
\(42t^{22}\)
5.6.7.13.
Answer.
\(-\frac{x^{13}}{21}\)
5.6.7.15.
Answer.
\(-300y^{20}\)
5.6.7.17.
Answer.
\(1\)
5.6.7.19.
Answer.
\(-1\)
5.6.7.21.
Answer.
\(2\)
5.6.7.23.
Answer.
\(32\)
5.6.7.25.
Answer.
\(1\)
5.6.7.27.
Answer.
\(\frac{x^{6}}{4}\)
5.6.7.29.
Answer.
\(\frac{-125}{216x^{30}}\)
5.6.7.31.
Answer.
\(\frac{729x^{18}}{64}\)
5.6.7.33.
Answer.
\(\frac{x^{4}}{4y^{14}z^{16}}\)
5.6.7.35.
Answer.
\(\frac{9x^{20}}{100y^{10}}\)
5.6.7.37.
Answer.
\(27\)
5.6.7.39.
Answer.
\(1\)
5.6.7.41.
Answer.
\(-{\frac{3}{28}}\)
5.6.7.43.
Answer.
\(\frac{14}{x^{11}}\)
5.6.7.45.
Answer.
\(19x^{3}\)
5.6.7.47.
Answer.
\(\frac{8}{x^{6}}\)
5.6.7.49.
Answer.
\(9x^{5}\)
5.6.7.51.
Answer.
\(\frac{6x^{13}}{7}\)
5.6.7.53.
Answer.
\(\frac{x^{5}}{t^{19}}\)
5.6.7.55.
Answer.
\(\frac{1}{y^{14}x^{16}}\)
5.6.7.57.
Answer.
\(\frac{y^{13}}{37}\)
5.6.7.59.
Answer.
\(\frac{1}{r^{2}}\)
5.6.7.61.
Answer.
\(\frac{10}{t^{13}}\)
5.6.7.63.
Answer.
\(\frac{7}{13x^{29}}\)
5.6.7.65.
Answer.
\(\frac{1}{y^{97}}\)
5.6.7.67.
Answer.
\(\frac{1}{r^{24}}\)
5.6.7.69.
Answer.
\(\frac{1}{r^{5}}\)
5.6.7.71.
Answer.
\(\frac{-27}{t^{10}}\)
5.6.7.73.
Answer.
\({\frac{49}{100}}\)
5.6.7.75.
Answer.
\({\frac{1}{25}}\)
5.6.7.77.
Answer.
\(-343\)
5.6.7.79.
Answer.
\(-128\)
5.6.7.81.
Answer.
\({\frac{1}{4}}\)
5.6.7.83.
Answer.
\({\frac{3}{8}}\)
5.6.7.85.
Answer.
\(216\)
5.6.7.87.
Answer.
\(-{\frac{1}{64}}\)
5.6.7.89.
Answer.
\(\frac{64}{t^{3}}\)
5.6.7.91.
Answer.
\(64x^{47}\)
5.6.7.93.
Answer.
\(\frac{1}{y^{4}}\)
5.6.7.95.
Answer.
\(\frac{1}{625r^{24}}\)
5.6.7.97.
Answer.
\(\frac{t^{34}}{4}\)
5.6.7.99.
Answer.
\(\frac{x^{10}}{9}\)
5.6.7.101.
Answer.
\(\frac{21y^{2}}{2}\)
5.6.7.103.
Answer.
\(y^{39}\)
5.6.7.105.
Answer.
\(8r^{2}\)
5.6.7.107.
Answer.
\(\frac{1}{t^{29}}\)
5.6.7.109.
Answer.
\(\frac{1}{x^{42}}\)
5.6.7.111.
Answer.
\(\frac{1}{y^{8}t^{8}}\)
5.6.7.113.
Answer.
\(\frac{r^{30}}{y^{20}}\)
5.6.7.115.
Answer.
\(\frac{16}{t^{36}}\)
5.6.7.117.
Answer.
\(\frac{t^{16}}{x^{20}}\)
5.6.7.119.
Answer.
\(\frac{x^{34}}{y^{28}}\)
5.6.7.121.
Answer.
\(\frac{8y^{5}}{27x^{22}z^{3}}\)
5.6.7.123.
Answer.
\(\frac{1}{x^{45}y^{18}z^{39}}\)

Challenge

5.6.7.125.
Answer 1.
\(9;\,-1;\,1\)
Answer 2.
\(6;\,-5;\,8\)
5.6.7.127.
Answer 1.
\(9;\,-1;\,1\)
Answer 2.
\(\text{NONE}\)
Answer 3.
\(\text{NONE}\)
Answer 4.
\(\text{NONE}\)

5.7 Exponents and Polynomials Chapter Review

Review Exercises for Chapter 5

Section 1: Adding and Subtracting Polynomials
5.7.1.
Answer 1.
\(\text{binomial}\)
Answer 2.
\(6\)
Answer 3.
\(-5z^{6}\)
Answer 4.
\(-5\)
5.7.3.
Answer.
\(y^{6}+3y-10\)
5.7.5.
Answer.
\(3r-9\)
5.7.7.
Answer.
\(3t^{7}-9t^{2}+7t^{8}\)
5.7.9.
Answer.
\(4x^{2}y^{3}-0.844444xy^{2}+0.142857y^{5}\)
5.7.11.
Answer 1.
\(14\)
Answer 2.
\(28\)
Answer 3.
\(68\)
5.7.13.
Answer.
\(0.2x^{2}+3.05x+2975\)
[cross-reference to target(s) "section-introduction-to-exponent-properties" missing or not unique]: [cross-reference to target(s) "section-introduction-to-exponent-properties" missing or not unique]
5.7.15.
Answer.
\(v^{21}\)
5.7.17.
Answer.
\(81a^{4}f^{4}\)
5.7.19.
Answer.
\(-16f^{10}\)
5.7.21.
Answer.
\(k^{10}+k^{17}\)
5.7.23.
Answer.
\(324r^{28}c^{7}\)
5.7.25.
Answer.
\(1285x^{16}\)
Section 3: Dividing by a Monomial
5.7.27.
Answer.
\(3c^{2}\)
5.7.29.
Answer.
\(\frac{2}{5}i^{10}r^{9}\)
5.7.31.
Answer.
\(-4j^{9}+\left(-6\right)j^{6}+\left(-8\right)j^{7}\)
5.7.33.
Answer.
\(7n^{9}i^{6}+2n^{7}i^{3}\)
Section 4: Multiplying Polynomials
5.7.35.
Answer.
\(18x^{2}+10x\)
5.7.37.
Answer.
\(32x^{21}y^{7}-16x^{6}y^{11}\)
5.7.39.
Answer.
\(y^{2}+y-30\)
5.7.41.
Answer.
\(12r^{3}-14r^{2}-48r+56\)
5.7.43.
Answer.
\(30a^{2}b^{2}+49ab+12\)
5.7.45.
Answer.
\(-2x^{3}-6x^{2}-14x-10\)
5.7.47.
Answer.
\(5w^{2}-4w\)
Section 5: Special Cases of Multiplying Polynomials
5.7.49.
Answer.
\(r^{2}+2r+1\)
5.7.51.
Answer.
\(81a^{2}+90ab+25b^{2}\)
5.7.53.
Answer.
\(x^{10}-36\)
5.7.55.
Answer.
\(16x^{2}-144\)
5.7.57.
Answer.
\(36x^{16}y^{16}-16y^{4}\)
5.7.59.
Answer.
\(125r^{3}-150r^{2}+60r-8\)
Section 6: More Exponent Rules
5.7.61.
Answer.
\(128x^{33}\)
5.7.63.
Answer.
\(1\)
5.7.65.
Answer.
\({\frac{25}{64}}\)
5.7.67.
Answer.
\(\frac{8x^{15}}{9}\)
5.7.69.
Answer.
\(\frac{11}{15t^{7}}\)
5.7.71.
Answer.
\({\frac{1}{100}}\)
5.7.73.
Answer.
\(-{\frac{1}{27}}\)
5.7.75.
Answer.
\(\frac{y^{12}}{125}\)
5.7.77.
Answer.
\(\frac{1}{r^{27}}\)
5.7.79.
Answer.
\(\frac{r^{44}}{t^{32}}\)

6 Radical Expressions and Equations
6.1 Square and \(n\)th Root Properties
6.1.10 Exercises

6.1.10.1.

Answer.
\(\text{64, 4, 9}\)

6.1.10.3.

6.1.10.3.a
Answer.
\(11\)
6.1.10.3.b
Answer.
\(6\)
6.1.10.3.c
Answer.
\(12\)

6.1.10.5.

6.1.10.5.a
Answer.
\({\frac{2}{11}}\)
6.1.10.5.b
Answer.
\(\text{not a real number}\)

6.1.10.7.

6.1.10.7.a
Answer.
\(5\)
6.1.10.7.b
Answer.
\(0.5\)
6.1.10.7.c
Answer.
\(50\)

6.1.10.9.

6.1.10.9.a
Answer.
\(7\)
6.1.10.9.b
Answer.
\(70\)
6.1.10.9.c
Answer.
\(700\)

6.1.10.11.

6.1.10.11.a
Answer.
\(9\)
6.1.10.11.b
Answer.
\(0.9\)
6.1.10.11.c
Answer.
\(0.09\)

6.1.10.13.

Answer.
\(\text{9.95}\)

6.1.10.15.

Answer.
\(\frac{3}{5}\)

6.1.10.17.

Answer.
\(-6\)

6.1.10.19.

Answer.
\(\text{not a real number}\)

6.1.10.21.

Answer.
\(\text{not a real number}\hbox{ or }0.909091i\)

6.1.10.23.

Answer.
\(\frac{-2}{5}\)

6.1.10.25.

6.1.10.25.a
Answer.
\(1\)
6.1.10.25.b
Answer.
\(3\)

6.1.10.27.

Answer.
\(4\)

6.1.10.29.

Answer.
\(\frac{1}{5}\)

6.1.10.31.

Answer.
\(7\sqrt{13}\)

6.1.10.33.

Answer.
\(6\sqrt{3}\)

6.1.10.35.

Answer.
\(\sqrt{231}\)

6.1.10.37.

Answer.
\(49\sqrt{14}\)

6.1.10.39.

Answer.
\(176\sqrt{3}\)

6.1.10.41.

Answer.
\(90\sqrt{2}\)

6.1.10.43.

Answer.
\(18\)

6.1.10.45.

Answer.
\(\frac{\sqrt{35}}{6}\)

6.1.10.47.

Answer.
\(\frac{5\sqrt{2}}{13}\)

6.1.10.49.

Answer.
\(-\sqrt{10}\)

6.1.10.51.

Answer.
\(13\sqrt{2}\)

6.1.10.53.

Answer.
\(8\sqrt{3}\)

6.1.10.55.

Answer.
\(-\sqrt{7}\)

6.1.10.57.

Answer.
\(7\sqrt{7}+8\sqrt{5}\)

6.1.10.59.

Answer.
\(5\sqrt{2}-10\sqrt{5}\)

6.1.10.61.

Answer.
\(\sqrt{22}+\sqrt{10}\)

6.1.10.63.

Answer.
\(18\sqrt{7}+87\)

6.1.10.65.

Answer.
\(75-54\sqrt{7}\)

6.1.10.67.

Answer.
\(84+18\sqrt{3}\)

6.1.10.69.

Answer.
\(9-4\sqrt{5}\)

6.1.10.71.

Answer.
\(24+6\sqrt{7}\)

6.1.10.73.

Answer.
\(616-80\sqrt{6}\)

6.1.10.75.

Answer.
\(36\)

6.1.10.77.

Answer.
\(-8\)

6.1.10.79.

Answer.
\(34\)

6.1.10.81.

Answer.
\(5\)

6.1.10.83.

Answer.
\(2\)

6.1.10.85.

Answer.
\(2\)

6.1.10.87.

Answer.
\(-3\)

6.1.10.89.

Answer.
\(\text{not a real number}\)

6.1.10.91.

Answer.
\(-2\)

6.1.10.93.

Answer.
\(3\sqrt[4]{2}\)

6.1.10.95.

Answer.
\(2\sqrt[3]{3}\)

6.1.10.97.

Answer.
\(3\sqrt[4]{2}\)

6.1.10.99.

Answer.
\(\frac{1}{2}\sqrt[5]{5}\)

6.1.10.101.

Answer.
\(\frac{2}{5}\sqrt[3]{9}\)

6.1.10.103.

Answer.
\(\frac{2}{3}\sqrt[4]{5}\)

6.1.10.105.

Answer.
\(\sqrt{10}\hbox{ or }-\sqrt{10}\)

6.1.10.107.

Answer.
\(\text{NONE}\)

6.1.10.109.

Answer.
\(\sqrt[3]{30}\)

6.1.10.111.

Answer.
\(\sqrt[3]{-41}\)

6.1.10.113.

Answer.
\(\sqrt[4]{3}\hbox{ or }-\sqrt[4]{3}\)

6.1.10.115.

Answer.
\(\text{NONE}\)

6.1.10.117.

Answer.
\(\sqrt[5]{-23}\)

6.2 Rationalizing the Denominator
6.2.4 Exercises

6.2.4.1.

Answer.
\(\frac{\sqrt{10}}{10}\)

6.2.4.3.

Answer.
\(5\sqrt{3}\)

6.2.4.5.

Answer.
\(\frac{\sqrt{2}}{6}\)

6.2.4.7.

Answer.
\(\frac{5\sqrt{2}}{6}\)

6.2.4.9.

Answer.
\(\frac{9}{8}\)

6.2.4.11.

Answer.
\(\frac{9\sqrt{2}}{2}\)

6.2.4.13.

Answer.
\(\frac{5\sqrt{3}}{9}\)

6.2.4.15.

Answer.
\(\frac{4\sqrt{15}}{3}\)

6.2.4.17.

Answer.
\(\frac{\sqrt{15}}{8}\)

6.2.4.19.

Answer.
\(\frac{3\sqrt{2}}{2}\)

6.2.4.21.

Answer.
\(\frac{\sqrt{30}}{10}\)

6.2.4.23.

Answer.
\(\frac{3\sqrt{35}}{5}\)

6.2.4.25.

Answer.
\(\frac{\sqrt{n}}{n}\)

6.2.4.27.

Answer.
\(\frac{\sqrt{55}}{30}\)

6.2.4.29.

Answer.
\(\frac{16-2\sqrt{19}}{45}\)

6.2.4.31.

Answer.
\(\frac{36-6\sqrt{19}}{17}\)

6.2.4.33.

Answer.
\(\frac{80-10\sqrt{11}-8\sqrt{3}+\sqrt{33}}{-53}\)

6.2.4.35.

Answer.
\(\frac{36-12\sqrt{11}-3\sqrt{5}+\sqrt{55}}{2}\)

6.3 Radical Expressions and Rational Exponents
6.3.4 Exercises

Review and Warmup

6.3.4.1.
Answer.
\(x^{39}\)
6.3.4.3.
Answer.
\(x^{15}\)
6.3.4.5.
Answer.
\(\frac{729x^{15}}{1000}\)
6.3.4.7.
Answer.
\(-64t^{24}\)
6.3.4.9.
Answer.
\(r^{13}\)
6.3.4.11.
Answer.
\(\frac{1}{x^{7}}\)
6.3.4.13.
Answer.
\(\frac{36}{y^{13}}\)

Skills Practice

6.3.4.15.
Answer.
\({\frac{1}{9}}\)
6.3.4.17.
Answer.
\(27\)
6.3.4.19.
Answer.
\(16\)
6.3.4.21.
Answer.
\(4\)
6.3.4.23.
Answer.
\(-\frac{2}{3}\)
6.3.4.25.
Answer.
\(-\frac{3}{4}\)
6.3.4.27.
6.3.4.27.a
Answer.
\(9\)
6.3.4.27.b
Answer.
\(\text{DNE}\)
6.3.4.27.c
Answer.
\(-9\)
6.3.4.29.
6.3.4.29.a
Answer.
\(2\)
6.3.4.29.b
Answer.
\(-2\)
6.3.4.29.c
Answer.
\(-2\)
6.3.4.31.
6.3.4.31.a
Answer.
\(2\)
6.3.4.31.b
Answer.
\(-2\)
6.3.4.31.c
Answer.
\(-2\)
6.3.4.33.
6.3.4.33.a
Answer.
\(2\)
6.3.4.33.b
Answer.
\(\text{DNE}\)
6.3.4.33.c
Answer.
\(-2\)
6.3.4.35.
Answer.
\(2.04767\)
6.3.4.37.
Answer.
\(9.1005\)
6.3.4.39.
Answer.
\(y^{\frac{1}{8}}\)
6.3.4.41.
Answer.
\(\left(2t+9\right)^{\frac{1}{4}}\)
6.3.4.43.
Answer.
\(m^{\frac{1}{5}}\)
6.3.4.45.
Answer.
\(b^{\frac{-4}{7}}\)
6.3.4.47.
Answer.
\(\sqrt[3]{x^{2}}\)
6.3.4.49.
Answer.
\(\sqrt[3]{z^{4}}\)
6.3.4.51.
Answer.
\(\sqrt[5]{2r^{4}}\)
6.3.4.53.
Answer.
\(\sqrt[8]{n^{5}}\)
6.3.4.55.
Answer.
\(\frac{1}{\sqrt[7]{c^{2}}}\)
6.3.4.57.
Answer.
\(\sqrt[7]{2y^{4}}\)
6.3.4.59.
Answer.
\(t^{\frac{2}{11}}\)
6.3.4.61.
Answer.
\(2m^{\frac{1}{2}}\)
6.3.4.63.
Answer.
\(5a^{\frac{1}{5}}\)
6.3.4.65.
Answer.
\(3x^{\frac{1}{2}}\)
6.3.4.67.
Answer.
\(z^{\frac{1}{2}}\)
6.3.4.69.
Answer.
\(r^{\frac{1}{12}}\)
6.3.4.71.
Answer.
\(n^{\frac{5}{8}}\)

Applications

6.3.4.73.
Answer 1.
\(1.49831\)
Answer 2.
\({\frac{3}{2}}\)

6.4 Solving Radical Equations
6.4.4 Exercises

Skills Practice

6.4.4.1.
Answer.
\(\left\{16\right\}\)
6.4.4.3.
Answer.
\(\left\{100\right\}\)
6.4.4.5.
Answer.
\(\left\{16\right\}\)
6.4.4.7.
Answer.
\(\text{no real solutions}\)
6.4.4.9.
Answer.
\(\left\{-28\right\}\)
6.4.4.11.
Answer.
\(\left\{1\right\}\)
6.4.4.13.
Answer.
\(\text{no real solutions}\)
6.4.4.15.
Answer.
\(\left\{\frac{81}{5}\right\}\)
6.4.4.17.
Answer.
\(\left\{520\right\}\)
6.4.4.19.
Answer.
\(\left\{15\right\}\)
6.4.4.21.
Answer.
\(\left\{-23\right\}\)
6.4.4.23.
Answer.
\(L = \frac{8T^{2}}{\pi ^{2}}\)

Applications

6.4.4.25.
Answer.
\(19.4618\ {\rm ft}\)

Challenge

6.4.4.27.
Answer.
\(\left\{\frac{1}{4}\right\}\)

6.5 Radical Expressions and Equations Chapter Review
6.5.5 Exercises

6.5.5.1.

Answer.
\(\frac{4}{7}\)

6.5.5.3.

Answer.
\(-8\)

6.5.5.5.

Answer.
\(5\)

6.5.5.7.

Answer.
\(2\sqrt{2}\)

6.5.5.9.

Answer.
\(75\sqrt{7}\)

6.5.5.11.

Answer.
\(\frac{\sqrt{5}}{6}\)

6.5.5.13.

Answer.
\(-\sqrt{2}\)

6.5.5.15.

Answer.
\(9\sqrt{7}\)

6.5.5.17.

Answer.
\(4\)

6.5.5.19.

Answer.
\(-2\)

6.5.5.21.

Answer.
\(\text{not a real number}\)

6.5.5.23.

Answer.
\(2\sqrt[6]{2}\)

6.5.5.25.

Answer.
\(\frac{1}{2}\sqrt[5]{7}\)

6.5.5.27.

Answer.
\(\frac{3}{4}\sqrt[3]{5}\)

6.5.5.29.

Answer.
\(\frac{\sqrt{6}}{9}\)

6.5.5.31.

Answer.
\(\frac{\sqrt{42}}{30}\)

6.5.5.33.

Answer.
\(\frac{45-9\sqrt{2}}{23}\)

6.5.5.35.

Answer.
\(\frac{48-6\sqrt{7}-8\sqrt{3}+\sqrt{21}}{-57}\)

6.5.5.37.

Answer.
\({\frac{1}{16}}\)

6.5.5.39.

Answer.
\(27\)

6.5.5.41.

Answer.
\(4\)

6.5.5.43.

Answer.
\(4\)

6.5.5.45.

Answer.
\(z^{\frac{1}{9}}\)

6.5.5.47.

Answer.
\(\left(3r+3\right)^{\frac{1}{3}}\)

6.5.5.49.

Answer.
\(\sqrt[5]{n^{4}}\)

6.5.5.51.

Answer.
\(\sqrt[9]{b^{8}}\)

6.5.5.53.

Answer.
\(\sqrt[3]{16x^{2}}\)

6.5.5.55.

Answer.
\(t^{\frac{2}{7}}\)

6.5.5.57.

Answer.
\(3m^{\frac{4}{3}}\)

6.5.5.59.

Answer.
\(5a^{\frac{-1}{2}}\)

6.5.5.61.

Answer.
\(c^{\frac{4}{3}}\)

6.5.5.63.

Answer.
\(12.9691\ {\rm ft}\)

7 Solving Quadratic Equations
7.1 Solving Quadratic Equations by Using a Square Root
7.1.4 Exercises

7.1.4.1.

Answer.
\(\left\{9,-9\right\}\)

7.1.4.3.

Answer.
\(\left\{-\frac{1}{11},\frac{1}{11}\right\}\)

7.1.4.5.

Answer.
\(\left\{2\sqrt{3},-2\sqrt{3}\right\}\)

7.1.4.7.

Answer.
\(\left\{\sqrt{13},-\sqrt{13}\right\}\)

7.1.4.9.

Answer.
\(\left\{-3,3\right\}\)

7.1.4.11.

Answer.
\(\left\{-\frac{9}{10},\frac{9}{10}\right\}\)

7.1.4.13.

Answer.
\(\left\{-\frac{3}{8},\frac{3}{8}\right\}\)

7.1.4.15.

Answer.
\(\left\{\frac{\sqrt{133}}{19},\frac{-\sqrt{133}}{19}\right\}\)

7.1.4.17.

Answer.
\(\left\{\frac{-\sqrt{15}}{5},\frac{\sqrt{15}}{5}\right\}\)

7.1.4.19.

Answer.
\(\text{no real solutions}\)

7.1.4.21.

Answer.
\(\left\{-3,-13\right\}\)

7.1.4.23.

Answer.
\(\left\{17,1\right\}\)

7.1.4.25.

Answer.
\(\left\{\frac{-15}{8},\frac{7}{8}\right\}\)

7.1.4.27.

Answer.
\(\left\{10,6\right\}\)

7.1.4.29.

Answer.
\(\left\{4+\sqrt{47},4-\sqrt{47}\right\}\)

7.1.4.31.

Answer.
\(\left\{9+7\sqrt{2},9-7\sqrt{2}\right\}\)

7.1.4.33.

Answer.
\(\left\{-9+2\sqrt{7},-9-2\sqrt{7}\right\}\)

7.1.4.35.

Answer.
\(26\)

7.1.4.37.

Answer.
\(24\)

7.1.4.39.

Answer.
\(8.30662\)

7.1.4.41.

Answer.
\(2\sqrt{74}\)

7.1.4.43.

Answer.
\(2\sqrt{13}\)

7.1.4.45.

Answer 1.
\(37.5\)
Answer 2.
\(20\)

7.1.4.47.

Answer 1.
\(5.1\)
Answer 2.
\(2.4\)

7.1.4.49.

Answer.
\(\sqrt{Z^{2}-L^{2}}\)

7.1.4.51.

Answer.
\(8.06226\)

7.2 The Quadratic Formula
7.2.3 Exercises

Review and Warmup

7.2.3.1.
Answer 1.
\({\frac{3}{10}}\)
Answer 2.
\(8\)
Answer 3.
\(-5\)
Answer 4.
\({\frac{7}{12}}\)
7.2.3.3.
Answer 1.
\({\frac{3}{5}}\)
Answer 2.
\(-{\frac{7}{3}}\)
Answer 3.
\({\frac{5}{6}}\)
Answer 4.
\({\frac{18}{7}}\)
7.2.3.5.
Answer.
\(33\)
7.2.3.7.
Answer.
\(89\)
7.2.3.9.
Answer.
\(4\sqrt{3}\)
7.2.3.11.
Answer.
\(2\sqrt{6}\)

Skills Practice

7.2.3.13.
Answer.
\(\left\{-3,6\right\}\)
7.2.3.15.
Answer.
\(\left\{\frac{1}{2},2\right\}\)
7.2.3.17.
Answer.
\(\left\{\frac{-8}{9},\frac{1}{3}\right\}\)
7.2.3.19.
Answer.
\(\text{no real solutions}\)
7.2.3.21.
Answer.
\(\left\{-7,\frac{1}{3}\right\}\)
7.2.3.23.
Answer.
\(\left\{4\right\}\)
7.2.3.25.
Answer.
\(\text{no real solutions}\)
7.2.3.27.
Answer.
\(\left\{\frac{-6}{5},\frac{4}{5}\right\}\)
7.2.3.29.
Answer.
\(\left\{-4-2\sqrt{3},-4+2\sqrt{3}\right\}\)
7.2.3.31.
Answer.
\(\left\{\frac{-1}{2}\right\}\)
7.2.3.33.
Answer.
\(\left\{-\left(-3\right)-\sqrt{3},-\left(-3\right)+\sqrt{3}\right\}\)
7.2.3.35.
Answer.
\(\left\{-\left(-1\right)-\frac{-1}{5}\sqrt{10},-\left(-1\right)+\frac{-1}{5}\sqrt{10}\right\}\)
7.2.3.37.
Answer.
\(\left\{\frac{-4}{9}\right\}\)
7.2.3.39.
Answer.
\(\left\{-\frac{1}{2}-\frac{1}{18}\sqrt{33},-\frac{1}{2}+\frac{1}{18}\sqrt{33}\right\}\)
7.2.3.41.
Answer.
\(\left\{2-\frac{1}{2}\sqrt{10},2+\frac{1}{2}\sqrt{10}\right\}\)
7.2.3.43.
Answer.
\(\left\{8.8\right\}\)
7.2.3.45.
Answer.
\(\left\{-6.5\right\}\)
7.2.3.47.
Answer.
\(\left\{-7.2,-2\right\}\)
7.2.3.49.
Answer.
\(\left\{0.285252,9.11475\right\}\)
7.2.3.51.
Answer.
\(\left\{0.558119,1.55509\right\}\)
7.2.3.53.
Answer.
\(\left\{-5,1\right\}\)
7.2.3.55.
Answer.
\(\left\{-3,7\right\}\)
7.2.3.57.
Answer.
\(\left\{-7,\frac{-7}{2}\right\}\)
7.2.3.59.
Answer.
\(\left\{-9,\frac{-4}{3}\right\}\)
7.2.3.61.
Answer.
\(\left\{\frac{8}{7},4\right\}\)
7.2.3.63.
Answer.
\(\left\{\frac{-7}{9},\frac{4}{5}\right\}\)
7.2.3.65.
Answer.
\(\text{no real solutions}\)
7.2.3.67.
Answer.
\(\left\{\frac{1}{3},-2\right\}\)
7.2.3.69.
Answer.
\(\left\{\frac{-5}{8},\frac{3}{4}\right\}\)
7.2.3.71.
Answer.
\(\left\{-\left(-3\right)-3\sqrt{2},-\left(-3\right)+3\sqrt{2}\right\}\)
7.2.3.73.
Answer.
\(\text{no real solutions}\)
7.2.3.75.
Answer.
\(\left\{-6,\frac{5}{7}\right\}\)
7.2.3.77.
Answer.
\(\left\{\frac{1}{6},\frac{5}{2}\right\}\)
7.2.3.79.
Answer.
\(\left\{-\frac{9}{16}-\frac{-1}{16}\sqrt{305},-\frac{9}{16}+\frac{-1}{16}\sqrt{305}\right\}\)
7.2.3.81.
Answer.
\(\left\{-2-\sqrt{11},-2+\sqrt{11}\right\}\)
7.2.3.83.
Answer.
\(\left\{-\frac{-11}{6}-\frac{-1}{6}\sqrt{13},-\frac{-11}{6}+\frac{-1}{6}\sqrt{13}\right\}\)
7.2.3.85.
Answer.
\(\left\{4,9\right\}\)
7.2.3.87.
Answer.
\(\left\{4\right\}\)
7.2.3.89.
Answer.
\(\text{no real solutions}\)
7.2.3.91.
Answer.
\(\text{no real solutions}\)
7.2.3.93.
Answer.
\(\left\{-2,1\right\}\)
7.2.3.95.
Answer.
\(\left\{\frac{2}{5},\frac{14}{5}\right\}\)
7.2.3.97.
Answer.
\(\left\{\frac{3}{2}\right\}\)

Applications

7.2.3.99.
Answer.
\(3.84129\ {\rm s}\)
7.2.3.101.
Answer.
\(4.05083\ {\rm s}\)
7.2.3.103.
Answer.
\(10.25\ {\rm ft}\)
7.2.3.105.
Answer.
\(3.29885\ {\rm cm}\)
7.2.3.107.
Answer.
\(\$48.50\)
7.2.3.109.
Answer.
\(3\)

Challenge

7.2.3.111.
Answer.
\(\frac{-n-\sqrt{n^{2}-4mp}}{2m}, \frac{-n+\sqrt{n^{2}-4mp}}{2m}\)

7.3 Complex Solutions to Quadratic Equations
7.3.5 Exercises

7.3.5.1.

Answer.
\(i\sqrt{70}\)

7.3.5.3.

Answer.
\(3i\sqrt{3}\)

7.3.5.5.

Answer.
\(3i\sqrt{15}\)

7.3.5.7.

Answer.
\(x = 9i or x = -9i\)

7.3.5.9.

Answer.
\(y = 3i or y = -3i\)

7.3.5.11.

Answer.
\(r = i\sqrt{2} or r = -i\sqrt{2}\)

7.3.5.13.

Answer.
\(t = 5i\sqrt{2} or t = \left(-5i\right)\sqrt{2}\)

7.3.5.15.

Answer.
\(x = 2+2i or x = 2-2i\)

7.3.5.17.

Answer.
\(y = 2+2i or y = 2-2i\)

7.3.5.19.

Answer.
\(r = i\sqrt{5}-2 or r = -2-i\sqrt{5}\)

7.4 Solving Equations in General
7.4.5 Exercises

7.4.5.1.

Answer.
\(\left\{\frac{-3}{2}\right\}\)

7.4.5.3.

Answer.
\(\left\{\frac{-3}{5}\right\}\)

7.4.5.5.

Answer.
\(\left\{\frac{-2}{9}\right\}\)

7.4.5.7.

Answer.
\(\left\{7,-7\right\}\)

7.4.5.9.

Answer.
\(\left\{4,22\right\}\)

7.4.5.11.

Answer.
\(\left\{11,-11\right\}\)

7.4.5.13.

Answer.
\(\left\{\frac{3}{5},-\frac{3}{5}\right\}\)

7.4.5.15.

Answer.
\(\left\{\frac{\sqrt{10}}{5},\frac{-\sqrt{10}}{5}\right\}\)

7.4.5.17.

Answer.
\(\left\{-6+\frac{\sqrt{42}}{6},-6-\frac{\sqrt{42}}{6}\right\}\)

7.4.5.19.

Answer.
\(\left\{\frac{3}{2}+\frac{-1}{2}\sqrt{3},\frac{3}{2}-\frac{-1}{2}\sqrt{3}\right\}\)

7.4.5.21.

Answer.
\(\left\{\frac{9}{4}+\frac{1}{4}\sqrt{89},\frac{9}{4}-\frac{1}{4}\sqrt{89}\right\}\)

7.4.5.23.

Answer.
\(\left\{\frac{2}{3}+\frac{1}{3}\sqrt{19},\frac{2}{3}-\frac{1}{3}\sqrt{19}\right\}\)

7.4.5.25.

Answer.
\(\left\{\frac{5}{4}+\frac{-1}{4}\sqrt{65},\frac{5}{4}-\frac{-1}{4}\sqrt{65}\right\}\)

7.4.5.27.

Answer.
\({\rm no\ real\ solutions}\hbox{ or }\text{no real solutions}\)

7.4.5.29.

Answer.
\(\left\{\frac{-211}{8}\right\}\)

7.4.5.31.

Answer.
\({\rm no\ real\ solutions}\hbox{ or }\text{no real solutions}\)

7.4.5.33.

Answer.
\({\rm no\ real\ solutions}\hbox{ or }\text{no real solutions}\)

7.4.5.35.

Answer.
\(\left\{5,2\right\}\)

7.4.5.37.

Answer.
\(b = \frac{A}{h}\)

7.4.5.39.

Answer.
\(l = \frac{P}{2}-w\)

7.4.5.41.

Answer.
\(b = \frac{2A}{h}\)

7.4.5.43.

Answer.
\(m = \frac{y-b}{x}\)

7.4.5.45.

Answer.
\(b = y-mx\)

7.4.5.47.

Answer.
\(h = x-\frac{y-k}{m}\)

7.4.5.49.

Answer.
\(r = \frac{c}{2\pi }\)

7.4.5.51.

Answer.
\(s = \sqrt{A}\)

7.4.5.53.

Answer.
\(r = \sqrt{\frac{V}{\pi h}}\)

7.4.5.55.

Answer.
\(h = \frac{V}{\pi r^{2}}\)

7.4.5.57.

Answer.
\(s = \sqrt[3]{V}\)

7.4.5.59.

Answer.
\(s = \sqrt{\frac{S}{6}}\)

7.4.5.61.

Answer.
\(d = vt\)

7.4.5.63.

Answer.
\(t = \frac{-v-\sqrt{v^{2}-2g\mathopen{}\left(d-p\right)}}{g}, t = \frac{-v+\sqrt{v^{2}-2g\mathopen{}\left(d-p\right)}}{g}\)

7.4.5.65.

Answer.
\(m = \frac{F}{a}\)

7.4.5.67.

Answer.
\(v = \sqrt{ar}\)

7.4.5.69.

Answer.
\(l = g\mathopen{}\left(\frac{T}{2\pi }\right)^{2}\)

7.5 Solving Quadratic Equations Chapter Review
7.5.5 Exercises

7.5.5.1.

Answer.
\(\left\{3\sqrt{11},-3\sqrt{11}\right\}\)

7.5.5.3.

Answer.
\(\left\{-\frac{11}{8},\frac{11}{8}\right\}\)

7.5.5.5.

Answer.
\(\left\{-6,-14\right\}\)

7.5.5.7.

Answer.
\(\left\{10,8\right\}\)

7.5.5.9.

Answer.
\(20\)

7.5.5.11.

Answer 1.
\(13.5\)
Answer 2.
\(7.2\)

7.5.5.13.

Answer.
\(\left\{4,8\right\}\)

7.5.5.15.

Answer.
\(\text{no real solutions}\)

7.5.5.17.

Answer.
\(\left\{\frac{-3}{2}\right\}\)

7.5.5.19.

Answer.
\(\left\{-9.77704,0.652038\right\}\)

7.5.5.21.

Answer.
\(\left\{\frac{-9}{5},\frac{5}{7}\right\}\)

7.5.5.23.

Answer.
\(\left\{\frac{7}{9},7\right\}\)

7.5.5.25.

Answer.
\(\left\{9\right\}\)

7.5.5.27.

Answer.
\(3i\sqrt{6}\)

7.5.5.29.

Answer.
\(r = i\sqrt{3} or r = -i\sqrt{3}\)

7.5.5.31.

Answer.
\(t = 8+3i or t = 8-3i\)

7.5.5.33.

Answer.
\(\left\{64\right\}\)

7.5.5.35.

Answer.
\(\{5\}\)

7.5.5.37.

Answer.
\(\left\{-1,2\right\}\)

7.5.5.39.

Answer.
\(\text{no solution}\)

7.5.5.41.

Answer.
\(\left\{-5-\sqrt{17},-5+\sqrt{17}\right\}\)

7.5.5.43.

Answer.
\(\left\{-1,-3\right\}\)

7.5.5.45.

Answer.
\(\{30\}\)

7.5.5.47.

Answer.
\(\left\{77\right\}\)

7.5.5.49.

Answer.
\(\text{no real solutions}\)

7.5.5.51.

Answer.
\(\left\{\frac{-3}{2},-6\right\}\)

7.5.5.53.

Answer.
\(\left\{12\right\}\)

8 Quantities in the Physical World
8.1 Scientific Notation
8.1.6 Exercises

8.1.6.1.

Answer.
\({2.7\mathbin{\times}10^{5}}\)

8.1.6.3.

Answer.
\({4.7\mathbin{\times}10^{2}}\)

8.1.6.5.

Answer.
\({6.7\mathbin{\times}10^{-3}}\)

8.1.6.7.

Answer.
\({8.7\mathbin{\times}10^{-2}}\)

8.1.6.9.

Answer.
\(170000\)

8.1.6.11.

Answer.
\(3690\)

8.1.6.13.

Answer.
\(5.69\)

8.1.6.15.

Answer.
\(0.077\)

8.1.6.17.

Answer.
\(0.000967\)

8.1.6.19.

Answer.
\({1.8\mathbin{\times}10^{6}}\)

8.1.6.21.

Answer.
\({4\mathbin{\times}10^{8}}\)

8.1.6.23.

Answer.
\({1.4\mathbin{\times}10^{9}}\)

8.1.6.25.

Answer.
\({5\mathbin{\times}10^{0}}\)

8.1.6.27.

Answer.
\({7\mathbin{\times}10^{2}}\)

8.1.6.29.

Answer.
\({2\mathbin{\times}10^{8}}\)

8.1.6.31.

Answer.
\({4\mathbin{\times}10^{6}}\)

8.1.6.33.

Answer.
\({7\mathbin{\times}10^{-9}}\)

8.1.6.35.

Answer.
\({9\mathbin{\times}10^{-8}}\)

8.1.6.37.

Answer.
\({1.6\mathbin{\times}10^{17}}\)

8.1.6.39.

Answer.
\({2.7\mathbin{\times}10^{22}}\)

8.1.6.41.

Answer.
\({6.4\mathbin{\times}10^{28}}\)

8.2 Unit Conversion
8.2.6 Exercises

8.2.6.1.

Answer.
\({\frac{4}{63}}\)

8.2.6.3.

Answer.
\({\frac{65}{42}}\)

8.2.6.5.

Answer.
\({\frac{25}{6}}\)

8.2.6.7.

Answer.
\(0.086\ {\rm g}\)

8.2.6.9.

Answer.
\(6.1\ {\rm cc}\)

8.2.6.11.

Answer.
\(51.5\ {\rm dm}\)

8.2.6.13.

Answer.
\(0.1805\ {\rm T}\)

8.2.6.15.

Answer.
\(5568.6\ {\rm ha}\)

8.2.6.17.

Answer.
\(9.9\times 10^{6}\ {\rm mg}\)

8.2.6.19.

Answer.
\(8.01086\times 10^{-5}\ {\rm MB}\)

8.2.6.21.

Answer.
\(547226\ {\rm b}\)

8.2.6.23.

Answer.
\(3.05\times 10^{-6}\ {\rm m^{2}}\)

8.2.6.25.

Answer.
\(2.09088\times 10^{9}\ {\rm ft^{2}}\)

8.2.6.27.

Answer.
\(0.0185185\ {\rm yd^{2}}\)

8.2.6.29.

Answer.
\(2.47211\ {\rm mi^{2}}\)

8.2.6.31.

Answer.
\(1158.57\ {\textstyle\frac{\rm\mathstrut dm}{\rm\mathstrut d}}\)

8.2.6.33.

Answer.
\(17733.3\ {\textstyle\frac{\rm\mathstrut acre}{\rm\mathstrut h}}\)

8.2.6.35.

Answer.
\(0.000425685\ {\textstyle\frac{\rm\mathstrut gal}{\rm\mathstrut min}}\)

8.2.6.37.

Answer.
\(0.00354167\ {\textstyle\frac{\rm\mathstrut lb}{\rm\mathstrut s}}\)

8.2.6.39.

Answer.
\(212.891\ {\textstyle\frac{\rm\mathstrut Mb}{\rm\mathstrut s}}\)

8.2.6.41.

Answer.
\(0.00601875\ {\textstyle\frac{\rm\mathstrut lb}{\rm\mathstrut cm^{3}}}\)

8.2.6.43.

Answer.
\(10.5556\ {\rm yd^{2}}\)

8.2.6.45.

Answer.
\(8.45443\ {\rm gal}\)

8.2.6.47.

Answer.
\(2.9059\ {\rm c}\)

8.2.6.49.

Answer.
\(16.5\ {\rm mi}\)

8.2.6.51.

Answer.
\(13.44\ {\rm kg}\)

8.2.6.53.

Answer.
\(13455\ {\rm MB}\)

8.3 Geometry Formulas
8.3.4 Exercises

8.3.4.1.

Answer 1.
\(48\ {\rm m}\)
Answer 2.
\(128\ {\rm m^{2}}\)

8.3.4.3.

Answer.
\(\frac{19}{20}\ {\rm m}\)

8.3.4.5.

Answer.
\(\frac{9}{35}\ {\rm m^{2}}\)

8.3.4.7.

Answer 1.
\(192.8\ {\rm in}\)
Answer 2.
\(2121.6\ {\rm in^{2}}\)

8.3.4.9.

Answer 1.
\(52\ {\rm cm}\)
Answer 2.
\(169\ {\rm cm^{2}}\)

8.3.4.11.

Answer 1.
\(44\ {\rm ft}\)
Answer 2.
\(76\ {\rm ft^{2}}\)

8.3.4.13.

Answer 1.
\(56\ {\rm cm}\)
Answer 2.
\(84\ {\rm cm^{2}}\)

8.3.4.15.

Answer 1.
\(65\ {\rm m}\)
Answer 2.
\(112.5\ {\rm m^{2}}\)

8.3.4.17.

Answer.
\(1 {\textstyle\frac{1}{2}}\)

8.3.4.19.

Answer.
\(2.34\ {\rm m^{2}}\)

8.3.4.21.

Answer 1.
\(69\ {\rm ft}\)
Answer 2.
\(299\ {\rm ft^{2}}\)

8.3.4.23.

Answer 1.
\(42\ {\rm m}\)
Answer 2.
\(64\ {\rm m^{2}}\)

8.3.4.25.

Answer 1.
\(56\ {\rm m}\)
Answer 2.
\(92\ {\rm m^{2}}\)

8.3.4.27.

Answer.
\(90\ {\rm m^{2}}\)

8.3.4.29.

Answer.
\(420\ {\rm in^{2}}\)

8.3.4.31.

Answer 1.
\(8\pi\ {\rm m}\)
Answer 2.
\(25.13\ {\rm m}\)
Answer 3.
\(16\pi\ {\rm m^{2}}\)
Answer 4.
\(50.27\ {\rm m^{2}}\)

8.3.4.33.

Answer 1.
\(12\pi\ {\rm m}\)
Answer 2.
\(37.7\ {\rm m}\)
Answer 3.
\(36\pi\ {\rm m^{2}}\)
Answer 4.
\(113.1\ {\rm m^{2}}\)

8.3.4.35.

Answer 1.
\(45.9911\ {\rm cm}\)
Answer 2.
\(146.969\ {\rm cm^{2}}\)

8.3.4.37.

Answer.
\(1350\ {\rm in^{3}}\)

8.3.4.39.

Answer.
\(756\ {\rm in^{3}}\)

8.3.4.41.

Answer.
\(125\ {\rm cm^{3}}\)

8.3.4.43.

Answer 1.
\(80\pi\ {\rm m^{3}}\)
Answer 2.
\(251.33\ {\rm m^{3}}\)

8.3.4.45.

Answer 1.
\(192\pi\ {\rm m^{3}}\)
Answer 2.
\(603.19\ {\rm m^{3}}\)

8.3.4.47.

Answer 1.
\(200\pi\ {\rm ft^{3}}\)
Answer 2.
\(628.319\ {\rm ft^{3}}\)

8.3.4.49.

Answer.
\(5832\ {\rm in^{3}}\)

8.3.4.51.

Answer 1.
\(P = 2\mathopen{}\left(l+w\right)\)
Answer 2.
\(A = lw\)
Answer 3.
\(A = 0.5bh\)
Answer 4.
\(c = \pi d\hbox{, }c = 2\pi r\hbox{, }C = \pi d\hbox{, or }C = 2\pi r\)
Answer 5.
\(A = \pi r^{2}\)
Answer 6.
\(V = wdh\hbox{, }V = lwh\hbox{, or }V = lhd\)
Answer 7.
\(V = \pi r^{2}h\)
Answer 8.
\(V = Bh\)

8.4 Geometry Applications
8.4.3 Exercises

8.4.3.1.

Answer 1.
\(18\ {\rm mm}\)
Answer 2.
\(9\ {\rm mm}\)

8.4.3.3.

Answer 1.
\(9.5493\ {\rm cm}\)
Answer 2.
\(4.77465\ {\rm cm}\)

8.4.3.5.

Answer 1.
\(8\ {\rm mm}\)
Answer 2.
\(4\ {\rm mm}\)

8.4.3.7.

Answer 1.
\(12.4141\ {\rm cm}\)
Answer 2.
\(6.20704\ {\rm cm}\)

8.4.3.9.

Answer.
\(8\ {\rm m}\)

8.4.3.11.

Answer.
\(29\ {\rm mm}\)

8.4.3.13.

Answer.
\(30\ {\rm ft}\)

8.4.3.15.

Answer.
\(17\ {\rm m}\)

8.4.3.17.

Answer.
\(96\ {\rm ft}\)

8.4.3.19.

Answer.
\(19\ {\rm ft}\)

8.5 Quantities in the Physical World Chapter Review
8.5.4 Exercises

8.5.4.1.

Answer.
\({1.1\mathbin{\times}10^{4}}\)

8.5.4.3.

Answer.
\({3.1\mathbin{\times}10^{-2}}\)

8.5.4.5.

Answer.
\(509\)

8.5.4.7.

Answer.
\(7.09\)

8.5.4.9.

Answer.
\(0.0907\)

8.5.4.11.

Answer.
\({4\mathbin{\times}10^{8}}\)

8.5.4.13.

Answer.
\({4\mathbin{\times}10^{6}}\)

8.5.4.15.

Answer.
\(4.96\ {\rm pt}\)

8.5.4.17.

Answer.
\(0.620625\ {\rm lb}\)

8.5.4.19.

Answer.
\(14616\ {\rm h}\)

8.5.4.21.

Answer.
\(0.0028\ {\rm m^{3}}\)

8.5.4.23.

Answer.
\(8\ {\textstyle\frac{\rm\mathstrut m}{\rm\mathstrut d}}\)

8.5.4.25.

Answer.
\(0.0162917\ {\textstyle\frac{\rm\mathstrut g}{\rm\mathstrut h}}\)

8.5.4.27.

Answer.
\(20.8889\ {\rm yd^{2}}\)

8.5.4.29.

Answer.
\(8.23333\ {\rm mi}\)

8.5.4.31.

Answer 1.
\(48\ {\rm m}\)
Answer 2.
\(128\ {\rm m^{2}}\)

8.5.4.33.

Answer.
\(\frac{9}{35}\ {\rm m^{2}}\)

8.5.4.35.

Answer 1.
\(44\ {\rm ft}\)
Answer 2.
\(76\ {\rm ft^{2}}\)

8.5.4.37.

Answer.
\(1 {\textstyle\frac{47}{70}}\)

8.5.4.39.

Answer 1.
\(42\ {\rm m}\)
Answer 2.
\(64\ {\rm m^{2}}\)

8.5.4.41.

Answer.
\(11025\ {\rm in^{2}}\)

8.5.4.43.

Answer 1.
\(45.9911\ {\rm cm}\)
Answer 2.
\(146.969\ {\rm cm^{2}}\)

8.5.4.45.

Answer.
\(729\ {\rm cm^{3}}\)

8.5.4.47.

Answer 1.
\(72\pi\ {\rm ft^{3}}\)
Answer 2.
\(226.195\ {\rm ft^{3}}\)

8.5.4.49.

Answer 1.
\(P = 2\mathopen{}\left(l+w\right)\)
Answer 2.
\(A = lw\)
Answer 3.
\(A = 0.5bh\)
Answer 4.
\(c = \pi d\hbox{, }c = 2\pi r\hbox{, }C = \pi d\hbox{, or }C = 2\pi r\)
Answer 5.
\(A = \pi r^{2}\)
Answer 6.
\(V = wdh\hbox{, }V = lwh\hbox{, or }V = lhd\)
Answer 7.
\(V = \pi r^{2}h\)
Answer 8.
\(V = Bh\)

8.5.4.51.

Answer 1.
\(13.0507\ {\rm cm}\)
Answer 2.
\(6.52535\ {\rm cm}\)

8.5.4.53.

Answer.
\(8\ {\rm m}\)

8.5.4.55.

Answer.
\(17\ {\rm m}\)

8.5.4.57.

Answer.
\(15\ {\rm ft}\)

9 Topics in Graphing
9.1 Review of Graphing
9.1.4 Exercises

9.1.4.1.

Answer 1.
\(\left(0,2\right)\)
Answer 2.
\(\left(-4,-1\right)\)
Answer 3.
\(\left(-2,-3\right)\)
Answer 4.
\(\left(3,0\right)\)

9.1.4.3.

Answer.
a Cartesian plot with the points labeled;(8,2) is right 8, up 2;(5,5) is right 5, up 5;(-3,0) is left 3, up 0;(2,-6) is right 2, down 6

9.1.4.5.

Answer.
\(-1;\,-12;\,0;\,0;\,1;\,12;\,2;\,24;\,3;\,36\)

9.1.4.7.

Answer.
\(-1;\,-8;\,0;\,2;\,1;\,12;\,2;\,22;\,3;\,32\)

9.1.4.9.

Answer.
\(-5;\,-25;\,0;\,-6;\,5;\,13;\,10;\,32;\,15;\,51\)

9.1.4.11.

Answer.
\(-3;\,4;\,0;\,-1;\,3;\,-6;\,6;\,-11;\,9;\,-16\)

9.1.4.13.

Answer.
\(x\) \(y=2x+3\) Point
\(-2\) \(-1\) \((-2,-1)\)
\(-1\) \(1\) \((-1,1)\)
\(0\) \(3\) \((0,3)\)
\(1\) \(5\) \((1,5)\)
\(2\) \(7\) \((2,7)\)

9.1.4.15.

Answer.
\(x\) \(y=\frac{4}{3}x\) Point
\(-3\) \(-4\) \((-3,-4)\)
\(0\) \(0\) \((0,0)\)
\(3\) \(4\) \((3,4)\)

9.1.4.17.

Answer.
\(x\) \(y=x^2+1\) Point
\(-2\) \(5\) \((-2,5)\)
\(-1\) \(2\) \((-1,2)\)
\(0\) \(1\) \((0,1)\)
\(1\) \(2\) \((1,2)\)
\(2\) \(5\) \((2,5)\)

9.1.4.19.

Answer 1.
\(0\)
Answer 2.
\(5\)
Answer 3.
\(\left(0,5\right)\)
Answer 4.
\(6\)
Answer 5.
\(0\)
Answer 6.
\(\left(6,0\right)\)

9.1.4.21.

Answer 1.
\(0\)
Answer 2.
\(24\)
Answer 3.
\(\left(0,24\right)\)
Answer 4.
\(-21\)
Answer 5.
\(0\)
Answer 6.
\(\left(-21,0\right)\)

9.1.4.23.

Answer.
\(x\)-intercept: \((2,0)\)
\(y\)-intercept: \((0,-5)\)

9.1.4.25.

Answer.
\(x\)-intercept: \((-15,0)\)
\(y\)-intercept: \((0,-3)\)

9.1.4.27.

Answer.

9.1.4.29.

Answer.

9.2 Key Features of Quadratic Graphs
9.2.6 Exercises

9.2.6.1.

Answer 1.
\(6\)
Answer 2.
\(\left(-2,6\right)\)
Answer 3.
\(5\)
Answer 4.
\(\left(-1,5\right)\)
Answer 5.
\(4\)
Answer 6.
\(\left(0,4\right)\)
Answer 7.
\(3\)
Answer 8.
\(\left(1,3\right)\)
Answer 9.
\(2\)
Answer 10.
\(\left(2,2\right)\)

9.2.6.3.

Answer 1.
\(-12\)
Answer 2.
\(\left(-16,-12\right)\)
Answer 3.
\(-7\)
Answer 4.
\(\left(-8,-7\right)\)
Answer 5.
\(-2\)
Answer 6.
\(\left(0,-2\right)\)
Answer 7.
\(3\)
Answer 8.
\(\left(8,3\right)\)
Answer 9.
\(8\)
Answer 10.
\(\left(16,8\right)\)

9.2.6.5.

Answer.
\(2\)

9.2.6.7.

Answer.
\(176\)

9.2.6.9.

Answer 1.
\(x = -2\)
Answer 2.
\(\left(-2,17\right)\)

9.2.6.11.

Answer 1.
\(x = -5\)
Answer 2.
\(\left(-5,78\right)\)

9.2.6.13.

Answer 1.
\(x = -2\)
Answer 2.
\(\left(-2,2\right)\)

9.2.6.15.

Answer 1.
\(x = -1\)
Answer 2.
\(\left(-1,-4\right)\)

9.2.6.17.

Answer 1.
\(x = 0\)
Answer 2.
\(\left(0,4\right)\)

9.2.6.19.

Answer 1.
\(x = {\frac{3}{2}}\)
Answer 2.
\(\left({\frac{3}{2}},{\frac{1}{2}}\right)\)

9.2.6.21.

Answer 1.
\(x = -0.5\)
Answer 2.
\(\left(-0.5,4.5\right)\)

9.2.6.23.

Answer 1.
\(x = 0\)
Answer 2.
\(\left(-0,0\right)\)

9.2.6.25.

Answer 1.
\(x = 0\)
Answer 2.
\(\left(-0,1\right)\)

9.2.6.27.

Answer 1.
\(x = 1\)
Answer 2.
\(\left(-\left(-1\right),3\right)\)

9.2.6.45.

Answer 1.
\(-3, 3\)
Answer 2.
\(-9\)

9.2.6.47.

Answer 1.
\(0.5, -2\)
Answer 2.
\(-1\)

9.2.6.49.

Answer 1.
\(245\ {\rm ft}\)
Answer 2.
\(122.5\ {\rm ft}\)
Answer 3.
\(30012.5\ {\rm ft^{2}}\)

9.2.6.51.

Answer 1.
\(200\ {\rm ft}\)
Answer 2.
\(100\ {\rm ft}\)
Answer 3.
\(20000\ {\rm ft^{2}}\)

9.2.6.53.

Answer 1.
\(56\ {\rm ft}\)
Answer 2.
\(42\ {\rm ft}\)
Answer 3.
\(2352\ {\rm ft^{2}}\)

9.2.6.55.

Answer 1.
\(36.8\ {\rm ft}\)
Answer 2.
\(23\ {\rm ft}\)
Answer 3.
\(846.4\ {\rm ft^{2}}\)

9.2.6.57.

Answer 1.
\(\$54{,}675.00\)
Answer 2.
\(\$405.00\)
Answer 3.
\(\$225.00\)
Answer 4.
\(\$585.00\)

9.3 Graphing Quadratic Expressions
9.3.6 Exercises

9.3.6.1.

Answer.
\(\left\{-10,-9\right\}\)

9.3.6.3.

Answer.
\(\left\{3\right\}\)

9.3.6.5.

Answer.
\(\left\{2,-2\right\}\)

9.3.6.7.

Answer.
\(\left\{\frac{\sqrt{1739}}{47},\frac{-\sqrt{1739}}{47}\right\}\)

9.3.6.9.

Answer.
\(\left\{\frac{4-2\sqrt{7}}{3},\frac{4+2\sqrt{7}}{3}\right\}\)

9.3.6.11.

Answer.
\(\text{no real solutions}\)

9.3.6.13.

Answer 1.
\(\left(0,8\right)\)
Answer 2.
\(\left(-2,0\right), \left(-4,0\right)\)

9.3.6.15.

Answer 1.
\(\left(0,-25\right)\)
Answer 2.
\(\left(5,0\right), \left(-5,0\right)\)

9.3.6.17.

Answer 1.
\(\left(0,0\right)\)
Answer 2.
\(\left(0,0\right), \left(3,0\right)\)

9.3.6.19.

Answer 1.
\(\left(0,25\right)\)
Answer 2.
\(\left(5,0\right)\)

9.3.6.21.

Answer 1.
\(\left(0,3\right)\)
Answer 2.
\(\text{DNE}\)

9.3.6.23.

Answer 1.
\(\left(0,5\right)\)
Answer 2.
\(\text{DNE}\)

9.3.6.25.

Answer 1.
\(\left(0,3\right)\)
Answer 2.
\(\left(-0.458619,0\right), \left(-6.54138,0\right)\)

9.3.6.27.

Answer 1.
\(\left(0,7\right)\)
Answer 2.
\(\left(-0.678175,0\right), \left(-10.3218,0\right)\)

9.3.6.29.

Answer 1.
\(\left(0,49\right)\)
Answer 2.
\(\left(-3.5,0\right)\)

9.3.6.31.

Answer 1.
\(\left(0,-15\right)\)
Answer 2.
\(\left(-2.5,0\right), \left(-3,0\right)\)

9.3.6.53.

Answer 1.
\(15\ {\rm s}\)
Answer 2.
\(3600\ {\rm ft}\)
Answer 3.
\(30\ {\rm s}\)
Answer 4.
\(2816\ {\rm ft}\)
Answer 5.
\(7\ {\rm s}\)
Answer 6.
\(23\ {\rm s}\)

9.3.6.55.

Answer 1.
\(25\ {\rm s}\)
Answer 2.
\(3162.5\ {\rm m}\)
Answer 3.
\(50.4049\ {\rm s}\)
Answer 4.
\(2569.6\ {\rm m}\)
Answer 5.
\(22\ {\rm s}\)
Answer 6.
\(28\ {\rm s}\)

9.3.6.57.

Answer.
\(\text{will}\)

9.3.6.59.

Answer.
\(\text{will}\)

9.3.6.61.

Answer 1.
\(0.408163\)
Answer 2.
\(20\)

9.3.6.63.

Answer 1.
\(\$130.00\)
Answer 2.
\(\$180.00\)

9.3.6.65.

Answer 1.
\(\left(\frac{-n-\sqrt{n^{2}-4p}}{2},0\right), \left(\frac{-n+\sqrt{n^{2}-4p}}{2},0\right)\)
Answer 2.
\(\left(0,p\right)\)
Answer 3.
\(\left(\frac{-n}{2},\frac{4p-n^{2}}{4}\right)\)

9.4 Graphically Solving Equations and Inequalities
9.4.4 Exercises

9.4.4.1.

Answer.
\(\text{two times}\)

9.4.4.3.

Answer.
\(\text{one time}\)

9.4.4.5.

Answer.
\(\text{two times}\)

9.4.4.7.

Answer.
\(\text{two times}\)

9.4.4.9.

Answer 1.
\(\left(-6,5\right), \left(2,5\right)\)
Answer 2.
\(\left\{-6,2\right\}\)
Answer 3.
\(\left(-\infty ,-6\right)\cup \left(2,\infty \right)\)

9.4.4.11.

Answer 1.
\(\left(-2.5,-5\right), \left(4,-5\right)\)
Answer 2.
\(\left\{-2.5,4\right\}\)
Answer 3.
\(\left(-2.5,4\right)\)

9.4.4.13.

Answer 1.
\(\left(-2,3\right), \left(2,-1\right)\)
Answer 2.
\(\left\{-2,2\right\}\)
Answer 3.
\(\left(-\infty ,-2\right)\cup \left(2,\infty \right)\)

9.4.4.15.

Answer 1.
\(\left(-2,-2\right), \left(0,0\right), \left(2,2\right)\)
Answer 2.
\(\left\{-2,0,2\right\}\)
Answer 3.
\(\left(-2,0\right)\cup \left(2,\infty \right)\)

9.4.4.17.

Answer 1.
\(\left(-3,1\right), \left(5,3\right)\)
Answer 2.
\(\left\{-3,5\right\}\)
Answer 3.
\(\left(-3,5\right)\)

9.4.4.19.

Answer 1.
\(\left(-2,-2\right), \left(0,0\right)\)
Answer 2.
\(\left\{-2,0\right\}\)
Answer 3.
\(\left(-\infty ,-2\right)\cup \left(0,\infty \right)\)

9.5 Topics in Graphing Chapter Review
9.5.5 Exercises

9.5.5.1.

Answer.
\(-1;\,14;\,0;\,0;\,1;\,-14;\,2;\,-28;\,3;\,-42\)

9.5.5.3.

Answer.
\(-7;\,-18;\,0;\,-2;\,7;\,14;\,14;\,30;\,21;\,46\)

9.5.5.5.

Answer.
\(x\) \(y=2x+3\) Point
\(-2\) \(-1\) \((-2,-1)\)
\(-1\) \(1\) \((-1,1)\)
\(0\) \(3\) \((0,3)\)
\(1\) \(5\) \((1,5)\)
\(2\) \(7\) \((2,7)\)

9.5.5.7.

Answer 1.
\(0\)
Answer 2.
\(-18\)
Answer 3.
\(\left(0,-18\right)\)
Answer 4.
\(-21\)
Answer 5.
\(0\)
Answer 6.
\(\left(-21,0\right)\)

9.5.5.9.

Answer.
\(x\)-intercept: \((-18,0)\)
\(y\)-intercept: \((0,15)\)

9.5.5.11.

Answer 1.
\(x = 4\)
Answer 2.
\(\left(4,-62\right)\)

9.5.5.13.

Answer 1.
\(x = 5\)
Answer 2.
\(\left(5,21\right)\)

9.5.5.15.

Answer 1.
\(x = 0\)
Answer 2.
\(\left(0,3\right)\)

9.5.5.17.

Answer 1.
\(x = 2.5\)
Answer 2.
\(\left(2.5,9.5\right)\)

9.5.5.19.

Answer 1.
\(x = 0\)
Answer 2.
\(\left(-0,-5\right)\)

9.5.5.29.

Answer 1.
\(-5, 5\)
Answer 2.
\(-25\)

9.5.5.31.

Answer 1.
\(\left(0,20\right)\)
Answer 2.
\(\left(-4,0\right), \left(-5,0\right)\)

9.5.5.33.

Answer 1.
\(\left(0,1\right)\)
Answer 2.
\(\left(-1,0\right)\)

9.5.5.35.

Answer 1.
\(\left(0,2\right)\)
Answer 2.
\(\left(-0.298438,0\right), \left(-6.70156,0\right)\)

9.5.5.37.

Answer 1.
\(\left(0,-3\right)\)
Answer 2.
\(\left(-0.6,0\right), \left(-1,0\right)\)

9.5.5.49.

Answer 1.
\(10\ {\rm s}\)
Answer 2.
\(1600\ {\rm ft}\)
Answer 3.
\(20\ {\rm s}\)
Answer 4.
\(1200\ {\rm ft}\)
Answer 5.
\(1\ {\rm s}\)
Answer 6.
\(19\ {\rm s}\)

9.5.5.51.

Answer 1.
\(0.650954\)
Answer 2.
\(15.6756\)

9.5.5.53.

Answer.
\(\text{two times}\)

9.5.5.55.

Answer.
\(\text{zero times}\)

9.5.5.57.

Answer 1.
\(\left(-6,5\right), \left(2,5\right)\)
Answer 2.
\(\left\{-6,2\right\}\)
Answer 3.
\(\left(-\infty ,-6\right)\cup \left(2,\infty \right)\)

9.5.5.59.

Answer 1.
\(\left(-2,3\right), \left(2,-1\right)\)
Answer 2.
\(\left\{-2,2\right\}\)
Answer 3.
\(\left(-\infty ,-2\right)\cup \left(2,\infty \right)\)

9.5.5.61.

Answer 1.
\(\left(-3,1\right), \left(5,3\right)\)
Answer 2.
\(\left\{-3,5\right\}\)
Answer 3.
\(\left(-3,5\right)\)

III Preparation for College Algebra
10 Factoring
10.1 Factoring Out the Common Factor
10.1.7 Exercises

10.1.7.1.

Answer.
\(7x^{2}+56x\)

10.1.7.3.

Answer.
\(-12x^{2}-4x\)

10.1.7.5.

Answer.
\(-5x^{3}+20x^{2}\)

10.1.7.7.

Answer.
\(14y^{4}-35y^{3}\)

10.1.7.9.

Answer.
\(9\hbox{ or }-9\)

10.1.7.11.

Answer.
\(3t\hbox{ or }-\left(3t\right)\)

10.1.7.13.

Answer.
\(6x^{3}\hbox{ or }-6x^{3}\)

10.1.7.15.

Answer.
\(9y^{14}\hbox{ or }-9y^{14}\)

10.1.7.17.

Answer.
\(2r^{6}\hbox{ or }-2r^{6}\)

10.1.7.19.

Answer.
\(8x^{12}y^{4}\hbox{ or }-8x^{12}y^{4}\)

10.1.7.21.

Answer.
\(8\mathopen{}\left(x+1\right)\)

10.1.7.23.

Answer.
\(2\mathopen{}\left(x-1\right)\)

10.1.7.25.

Answer.
\(-4\mathopen{}\left(y+1\right)\)

10.1.7.27.

Answer.
\(7\mathopen{}\left(r-6\right)\)

10.1.7.29.

Answer.
\(10\mathopen{}\left(8t^{2}+5\right)\)

10.1.7.31.

Answer.
\(9\mathopen{}\left(6x^{2}+9x+7\right)\)

10.1.7.33.

Answer.
\(8y^{2}\mathopen{}\left(6y^{2}-10y+7\right)\)

10.1.7.35.

Answer.
\(10r^{3}\mathopen{}\left(6r^{2}+3r+7\right)\)

10.1.7.37.

Answer.
\(7t\mathopen{}\left(4+5t+3t^{2}\right)\)

10.1.7.39.

Answer.
\(\text{prime}\)

10.1.7.41.

Answer.
\(4y\mathopen{}\left(x+1\right)\)

10.1.7.43.

Answer.
\(6y^{7}\mathopen{}\left(x^{5}-2\right)\)

10.1.7.45.

Answer.
\(5x^{3}y^{4}\mathopen{}\left(10x^{2}+x+4\right)\)

10.1.7.47.

Answer.
\(5x^{3}y^{10}z^{2}\mathopen{}\left(6x^{2}z^{2}+5xz+3\right)\)

10.2 Factoring by Grouping
10.2.4 Exercises

10.2.4.1.

Answer.
\(-10\mathopen{}\left(y+1\right)\)

10.2.4.3.

Answer.
\(4\mathopen{}\left(r+9\right)\)

10.2.4.5.

Answer.
\(6\mathopen{}\left(5t^{2}-7\right)\)

10.2.4.7.

Answer.
\(\left(x-9\right)\mathopen{}\left(x-8\right)\)

10.2.4.9.

Answer.
\(\left(x-4\right)\mathopen{}\left(y-5\right)\)

10.2.4.11.

Answer.
\(\left(7x-6\right)\mathopen{}\left(x+y\right)\)

10.2.4.13.

Answer.
\(\left(8t^{8}+1\right)\mathopen{}\left(10t-3\right)\)

10.2.4.15.

Answer.
\(6x^{2}\mathopen{}\left(x-20\right)\mathopen{}\left(6x^{2}-7x+10\right)\)

10.2.4.17.

Answer.
\(\left(x-3\right)\mathopen{}\left(x+5\right)\)

10.2.4.19.

Answer.
\(\left(y-7\right)\mathopen{}\left(y-8\right)\)

10.2.4.21.

Answer.
\(\left(r^{2}-2\right)\mathopen{}\left(r-10\right)\)

10.2.4.23.

Answer.
\(\left(t^{2}-6\right)\mathopen{}\left(t-5\right)\)

10.2.4.25.

Answer.
\(\left(x+10\right)\mathopen{}\left(y+3\right)\)

10.2.4.27.

Answer.
\(\left(x-9\right)\mathopen{}\left(y+5\right)\)

10.2.4.29.

Answer.
\(\left(7x+9y\right)\mathopen{}\left(x-6y\right)\)

10.2.4.31.

Answer.
\(\left(9x+2y\right)\mathopen{}\left(x+y\right)\)

10.2.4.33.

Answer.
\(\left(x^{3}+2\right)\mathopen{}\left(1+4y\right)\)

10.2.4.35.

Answer.
\(\left(x^{3}-4\right)\mathopen{}\left(1-3y\right)\)

10.2.4.37.

Answer.
\(2y^{2}\mathopen{}\left(y+3\right)\mathopen{}\left(5y^{2}+2y+3\right)\)

10.3 Factoring Trinomials with Leading Coefficient One
10.3.7 Exercises

10.3.7.1.

Answer.
\(t^{2}+8t+7\)

10.3.7.3.

Answer.
\(x^{2}-2x-24\)

10.3.7.5.

Answer.
\(y^{2}-11y+28\)

10.3.7.7.

Answer.
\(3x^{2}+15x+18\)

10.3.7.9.

Answer.
\(-4y^{2}+40y-36\)

10.3.7.11.

Answer.
\(\left(t+6\right)\mathopen{}\left(t+9\right)\)

10.3.7.13.

Answer.
\(\left(x+9\right)\mathopen{}\left(x+7\right)\)

10.3.7.15.

Answer.
\(\left(y-2\right)\mathopen{}\left(y+6\right)\)

10.3.7.17.

Answer.
\(\left(r-5\right)\mathopen{}\left(r+1\right)\)

10.3.7.19.

Answer.
\(\left(t-8\right)\mathopen{}\left(t-2\right)\)

10.3.7.21.

Answer.
\(\left(x-1\right)\mathopen{}\left(x-10\right)\)

10.3.7.23.

Answer.
\(\left(y+4\right)\mathopen{}\left(y+9\right)\)

10.3.7.25.

Answer.
\(\left(r+7\right)\mathopen{}\left(r+9\right)\)

10.3.7.27.

Answer.
\(\left(t-10\right)\mathopen{}\left(t+3\right)\)

10.3.7.29.

Answer.
\(\left(t-3\right)\mathopen{}\left(t+8\right)\)

10.3.7.31.

Answer.
\(\left(x-6\right)\mathopen{}\left(x-2\right)\)

10.3.7.33.

Answer.
\(\left(y-10\right)\mathopen{}\left(y-6\right)\)

10.3.7.35.

Answer.
\(\text{prime}\)

10.3.7.37.

Answer.
\(\text{prime}\)

10.3.7.39.

Answer.
\(\left(x+10\right)\mathopen{}\left(x+10\right)\)

10.3.7.41.

Answer.
\(\left(y+2\right)\mathopen{}\left(y+2\right)\)

10.3.7.43.

Answer.
\(\left(r-6\right)\mathopen{}\left(r-6\right)\)

10.3.7.45.

Answer.
\(\left(t-9\right)\mathopen{}\left(t-9\right)\)

10.3.7.47.

Answer.
\(2\mathopen{}\left(t+6\right)\mathopen{}\left(t-1\right)\)

10.3.7.49.

Answer.
\(4\mathopen{}\left(x+4\right)\mathopen{}\left(x-2\right)\)

10.3.7.51.

Answer.
\(6\mathopen{}\left(y-3\right)\mathopen{}\left(y-1\right)\)

10.3.7.53.

Answer.
\(2\mathopen{}\left(r-1\right)\mathopen{}\left(r-7\right)\)

10.3.7.55.

Answer.
\(2t^{7}\mathopen{}\left(t+4\right)\mathopen{}\left(t+1\right)\)

10.3.7.57.

Answer.
\(2x^{4}\mathopen{}\left(x+3\right)\mathopen{}\left(x+5\right)\)

10.3.7.59.

Answer.
\(2y^{6}\mathopen{}\left(y-3\right)\mathopen{}\left(y+7\right)\)

10.3.7.61.

Answer.
\(3r^{7}\mathopen{}\left(r-5\right)\mathopen{}\left(r+1\right)\)

10.3.7.63.

Answer.
\(2t^{5}\mathopen{}\left(t-4\right)\mathopen{}\left(t-2\right)\)

10.3.7.65.

Answer.
\(2t^{5}\mathopen{}\left(t-1\right)\mathopen{}\left(t-2\right)\)

10.3.7.67.

Answer.
\(-\left(x-1\right)\mathopen{}\left(x+2\right)\)

10.3.7.69.

Answer.
\(-\left(y+4\right)\mathopen{}\left(y-7\right)\)

10.3.7.71.

Answer.
\(\left(r+t\right)\mathopen{}\left(r+5t\right)\)

10.3.7.73.

Answer.
\(\left(t+6r\right)\mathopen{}\left(t-5r\right)\)

10.3.7.75.

Answer.
\(\left(x-6y\right)\mathopen{}\left(x-y\right)\)

10.3.7.77.

Answer.
\(\left(y+4r\right)\mathopen{}\left(y+4r\right)\)

10.3.7.79.

Answer.
\(\left(r-2t\right)\mathopen{}\left(r-2t\right)\)

10.3.7.81.

Answer.
\(5\mathopen{}\left(r+2\right)\mathopen{}\left(r+1\right)\)

10.3.7.83.

Answer.
\(5y\mathopen{}\left(x+1\right)\mathopen{}\left(x+2\right)\)

10.3.7.85.

Answer.
\(2b\mathopen{}\left(a+3\right)\mathopen{}\left(a-6\right)\)

10.3.7.87.

Answer.
\(2y\mathopen{}\left(x-3\right)\mathopen{}\left(x-5\right)\)

10.3.7.89.

Answer.
\(6xy\mathopen{}\left(x+2\right)\mathopen{}\left(x+1\right)\)

10.3.7.91.

Answer.
\(x^{2}\mathopen{}\left(y+9z\right)\mathopen{}\left(y-2z\right)\)

10.3.7.93.

Answer.
\(\left(x+0.2\right)\mathopen{}\left(x+0.9\right)\)

10.3.7.95.

Answer.
\(\left(yt+4\right)\mathopen{}\left(yt+5\right)\)

10.3.7.97.

Answer.
\(\left(rt-7\right)\mathopen{}\left(rt+1\right)\)

10.3.7.99.

Answer.
\(\left(rt-4\right)\mathopen{}\left(rt-7\right)\)

10.3.7.101.

Answer.
\(4\mathopen{}\left(ty+4\right)\mathopen{}\left(ty+1\right)\)

10.3.7.103.

Answer.
\(2\mathopen{}\left(xr-1\right)\mathopen{}\left(xr+9\right)\)

10.3.7.105.

Answer.
\(2y\mathopen{}\left(xy-6\right)\mathopen{}\left(xy-2\right)\)

10.3.7.107.

Answer.
\(\left(a+b\right)\mathopen{}\left(r+2\right)\mathopen{}\left(r+9\right)\)

10.3.7.109.

Answer.
\(-17, 17, -7, 7, -3, 3\)

10.4 Factoring Trinomials with a Nontrivial Leading Coefficient
10.4.4 Exercises

10.4.4.1.

Answer.
\(8t^{2}+22t+9\)

10.4.4.3.

Answer.
\(20x^{2}-29x+6\)

10.4.4.5.

Answer.
\(8y^{2}+13y-6\)

10.4.4.7.

Answer.
\(2r^{5}+10r^{3}+6r^{2}+30\)

10.4.4.9.

Answer.
\(\left(3t+5\right)\mathopen{}\left(t+1\right)\)

10.4.4.11.

Answer.
\(\left(5x-3\right)\mathopen{}\left(x+4\right)\)

10.4.4.13.

Answer.
\(\left(5y-2\right)\mathopen{}\left(y-3\right)\)

10.4.4.15.

Answer.
\(\text{prime}\)

10.4.4.17.

Answer.
\(\left(4r+9\right)\mathopen{}\left(r+2\right)\)

10.4.4.19.

Answer.
\(\left(8t+3\right)\mathopen{}\left(t-3\right)\)

10.4.4.21.

Answer.
\(\left(6x-1\right)\mathopen{}\left(x-1\right)\)

10.4.4.23.

Answer.
\(\left(2y+1\right)\mathopen{}\left(3y+7\right)\)

10.4.4.25.

Answer.
\(\left(5r+1\right)\mathopen{}\left(4r-3\right)\)

10.4.4.27.

Answer.
\(\left(2t-1\right)\mathopen{}\left(2t-5\right)\)

10.4.4.29.

Answer.
\(6\mathopen{}\left(2x+1\right)\mathopen{}\left(x+1\right)\)

10.4.4.31.

Answer.
\(5\mathopen{}\left(2y-5\right)\mathopen{}\left(y+1\right)\)

10.4.4.33.

Answer.
\(6\mathopen{}\left(2r-1\right)\mathopen{}\left(r-2\right)\)

10.4.4.35.

Answer.
\(4r^{3}\mathopen{}\left(2r+3\right)\mathopen{}\left(r+1\right)\)

10.4.4.37.

Answer.
\(8t^{2}\mathopen{}\left(3t-1\right)\mathopen{}\left(t+1\right)\)

10.4.4.39.

Answer.
\(2x^{7}\mathopen{}\left(5x-1\right)\mathopen{}\left(x-3\right)\)

10.4.4.41.

Answer.
\(\left(5yx+4\right)\mathopen{}\left(yx+2\right)\)

10.4.4.43.

Answer.
\(\left(2rt+5\right)\mathopen{}\left(rt-5\right)\)

10.4.4.45.

Answer.
\(\left(2ty-1\right)\mathopen{}\left(ty-4\right)\)

10.4.4.47.

Answer.
\(\left(5x+7y\right)\mathopen{}\left(x+y\right)\)

10.4.4.49.

Answer.
\(\left(5y+9x\right)\mathopen{}\left(y-x\right)\)

10.4.4.51.

Answer.
\(\left(5y-6t\right)\mathopen{}\left(y-2t\right)\)

10.4.4.53.

Answer.
\(\left(8r+5x\right)\mathopen{}\left(r+x\right)\)

10.4.4.55.

Answer.
\(\left(8t+9y\right)\mathopen{}\left(t-y\right)\)

10.4.4.57.

Answer.
\(\left(6x-7r\right)\mathopen{}\left(x-r\right)\)

10.4.4.59.

Answer.
\(\left(4y+t\right)\mathopen{}\left(2y+3t\right)\)

10.4.4.61.

Answer.
\(\left(2r+3y\right)\mathopen{}\left(3r-5y\right)\)

10.4.4.63.

Answer.
\(\left(3t-2r\right)\mathopen{}\left(5t-2r\right)\)

10.4.4.65.

Answer.
\(3\mathopen{}\left(3xt+1\right)\mathopen{}\left(xt+3\right)\)

10.4.4.67.

Answer.
\(7\mathopen{}\left(2yx-1\right)\mathopen{}\left(yx+2\right)\)

10.4.4.69.

Answer.
\(2y^{2}\mathopen{}\left(5yr-8\right)\mathopen{}\left(yr-1\right)\)

10.4.4.71.

Answer.
\(3\mathopen{}\left(2x+y\right)\mathopen{}\left(x+4y\right)\)

10.4.4.73.

Answer.
\(2\mathopen{}\left(2a-b\right)\mathopen{}\left(a+6b\right)\)

10.4.4.75.

Answer.
\(5\mathopen{}\left(2x-3y\right)\mathopen{}\left(x-y\right)\)

10.4.4.77.

Answer.
\(3y\mathopen{}\left(2x+y\right)\mathopen{}\left(x+4y\right)\)

10.4.4.79.

Answer.
\(5\mathopen{}\left(y+7\right)\mathopen{}\left(5x+1\right)\mathopen{}\left(x+1\right)\)

10.4.4.81.

Answer.
\(3\mathopen{}\left(y+1\right)\mathopen{}\left(2x+1\right)\mathopen{}\left(x+4\right)\)

10.4.4.83.

Answer 1.
\(\left(2x+7\right)\mathopen{}\left(x+3\right)\)
Answer 2.
\(\left(2y+9\right)\mathopen{}\left(y+4\right)\)

10.4.4.85.

Answer.
\(13, -13, 8, -8, 7, -7\)

10.5 Factoring Special Polynomials
10.5.5 Exercises

10.5.5.1.

Answer.
\(36r^{2}+96r+64\)

10.5.5.3.

Answer.
\(t^{2}-4t+4\)

10.5.5.5.

Answer.
\(x^{12}-18x^{6}+81\)

10.5.5.7.

Answer.
\(y^{2}-1\)

10.5.5.9.

Answer.
\(25r^{2}-64\)

10.5.5.11.

Answer.
\(4t^{6}-144\)

10.5.5.13.

Answer.
\(\left(x+5\right)\mathopen{}\left(x-5\right)\)

10.5.5.15.

Answer.
\(\left(9y+8\right)\mathopen{}\left(9y-8\right)\)

10.5.5.17.

Answer.
\(\left(yt+6\right)\mathopen{}\left(yt-6\right)\)

10.5.5.19.

Answer.
\(\left(4ry+11\right)\mathopen{}\left(4ry-11\right)\)

10.5.5.21.

Answer.
\(\left(2+t\right)\mathopen{}\left(2-t\right)\)

10.5.5.23.

Answer.
\(\left(12+11x\right)\mathopen{}\left(12-11x\right)\)

10.5.5.25.

Answer.
\(\left(y^{2}+10\right)\mathopen{}\left(y^{2}-10\right)\)

10.5.5.27.

Answer.
\(\left(7r^{2}+8\right)\mathopen{}\left(7r^{2}-8\right)\)

10.5.5.29.

Answer.
\(\left(t^{5}+10\right)\mathopen{}\left(t^{5}-10\right)\)

10.5.5.31.

Answer.
\(\left(2x^{2}+7y^{2}\right)\mathopen{}\left(2x^{2}-7y^{2}\right)\)

10.5.5.33.

Answer.
\(\left(x^{3}+6y^{5}\right)\mathopen{}\left(x^{3}-6y^{5}\right)\)

10.5.5.35.

Answer.
\(\left(y+9\right)\mathopen{}\left(y+9\right)\)

10.5.5.37.

Answer.
\(\left(r-1\right)\mathopen{}\left(r-1\right)\)

10.5.5.39.

Answer.
\(\left(5t+1\right)\mathopen{}\left(5t+1\right)\)

10.5.5.41.

Answer.
\(\left(8x-1\right)\mathopen{}\left(8x-1\right)\)

10.5.5.43.

Answer.
\(\left(5yt-1\right)\mathopen{}\left(5yt-1\right)\)

10.5.5.45.

Answer.
\(\left(r+2x\right)\mathopen{}\left(r+2x\right)\)

10.5.5.47.

Answer.
\(\left(t-12r\right)\mathopen{}\left(t-12r\right)\)

10.5.5.49.

Answer.
\(\left(3x+5t\right)\mathopen{}\left(3x+5t\right)\)

10.5.5.51.

Answer.
\(\left(2x-9r\right)\mathopen{}\left(2x-9r\right)\)

10.5.5.53.

Answer.
\(\left(2y-3\right)\mathopen{}\left(2y+3\right)\mathopen{}\left(4y^{2}+9\right)\)

10.5.5.55.

Answer.
\(3\mathopen{}\left(r+5\right)\mathopen{}\left(r-5\right)\)

10.5.5.57.

Answer.
\(3t\mathopen{}\left(t+1\right)\mathopen{}\left(t-1\right)\)

10.5.5.59.

Answer.
\(5xy^{2}\mathopen{}\left(xy+3\right)\mathopen{}\left(xy-3\right)\)

10.5.5.61.

Answer.
\(8\mathopen{}\left(3+y\right)\mathopen{}\left(3-y\right)\)

10.5.5.63.

Answer.
\(2\mathopen{}\left(3r+1\right)\mathopen{}\left(3r+1\right)\)

10.5.5.65.

Answer.
\(3\mathopen{}\left(3ty+1\right)\mathopen{}\left(3ty+1\right)\)

10.5.5.67.

Answer.
\(9\mathopen{}\left(2x-1\right)\mathopen{}\left(2x-1\right)\)

10.5.5.69.

Answer.
\(x^{2}\mathopen{}\left(11x+1\right)\mathopen{}\left(11x+1\right)\)

10.5.5.71.

Answer.
\(y^{8}\mathopen{}\left(4y-1\right)\mathopen{}\left(4y-1\right)\)

10.5.5.73.

Answer.
\(2r^{8}\mathopen{}\left(6r+1\right)\mathopen{}\left(6r+1\right)\)

10.5.5.75.

Answer.
\(9t^{6}\mathopen{}\left(2t-1\right)\mathopen{}\left(2t-1\right)\)

10.5.5.77.

Answer.
\(12\mathopen{}\left(x-1\right)\mathopen{}\left(x+1\right)\mathopen{}\left(x^{2}+1\right)\)

10.5.5.79.

Answer.
\(\text{prime}\)

10.5.5.81.

Answer.
\(2r\mathopen{}\left(r^{2}+4\right)\)

10.5.5.83.

Answer.
\(t\mathopen{}\left(0.1+t\right)\mathopen{}\left(0.1-t\right)\)

10.5.5.85.

Answer.
\(\text{555(-333)}\)

10.6 Factoring Strategies
10.6.3 Exercises

10.6.3.15.

Answer.
\(3\mathopen{}\left(r+1\right)\)

10.6.3.17.

Answer.
\(8\mathopen{}\left(9t^{2}+5\right)\)

10.6.3.19.

Answer.
\(8x\mathopen{}\left(9+6x+2x^{2}\right)\)

10.6.3.21.

Answer.
\(10x^{3}y^{4}\mathopen{}\left(9x^{2}+10x+6\right)\)

10.6.3.23.

Answer.
\(\left(x-5\right)\mathopen{}\left(y-6\right)\)

10.6.3.25.

Answer.
\(\left(t-7\right)\mathopen{}\left(t+10\right)\)

10.6.3.27.

Answer.
\(\left(2tx-5\right)\mathopen{}\left(tx+1\right)\)

10.6.3.29.

Answer.
\(\left(4x+1\right)\mathopen{}\left(x-4\right)\)

10.6.3.31.

Answer.
\(\left(2y-9\right)\mathopen{}\left(3y-1\right)\)

10.6.3.33.

Answer.
\(\left(3r-2t\right)\mathopen{}\left(r-3t\right)\)

10.6.3.35.

Answer.
\(\left(3t+8x\right)\mathopen{}\left(2t+x\right)\)

10.6.3.37.

Answer.
\(2\mathopen{}\left(3x-5\right)\mathopen{}\left(x+2\right)\)

10.6.3.39.

Answer.
\(10y^{6}\mathopen{}\left(2y+1\right)\mathopen{}\left(y+1\right)\)

10.6.3.41.

Answer.
\(2\mathopen{}\left(2x+9y\right)\mathopen{}\left(x+y\right)\)

10.6.3.43.

Answer.
\(\left(t+4\right)\mathopen{}\left(t+8\right)\)

10.6.3.45.

Answer.
\(\left(t+6r\right)\mathopen{}\left(t+2r\right)\)

10.6.3.47.

Answer.
\(\left(x-4t\right)\mathopen{}\left(x-3t\right)\)

10.6.3.49.

Answer.
\(7\mathopen{}\left(y-4\right)\mathopen{}\left(y+1\right)\)

10.6.3.51.

Answer.
\(9r^{8}\mathopen{}\left(r-1\right)\mathopen{}\left(r-2\right)\)

10.6.3.53.

Answer.
\(9y\mathopen{}\left(x-2\right)\mathopen{}\left(x-1\right)\)

10.6.3.55.

Answer.
\(x^{2}\mathopen{}\left(y-z\right)\mathopen{}\left(y+8z\right)\)

10.6.3.57.

Answer.
\(\left(y+7\right)\mathopen{}\left(y-7\right)\)

10.6.3.59.

Answer.
\(\left(5+r\right)\mathopen{}\left(5-r\right)\)

10.6.3.61.

Answer.
\(\left(t^{3}+3\right)\mathopen{}\left(t^{3}-3\right)\)

10.6.3.63.

Answer.
\(\left(2t-1\right)\mathopen{}\left(2t+1\right)\mathopen{}\left(4t^{2}+1\right)\)

10.6.3.65.

Answer.
\(\text{prime}\)

10.6.3.67.

Answer.
\(\left(y+1\right)\mathopen{}\left(y+1\right)\)

10.6.3.69.

Answer.
\(\left(r-5\right)\mathopen{}\left(r-5\right)\)

10.6.3.71.

Answer.
\(\left(t+5r\right)\mathopen{}\left(t+5r\right)\)

10.6.3.73.

Answer.
\(5\mathopen{}\left(4xt+1\right)\mathopen{}\left(4xt+1\right)\)

10.6.3.75.

Answer.
\(2y^{7}\mathopen{}\left(4y+1\right)\mathopen{}\left(4y+1\right)\)

10.6.3.77.

Answer.
\(5\mathopen{}\left(r-2\right)\mathopen{}\left(r+2\right)\mathopen{}\left(r^{2}+4\right)\)

10.7 Solving Quadratic Equations by Factoring
10.7.5 Exercises

10.7.5.1.

Answer.
\(6\mathopen{}\left(t-3\right)\)

10.7.5.3.

Answer.
\(\left(x+9\right)\mathopen{}\left(x-3\right)\)

10.7.5.5.

Answer.
\(\left(2y-5\right)\mathopen{}\left(y-1\right)\)

10.7.5.7.

Answer.
\(3\mathopen{}\left(5r^{2}+3r+6\right)\)

10.7.5.9.

Answer.
\(\left(10r^{2}+3\right)\mathopen{}\left(10r^{2}-3\right)\)

10.7.5.11.

Answer.
\(\left\{-12,11\right\}\)

10.7.5.13.

Answer.
\(\left\{7,\frac{-1}{8}\right\}\)

10.7.5.15.

Answer.
\(\left\{-5,-7\right\}\)

10.7.5.17.

Answer.
\(\left\{-3,10\right\}\)

10.7.5.19.

Answer.
\(\left\{2,8\right\}\)

10.7.5.21.

Answer.
\(\left\{11,-2\right\}\)

10.7.5.23.

Answer.
\(\left\{5,-9\right\}\)

10.7.5.25.

Answer.
\(\left\{-6,-2\right\}\)

10.7.5.27.

Answer.
\(\left\{-5,10\right\}\)

10.7.5.29.

Answer.
\(\left\{1,3\right\}\)

10.7.5.31.

Answer.
\(\left\{0,7\right\}\)

10.7.5.33.

Answer.
\(\left\{0,2\right\}\)

10.7.5.35.

Answer.
\(\left\{0,\frac{-4}{7}\right\}\)

10.7.5.37.

Answer.
\(\left\{11\right\}\)

10.7.5.39.

Answer.
\(\left\{1\right\}\)

10.7.5.41.

Answer.
\(\left\{\frac{-5}{11}\right\}\)

10.7.5.43.

Answer.
\(\left\{\frac{-3}{5},-8\right\}\)

10.7.5.45.

Answer.
\(\left\{-5,5\right\}\)

10.7.5.47.

Answer.
\(\left\{\frac{-7}{10},\frac{7}{10}\right\}\)

10.7.5.49.

Answer.
\(\left\{\frac{-11}{3},\frac{11}{3}\right\}\)

10.7.5.51.

Answer.
\(\left\{3,-2\right\}\)

10.7.5.53.

Answer.
\(\left\{\frac{1}{4},-10\right\}\)

10.7.5.55.

Answer.
\(\left\{-3,-5\right\}\)

10.7.5.57.

Answer.
\(\left\{1,2\right\}\)

10.7.5.59.

Answer.
\(\left\{5\right\}\)

10.7.5.61.

Answer.
\(\left\{\frac{-10}{3}\right\}\)

10.7.5.63.

Answer.
\(\left\{-8,-10,5\right\}\)

10.7.5.65.

Answer.
\(\left\{-10,10,0\right\}\)

10.7.5.67.

Answer.
\(\left\{0,7,-2\right\}\)

10.7.5.69.

Answer.
\(-6, 9\)

10.7.5.71.

Answer 1.
\(8\ {\rm cm}\)
Answer 2.
\(13\ {\rm cm}\)

10.7.5.73.

Answer 1.
\(5\ {\rm in}\)
Answer 2.
\(13\ {\rm in}\)

10.7.5.75.

Answer.
\(3\ {\rm ft}\)

10.7.5.77.

Answer.
\((x-3)*(x--9)*(x-2/3)=0\)

10.8 Factoring Chapter Review
10.8.8 Exercises

10.8.8.1.

Answer.
\(5y\hbox{ or }-\left(5y\right)\)

10.8.8.3.

Answer.
\(8r^{10}\hbox{ or }-8r^{10}\)

10.8.8.5.

Answer.
\(8x^{5}y^{4}\hbox{ or }-8x^{5}y^{4}\)

10.8.8.7.

Answer.
\(6\mathopen{}\left(6x^{2}+x+9\right)\)

10.8.8.9.

Answer.
\(\text{prime}\)

10.8.8.11.

Answer.
\(\left(r+10\right)\mathopen{}\left(r-2\right)\)

10.8.8.13.

Answer.
\(\left(t-6\right)\mathopen{}\left(t+4\right)\)

10.8.8.15.

Answer.
\(\left(x^{2}-10\right)\mathopen{}\left(x-6\right)\)

10.8.8.17.

Answer.
\(\left(x+2\right)\mathopen{}\left(y+4\right)\)

10.8.8.19.

Answer.
\(\left(6x+7y\right)\mathopen{}\left(x+7y\right)\)

10.8.8.21.

Answer.
\(\left(r+5\right)\mathopen{}\left(r+1\right)\)

10.8.8.23.

Answer.
\(\left(t+8\right)\mathopen{}\left(t-10\right)\)

10.8.8.25.

Answer.
\(\text{prime}\)

10.8.8.27.

Answer.
\(\left(y-5\right)\mathopen{}\left(y-5\right)\)

10.8.8.29.

Answer.
\(3\mathopen{}\left(r-4\right)\mathopen{}\left(r-2\right)\)

10.8.8.31.

Answer.
\(-\left(t-2\right)\mathopen{}\left(t+2\right)\)

10.8.8.33.

Answer.
\(\left(x+y\right)\mathopen{}\left(x-8y\right)\)

10.8.8.35.

Answer.
\(\left(y-2r\right)\mathopen{}\left(y-7r\right)\)

10.8.8.37.

Answer.
\(\left(5y+4\right)\mathopen{}\left(y-2\right)\)

10.8.8.39.

Answer.
\(\text{prime}\)

10.8.8.41.

Answer.
\(\left(5t-1\right)\mathopen{}\left(2t-5\right)\)

10.8.8.43.

Answer.
\(3\mathopen{}\left(2x-1\right)\mathopen{}\left(x-4\right)\)

10.8.8.45.

Answer.
\(9y^{5}\mathopen{}\left(2y-1\right)\mathopen{}\left(y-1\right)\)

10.8.8.47.

Answer.
\(5\mathopen{}\left(3ry-4\right)\mathopen{}\left(ry+2\right)\)

10.8.8.49.

Answer.
\(2\mathopen{}\left(5x+7y\right)\mathopen{}\left(x+y\right)\)

10.8.8.51.

Answer.
\(\left(x+1\right)\mathopen{}\left(x-1\right)\)

10.8.8.53.

Answer.
\(\left(4y+5\right)\mathopen{}\left(4y-5\right)\)

10.8.8.55.

Answer.
\(\left(y^{5}+8\right)\mathopen{}\left(y^{5}-8\right)\)

10.8.8.57.

Answer.
\(\left(12r-1\right)\mathopen{}\left(12r-1\right)\)

10.8.8.59.

Answer.
\(\left(5t-7x\right)\mathopen{}\left(5t-7x\right)\)

10.8.8.61.

Answer.
\(\left(2x-3\right)\mathopen{}\left(2x+3\right)\mathopen{}\left(4x^{2}+9\right)\)

10.8.8.63.

Answer.
\(2y\mathopen{}\left(y+2\right)\mathopen{}\left(y-2\right)\)

10.8.8.65.

Answer.
\(5r^{2}x^{2}\mathopen{}\left(rx+1\right)\mathopen{}\left(rx-1\right)\)

10.8.8.67.

Answer.
\(3\mathopen{}\left(6+t\right)\mathopen{}\left(6-t\right)\)

10.8.8.69.

Answer.
\(\text{prime}\)

10.8.8.73.

Answer.
\(4y\mathopen{}\left(8+4y+5y^{2}\right)\)

10.8.8.75.

Answer.
\(\left(2r-7y\right)\mathopen{}\left(4r-y\right)\)

10.8.8.77.

Answer.
\(\left(8t+3y\right)\mathopen{}\left(8t+3y\right)\)

10.8.8.79.

Answer.
\(\left(5x+3y\right)\mathopen{}\left(3x+2y\right)\)

10.8.8.81.

Answer.
\(\left(2y-1\right)\mathopen{}\left(2y+1\right)\mathopen{}\left(4y^{2}+1\right)\)

10.8.8.83.

Answer.
\(\left\{-2,9\right\}\)

10.8.8.85.

Answer.
\(\left\{-8,-3\right\}\)

10.8.8.87.

Answer.
\(\left\{0,10\right\}\)

10.8.8.89.

Answer.
\(\left\{3\right\}\)

10.8.8.91.

Answer.
\(\left\{\frac{-2}{3},-3\right\}\)

10.8.8.93.

Answer 1.
\(4\ {\rm in}\)
Answer 2.
\(11\ {\rm in}\)

11 Functions
11.1 Function Basics
11.1.5 Exercises

11.1.5.1.

Answer 1.
\(\left(0,4\right)\)
Answer 2.
\(\left(3,2\right)\)
Answer 3.
\(\left(-2,1\right)\)
Answer 4.
\(\left(-4,0\right)\)

11.1.5.3.

Answer.
\({\frac{1}{3}}\)

11.1.5.5.

Answer 1.
\(18\)
Answer 2.
\(36\)

11.1.5.7.

Answer 1.
\(-1\)
Answer 2.
\(-7\)
Answer 3.
\(-3\)

11.1.5.9.

Answer 1.
\(6\)
Answer 2.
\(-12\)
Answer 3.
\(0\)

11.1.5.11.

Answer 1.
\(8\)
Answer 2.
\(14\)
Answer 3.
\(10\)

11.1.5.13.

Answer 1.
\(-2\)
Answer 2.
\(5\)
Answer 3.
\(2\)

11.1.5.15.

Answer 1.
\(27\)
Answer 2.
\(6\)
Answer 3.
\(2\)

11.1.5.17.

Answer 1.
\(-5\)
Answer 2.
\(-5\)
Answer 3.
\(-1\)

11.1.5.19.

Answer 1.
\(-5\)
Answer 2.
\(-5\)
Answer 3.
\(-5\)

11.1.5.21.

Answer 1.
\(-{\frac{9}{26}}\)
Answer 2.
\(-{\frac{2}{5}}\)

11.1.5.23.

Answer 1.
\(3\)
Answer 2.
\(\text{undefined}\)

11.1.5.25.

Answer 1.
\(3\)
Answer 2.
\(9\)

11.1.5.27.

Answer 1.
\(1\)
Answer 2.
\(19\)

11.1.5.29.

Answer 1.
\(-27\)
Answer 2.
\(-51\)

11.1.5.31.

Answer 1.
\(9\)
Answer 2.
\({\frac{3}{2}}\)
Answer 3.
\(\text{not a real number}\)

11.1.5.33.

Answer 1.
\(-5\)
Answer 2.
\({\frac{1}{5}}\)

11.1.5.35.

Answer 1.
\(-1\)
Answer 2.
\(-1\)

11.1.5.37.

Answer 1.
\(\left\{-2\right\}\)
Answer 2.
\(\left\{\frac{-2}{5}\right\}\)

11.1.5.39.

Answer 1.
\(\left\{4,-4\right\}\)
Answer 2.
\(\text{no real solutions}\)

11.1.5.41.

Answer.
\(\left\{2,1\right\}\)

11.1.5.43.

Answer 1.
\(-7\)
Answer 2.
\(\left\{\frac{-7}{3}\right\}\)

11.1.5.45.

Answer 1.
\(-7\)
Answer 2.
\(\left\{\sqrt{7},-\sqrt{7}\right\}\)

11.1.5.47.

Answer 1.
\(-50\)
Answer 2.
\(\left\{5,-10\right\}\)

11.1.5.49.

Answer 1.
\(\left(7,10\right)\)
Answer 2.
\(3\)

11.1.5.51.

Answer.
\(\left(t,r\right)\)

11.1.5.53.

Answer.
\(y\)

11.1.5.57.

Answer 1.
\(3.5\)
Answer 2.
\(0.5\)

11.1.5.59.

Answer 1.
\(-1\)
Answer 2.
\(0\)

11.1.5.61.

Answer 1.
\(0\)
Answer 2.
\(-9\)

11.1.5.63.

Answer 1.
\(5\)
Answer 2.
\(\left\{2,-3\right\}\)

11.1.5.65.

Answer 1.
\(-3\)
Answer 2.
\(\left\{0\right\}\)

11.1.5.67.

Answer 1.
\(1\)
Answer 2.
\(\left\{-2,0\right\}\)

11.1.5.69.

Answer 1.
\(-1.9\)
Answer 2.
\(0.2\)

11.1.5.71.

Answer.
\(-2;\,-8;\,-1;\,-2;\,0;\,0;\,1;\,-2;\,2;\,-8\)

11.1.5.73.

Answer 1.
\(0\)
Answer 2.
\(1\)
Answer 3.
\(4\)
Answer 4.
\(9\)
Answer 5.
\(16\)
Answer 6.
\(G\mathopen{}\left(x\right) = x^{2}\)

11.1.5.75.

Answer 1.
\(-8\)
Answer 2.
\(-5\)
Answer 3.
\(-2\)
Answer 4.
\(1\)
Answer 5.
\(4\)
Answer 6.
\(K\mathopen{}\left(x\right) = 3x-8\)

11.1.5.77.

Answer 1.
\(19\)
Answer 2.
\({\frac{26}{3}}\)
Answer 3.
\({\frac{7}{3}}\)
Answer 4.
\(0\)
Answer 5.
\({\frac{5}{3}}\)
Answer 6.
\({\frac{22}{3}}\)
Answer 7.
\(17\)

11.1.5.79.

Answer 1.
\({\frac{5}{2}}\)
Answer 2.
\({\frac{4}{3}}\)
Answer 3.
\({\frac{3}{4}}\)
Answer 4.
\({\frac{2}{5}}\)
Answer 5.
\({\frac{1}{6}}\)
Answer 6.
\(0\)
Answer 7.
\(-{\frac{1}{8}}\)

11.1.5.81.

Answer.
Note that \(M(t)\) tells us the amount of money, in dollars, in the account \(t\) months after the account was initially setup. Thus \(M(20)=115\) must tell us that after \(20\) months, the account will have \(115\) dollars.

11.1.5.83.

Answer.
Note that \(G(x)\) tells us the oxygen concentration, as a percentage, when the salinity is at \(x\) percent. Thus \(G(35)=87.75\) must tell us that the oxygen concentration is \(87.75\%\) when the salinity is \(35\%\text{.}\)

11.1.5.85.

Answer.
\(\text{D}\)

11.1.5.87.

Answer.
\(\text{D}\)

11.1.5.89.

Answer.
\(f\mathopen{}\left(x\right) = 3.1536\times 10^{7}x\)

11.1.5.91.

Answer 1.
\(M\mathopen{}\left(x\right) = \frac{x}{5280}\)
Answer 2.
\(2.65152\)
Answer 3.
\(14000\)

11.1.5.93.

Answer.
\(f\mathopen{}\left(t\right) = 0.16t+2.7\)

11.1.5.95.

Answer.
\(f\mathopen{}\left(x\right) = 10x\)

11.1.5.97.

Answer 1.
\(\text{s(2.3)}\)
Answer 2.
\(166.47\ {\rm mi}\)
Answer 3.
\(v\mathopen{}\left(t\right) = 61\)
Answer 4.
\(214\ {\rm mi}\)

11.1.5.101.

Answer 1.
\(8\)
Answer 2.
\(\text{D}\)
Answer 3.
\(3, 7\)
Answer 4.
\(\text{C}\)

11.1.5.103.

Answer 1.
\(\left(b,a\right)\)
Answer 2.
\(\left(d,e\right)\)
Answer 3.
\(a\)
Answer 4.
\(x = d\)
Answer 5.
\(x = h\)

11.2 Domain and Range
11.2.5 Exercises

11.2.5.1.

Answer 1.
\(\left\{c \mid c > -2.5\right\}\)
Answer 2.
\(\left(-2.5,\infty \right)\)

11.2.5.3.

Answer 1.
\(\left\{k \mid k\ge -0.5\right\}\)
Answer 2.
\(\left[-0.5,\infty \right)\)

11.2.5.5.

Answer.
\(\left(1,4\right)\)

11.2.5.7.

Answer.
\(\left(-\infty ,-5\right)\cup \left(-3,\infty \right)\)

11.2.5.9.

Answer 1.
\(\left\{-7,-1,0\right\}\)
Answer 2.
\(\left\{4,5\right\}\)

11.2.5.11.

Answer 1.
\(\left[-3,1\right)\)
Answer 2.
\(\left(0,4\right]\)

11.2.5.13.

Answer 1.
\(\left[-4,3\right)\)
Answer 2.
\(\left\{4\right\}\)

11.2.5.15.

Answer 1.
\(\left(-5,2\right)\)
Answer 2.
\(\left[3,19\right)\)

11.2.5.17.

Answer 1.
\(\left(-\infty ,3\right)\cup \left(3,\infty \right)\)
Answer 2.
\(\left(-\infty ,1\right)\cup \left(1,\infty \right)\)

11.2.5.19.

Answer 1.
\(\left(-\infty ,-2\right)\cup \left(-2,\infty \right)\)
Answer 2.
\(\left(-\infty ,3\right)\)

11.2.5.21.

Answer 1.
\(\left(-\infty ,\infty \right)\)
Answer 2.
\(\left[-2,\infty \right)\)

11.2.5.23.

Answer 1.
\(\left[-2,2\right)\)
Answer 2.
\(\left[-5,5\right]\)

11.2.5.25.

Answer 1.
\(\left[1,7\right]\)
Answer 2.
\(\left[-4,0\right]\)

11.2.5.27.

Answer 1.
\(\left(-\infty ,\infty \right)\)
Answer 2.
\(\left[-3,\infty \right)\)

11.2.5.29.

Answer 1.
\(\left[0,\infty \right)\)
Answer 2.
\(\left[0,\infty \right)\)

11.2.5.31.

Answer 1.
\(\left(-\infty ,2\right]\)
Answer 2.
\(\left[1,\infty \right)\)

11.2.5.33.

Answer 1.
\(\left[-2,7\right]\)
Answer 2.
\(\left[-1,2\right]\)

11.2.5.35.

Answer 1.
\(\left(0,5\right]\)
Answer 2.
\(\left(-4,-1\right]\cup \left(1,3\right]\)

11.2.5.37.

Answer.
\(\left(-\infty ,\infty \right)\)

11.2.5.39.

Answer.
\(\left(-\infty ,\infty \right)\)

11.2.5.41.

Answer.
\(\left(-\infty ,\infty \right)\)

11.2.5.43.

Answer.
\(\left(-\infty ,1\right)\cup \left(1,\infty \right)\)

11.2.5.45.

Answer.
\(\left(-\infty,\frac{7}{9}\right)\cup\left(\frac{7}{9},\infty\right)\)

11.2.5.47.

Answer.
\(\left(-\infty ,-9\right)\cup \left(-9,5\right)\cup \left(5,\infty \right)\)

11.2.5.49.

Answer.
\(\left(-\infty ,-4\right)\cup \left(-4,0\right)\cup \left(0,\infty \right)\)

11.2.5.51.

Answer.
\(\left(-\infty ,-9\right)\cup \left(-9,9\right)\cup \left(9,\infty \right)\)

11.2.5.53.

Answer.
\(\left(-\infty,-\frac{9}{7}\right)\left(-\frac{9}{7},\frac{9}{7}\right)\cup\left(\frac{9}{7},\infty\right)\)

11.2.5.55.

Answer.
\(\left(-\infty ,\infty \right)\)

11.2.5.57.

Answer.
\(\left(1,\infty \right)\)

11.2.5.59.

Answer.
\(\left(-\infty ,10\right]\)

11.2.5.61.

Answer.
\(\left[\frac{-4}{9},\infty \right)\)

11.2.5.63.

Answer.
\(\left(-\infty ,-12\right)\cup \left(-12,12\right)\cup \left(12,\infty \right)\)

11.2.5.65.

Answer.
\(\left(-\infty ,-6\right)\cup \left(-6,3\right)\cup \left(3,\infty \right)\)

11.2.5.67.

Answer.
\(\left[-11,2\right)\cup \left(2,\infty \right)\)

11.2.5.69.

Answer 1.
\(\left[0,28\right]\hbox{ or }\left[0,\infty \right)\)
Answer 2.
\(\left[0,8400\right]\)

11.2.5.71.

Answer 1.
\(\left[0,250\right]\)
Answer 2.
\(\left[0,10\right]\)

11.2.5.73.

Answer 1.
\(\left[11,56\right]\)
Answer 2.
\(\left[210,1335\right]\)

11.2.5.75.

Answer 1.
\(\left[0,180\right]\)
Answer 2.
\(\left[2.8,74.8\right]\)

11.2.5.77.

Answer 1.
\(\left[0,32\right]\)
Answer 2.
\(\left[0,4096\right]\)

11.2.5.79.

Answer 1.
\(\left[0,20.1\right]\hbox{ or }\left[0,\infty \right)\)
Answer 2.
\(\left[0,545.382\right]\)

11.2.5.81.

Answer 1.
\(\left[0,200\right]\)
Answer 2.
\(\left[0,20000\right]\)

11.2.5.83.

Answer.
  1. the set of all possible student identification numbers at that particular school
  2. the set of all first names of students who attend that school

11.3 Using Technology to Explore Functions
11.3.5 Exercises

11.3.5.1.

Answer.
\(-2;\,16;\,-1;\,6;\,0;\,-2;\,1;\,-8;\,2;\,-12;\,3;\,-14;\,4;\,-14\)

11.3.5.3.

Answer.
\(-2;\,360.8;\,-1;\,200.45;\,0;\,47;\,1;\,-99.55;\,2;\,-239.2;\,3;\,-371.95;\,4;\,-497.8\)

11.3.5.5.

Answer.
\(-2;\,-408;\,-1;\,-257;\,0;\,-64;\,1;\,129;\,2;\,280;\,3;\,347;\,4;\,288\)

11.3.5.7.

Answer.
\(\left[-0.93,0.05\right];\,\left[-500,8800\right]\)

11.3.5.9.

Answer.
\(\left[-0.3,4.1\right];\,\left[-690,40\right]\)

11.3.5.11.

Answer.
\(\left[-2.8,4.1\right];\,\left[-300,3900\right]\)

11.3.5.13.

Answer.
\(\left[-33,40\right];\,\left[-0.02,0.38\right]\)

11.3.5.15.

Answer.
\(\text{two times}\)

11.3.5.17.

Answer.
\(\text{one time}\)

11.3.5.19.

Answer.
\(\text{zero times}\)

11.3.5.21.

Answer.
\(\text{two times}\)

11.3.5.23.

Answer 1.
\(\left(-0.873,0\right), \left(6.873,0\right), \left(0,2.4\right)\)
Answer 2.
\(\left(3,6\right)\)
Answer 3.
\(\left(-\infty ,\infty \right)\)
Answer 4.
\(\left(-\infty ,6\right]\)

11.3.5.25.

Answer 1.
\(\left(0,4\right)\)
Answer 2.
\(\left(-0.00166667,3.99167\right)\)
Answer 3.
\(\left(-\infty ,\infty \right)\)
Answer 4.
\(\left[3.99167,\infty \right)\)

11.3.5.27.

Answer 1.
\(\left(0.0035,0\right), \left(0,1.1025\right)\)
Answer 2.
\(\left(0.0035,0\right)\)
Answer 3.
\(\left(-\infty ,\infty \right)\)
Answer 4.
\(\left[0,\infty \right)\)

11.3.5.29.

Answer 1.
\(\left(-10,50\right), \left(15,25\right)\)
Answer 2.
\(\left\{-10,15\right\}\)
Answer 3.
\(\left(-\infty ,-10\right)\cup \left(15,\infty \right)\)
Answer 4.
\(\left[-10,15\right]\)

11.3.5.31.

Answer 1.
\(\left(-2,5\right), \left(0.75,5\right)\)
Answer 2.
\(\left\{-2,0.75\right\}\)
Answer 3.
\(\left(-2,0.75\right)\)
Answer 4.
\(\left(-\infty ,-2\right]\cup \left[0.75,\infty \right)\)

11.3.5.33.

Answer 1.
\(\left(-6,10\right), \left(-0.5,21\right)\)
Answer 2.
\(\left\{-6,-0.5\right\}\)
Answer 3.
\(\left(-6,-0.5\right)\)
Answer 4.
\(\left(-\infty ,-6\right]\cup \left[-0.5,\infty \right)\)

11.3.5.35.

Answer.
\(\left\{-3.25,2\right\}\)

11.3.5.37.

Answer.
\(\left\{-10,20\right\}\)

11.3.5.39.

Answer.
\(\left\{-1.5,0,1.5\right\}\)

11.3.5.41.

Answer.
\(\left\{-23.162,-16.838\right\}\)

11.3.5.43.

Answer.
\(\text{no real solutions}\)

11.3.5.45.

Answer.
\(\left(-\infty ,-2\right)\cup \left(-0.5,\infty \right)\)

11.3.5.47.

Answer.
\(\left[0,1.1\right]\)

11.3.5.49.

Answer.
\(\left(-6.37228,-0.627719\right)\)

11.3.5.51.

Answer.
\(\left(-\infty ,0.090098\right]\cup \left[1.1099,\infty \right)\hbox{ or }\left(-\infty ,0.09\right]\cup \left[1.1099,\infty \right)\)

11.3.5.53.

Answer.
\(\left(-\infty ,\infty \right)\)

11.4 Simplifying Expressions with Function Notation
11.4.4 Exercises

11.4.4.1.

Answer.
\(3c+21\)

11.4.4.3.

Answer.
\(-6c+36\)

11.4.4.5.

Answer.
\(3t^{2}+48t+192\)

11.4.4.7.

Answer.
\(4x^{2}+28x+49\)

11.4.4.9.

Answer.
\(y+11\)

11.4.4.11.

Answer.
\(8-6r\)

11.4.4.13.

Answer.
\(-0.9t-4.4\)

11.4.4.15.

Answer.
\(\frac{-2}{9}x+\frac{-95}{54}\)

11.4.4.17.

Answer.
\(-3x+4\)

11.4.4.19.

Answer.
\(4.5y\)

11.4.4.21.

Answer.
\(-405r^{2}-18r-1\)

11.4.4.23.

Answer.
\(6t^{2}-3t-1\)

11.4.4.25.

Answer.
\(-42x^{2}-7x-21\)

11.4.4.27.

Answer.
\(-1.6y^{2}-6.2y+3.4\)

11.4.4.29.

Answer.
\(-8r^{2}-2r+1\)

11.4.4.31.

Answer.
\(\sqrt{-x-10}\)

11.4.4.33.

Answer.
\(\sqrt{-3+7x}+1\)

11.4.4.35.

Answer.
\(-3x-12+\sqrt{-6x-27}\)

11.4.4.37.

Answer.
\(-\frac{3}{5z+26}\)

11.4.4.39.

Answer.
\(-\frac{2s}{-48s^{2}-1}\)

11.4.4.41.

Answer 1.
\(-9x+4\)
Answer 2.
\(-9x-66\)
Answer 3.
\(-63x-21\)
Answer 4.
\(-63x-3\)

11.4.4.43.

Answer 1.
\(2x^{2}-4x-5\)
Answer 2.
\(2x^{2}-24x+70\)
Answer 3.
\(-10x^{2}+20x\)
Answer 4.
\(50x^{2}+20x\)

11.4.4.45.

Answer.
\(\pi \mathopen{}\left(12t-0.3t^{2}\right)^{2}\ {\rm ft^{2}}\)

11.4.4.47.

Answer.
\(25600-\frac{51200}{t+2}\)

11.5 Technical Definition of a Function
11.5.4 Exercises

11.5.4.1.

Answer 1.
\(\text{describes}\)
Answer 2.
\(\left\{-10,0\right\}\)
Answer 3.
\(\left\{8,10\right\}\)
Answer 4.
\(\text{describes}\)
Answer 5.
\(\left\{-9,-8,1\right\}\)
Answer 6.
\(\left\{3,6\right\}\)
Answer 7.
\(\text{describes}\)
Answer 8.
\(\left\{-9,-7,-1,4\right\}\)
Answer 9.
\(\left\{0,7,8,9\right\}\)
Answer 10.
\(\text{does not describe}\)
Answer 11.
\(\left\{-8,-7,-6,-3\right\}\)
Answer 12.
\(\left\{2,5,9,10\right\}\)

11.5.4.3.

Answer 1.
\(\text{does not describe}\)
Answer 2.
\(\left\{-7,-5,6,8\right\}\)
Answer 3.
\(\left\{0,5,6,10\right\}\)

11.5.4.5.

Answer 1.
\(\left\{\left(0,5\right), \left(2,-3\right), \left(3,-3\right)\right\}\)
Answer 2.
\(\left\{0,2,3\right\}\)
Answer 3.
\(\left\{-3,5\right\}\)

11.5.4.7.

Answer 1.
\(\text{does not}\)
Answer 2.
\(\text{does not}\)

11.5.4.9.

Answer 1.
\(\text{does}\)
Answer 2.
\(\text{does not}\)

11.5.4.11.

Answer 1.
\(\text{yes}\)
Answer 2.
\(\text{None, the table represents a function.}\)

11.5.4.13.

Answer 1.
\(\text{no}\)
Answer 2.
\(\text{-3}\)

11.5.4.15.

Answer.
Yes, this table does make the outputs a function of the inputs because there are no repeated inputs.

11.5.4.17.

Answer.
No, this table does not make the outputs a function of the inputs because the input \(-2\) is repeated and it corresponds to two different outputs, \(7\) and \(6\text{.}\)
To fix this, you need to either change one of the \(-2\)’s into a different number from all the other inputs, or change both \(7\) and \(6\) into the same number so that \(-2\) only corresponds to one value.

11.6 Functions Chapter Review
11.6.6 Exercises

11.6.6.1.

Answer.
\(\text{A}\)

11.6.6.3.

Answer 1.
\(7\)
Answer 2.
\(\text{undefined}\)

11.6.6.5.

Answer 1.
\(1\)
Answer 2.
\(0\)

11.6.6.7.

Answer 1.
\(0.5\)
Answer 2.
\(0.8\)

11.6.6.9.

Answer.
\(-2;\,20;\,-1;\,5;\,0;\,0;\,1;\,5;\,2;\,20\)

11.6.6.11.

Answer 1.
\(3\)
Answer 2.
\(\text{A}\)
Answer 3.
\(2, 8\)
Answer 4.
\(\text{B}\)

11.6.6.13.

Answer 1.
\(\left(-\infty ,-1\right)\cup \left(-1,\infty \right)\)
Answer 2.
\(\left(-\infty ,-1\right)\cup \left(-1,\infty \right)\)

11.6.6.15.

Answer 1.
\(\left[-3,6\right]\)
Answer 2.
\(\left[-2,2\right]\)

11.6.6.17.

Answer 1.
\(\left(-\infty ,\infty \right)\)
Answer 2.
\(\left[0,\infty \right)\)

11.6.6.19.

Answer.
\(\left[-20,3\right)\cup \left(3,\infty \right)\)

11.6.6.21.

Answer 1.
\(\left[0,24\right]\)
Answer 2.
\(\left[0,2304\right]\)

11.6.6.23.

Answer.
\(-2;\,42;\,-1;\,20;\,0;\,4;\,1;\,-6;\,2;\,-10;\,3;\,-8;\,4;\,0\)

11.6.6.25.

Answer.
\(\left[-0.17,0.01\right];\,\left[-1200,100\right]\)

11.6.6.27.

Answer.
\(\text{two times}\)

11.6.6.29.

Answer 1.
\(\left(0,4\right)\)
Answer 2.
\(\left(-0.00166667,3.99167\right)\)
Answer 3.
\(\left(-\infty ,\infty \right)\)
Answer 4.
\(\left[3.99167,\infty \right)\)

11.6.6.31.

Answer 1.
\(\left(-2,5\right), \left(0.75,5\right)\)
Answer 2.
\(\left\{-2,0.75\right\}\)
Answer 3.
\(\left(-2,0.75\right)\)
Answer 4.
\(\left(-\infty ,-2\right]\cup \left[0.75,\infty \right)\)

11.6.6.33.

Answer.
\(\text{no real solutions}\)

11.6.6.35.

Answer.
\(\left(-\infty ,\infty \right)\)

11.6.6.37.

Answer 1.
\(-5x^{2}-5x-2\)
Answer 2.
\(-5x^{2}+15x-10\)
Answer 3.
\(10x^{2}+10x\)
Answer 4.
\(-20x^{2}+10x\)

11.6.6.39.

Answer.
\(-2-6x\)

11.6.6.41.

Answer.
\(42y^{2}-21y-49\)

11.6.6.43.

Answer 1.
\(\text{describes}\)
Answer 2.
\(\left\{-5,2,3,4,6\right\}\)
Answer 3.
\(\left\{1,8,9,10\right\}\)

11.6.6.45.

Answer 1.
\(\left\{\left(-1,4\right), \left(1,0\right), \left(3,-4\right)\right\}\)
Answer 2.
\(\left\{-1,1,3\right\}\)
Answer 3.
\(\left\{-4,0,4\right\}\)

11.6.6.47.

Answer 1.
\(\text{does not}\)
Answer 2.
\(\text{does}\)

11.6.6.51.

Answer 1.
\(\text{yes}\)
Answer 2.
\(\text{None, the table represents a function.}\)

11.6.6.53.

Answer 1.
\(\text{no}\)
Answer 2.
\(\text{-3}\)

12 Rational Functions and Equations
12.1 Introduction to Rational Functions
12.1.3 Exercises

12.1.3.1.

Answer 1.
\(310\)
Answer 2.
\(236\)
Answer 3.
\(14\)
Answer 4.
\(230\)

12.1.3.3.

Answer 1.
\(3\)
Answer 2.
\(54\)

12.1.3.7.

Answer.
\(\left(-\infty ,-4\right)\cup \left(-4,\infty \right)\)

12.1.3.9.

Answer.
\(\left(-\infty ,1\right)\cup \left(1,10\right)\cup \left(10,\infty \right)\)

12.1.3.11.

Answer.
\(\left(-\infty ,-9\right)\cup \left(-9,0\right)\cup \left(0,\infty \right)\)

12.1.3.13.

Answer.
\(\left(-\infty ,-7\right)\cup \left(-7,7\right)\cup \left(7,\infty \right)\)

12.1.3.15.

Answer.
\(\left(-\infty ,0\right)\cup \left(0,\infty \right)\)

12.1.3.17.

Answer.
\(\left(-\infty ,\infty \right)\)

12.1.3.19.

Answer.
\(\left(-\infty ,9\right)\cup \left(9,\infty \right)\)

12.1.3.21.

Answer.
\(\left(-\infty ,-1\right)\cup \left(-1,\infty \right)\)

12.1.3.23.

Answer.
\(\left(-\infty ,-3\right)\cup \left(-3,5\right)\cup \left(5,\infty \right)\)

12.1.3.25.

Answer 1.
\(\left(-\infty ,2\right)\cup \left(2,\infty \right)\)
Answer 2.
\(\left(-\infty ,-3\right)\cup \left(-3,\infty \right)\)

12.1.3.27.

Answer 1.
\(\left(-\infty ,3\right)\cup \left(3,\infty \right)\)
Answer 2.
\(\left(-\infty ,-1\right)\)

12.1.3.29.

Answer.
\(315\)

12.1.3.31.

Answer.
\(350\)

12.1.3.33.

Answer 1.
\(0.796974\)
Answer 2.
\(0.8, 6.27\)

12.1.3.35.

Answer.
\(0\)

12.2 Multiplication and Division of Rational Expressions
12.2.5 Exercises

12.2.5.1.

Answer.
\(-{\frac{65}{14}}\)

12.2.5.3.

Answer.
\({\frac{36}{133}}\)

12.2.5.5.

Answer.
\({\frac{12}{25}}\)

12.2.5.7.

Answer.
\(-{\frac{3}{28}}\)

12.2.5.9.

Answer.
\(\left(t+6\right)\mathopen{}\left(t-6\right)\)

12.2.5.11.

Answer.
\(\left(x+8\right)\mathopen{}\left(x+7\right)\)

12.2.5.13.

Answer.
\(\left(y-1\right)\mathopen{}\left(y-6\right)\)

12.2.5.15.

Answer.
\(2\mathopen{}\left(r-2\right)\mathopen{}\left(r-7\right)\)

12.2.5.17.

Answer.
\(8r^{6}\mathopen{}\left(r+1\right)\mathopen{}\left(r+2\right)\)

12.2.5.19.

Answer.
\(\left(12t-1\right)\mathopen{}\left(12t-1\right)\)

12.2.5.21.

Answer 1.
\(1, x\ne -4\)
Answer 2.
\(1, x\ne -4\)
Answer 3.
\(1, x\ne 4\)
Answer 4.
\(-1, x\ne 4\)

12.2.5.25.

Answer.
\(\frac{1}{r-5}, r\ne -9\)

12.2.5.27.

Answer.
\(-\frac{10}{t-9}, t\ne 3\)

12.2.5.29.

Answer.
\(-x+6, x\ne 3\)

12.2.5.31.

Answer.
\(-9, y\ne 8\)

12.2.5.33.

Answer.
\(-\frac{3}{r+2}, r\ne 0\)

12.2.5.35.

Answer.
\(-\frac{r}{r+5}, r\ne 3\)

12.2.5.37.

Answer.
\(-\frac{t}{t+5}, t\ne 5\)

12.2.5.39.

Answer.
\(\frac{x}{x-3}, x\ne 1\)

12.2.5.41.

Answer.
\(-\frac{2y+3}{6y-5}, y\ne -1\)

12.2.5.43.

Answer.
\(-\frac{r-4}{r-3}, \left(-\infty ,\infty \right)\)

12.2.5.45.

Answer.
\(-\frac{t+6}{t+5}, t\ne 5\)

12.2.5.47.

Answer.
\(-\frac{2x-5}{6x+5}, x\ne -1\)

12.2.5.49.

Answer.
\(-\frac{y^{3}}{y+2}, y\ne -1\)

12.2.5.51.

Answer.
\(\frac{r-5}{r-6}, r\ne 2\hbox{ and }r\ne 0\)

12.2.5.53.

Answer.
\(\frac{r^{2}+2r+4}{r+2}, r\ne 2\)

12.2.5.55.

Answer.
\(-\frac{ty}{ty+5}\)

12.2.5.57.

Answer.
\(\frac{6}{x+5t}\)

12.2.5.59.

Answer.
\(-\frac{y+5x}{y-6x}\)

12.2.5.61.

Answer.
\(-\frac{3ry-5}{2ry+3}\)

12.2.5.63.

Answer.
\(\frac{1}{t+9}, t\ne -4\)

12.2.5.65.

Answer.
\(\frac{x-3}{x-8}, x\ne -3\hbox{ and }x\ne 0\)

12.2.5.67.

Answer.
\(\frac{y-5}{5y+2}, y\ne 5\hbox{ and }y\ne 0\)

12.2.5.69.

Answer.
\(\frac{r}{r+3}, r\ne -0.2\hbox{ and }r\ne 0\)

12.2.5.73.

Answer 1.
\(-\frac{t^{7}}{t+4}, \left(-\infty ,\infty \right)\)
Answer 2.
\(-\frac{t}{t+4}, t\ne 0\)

12.2.5.75.

Answer.
\(5\mathopen{}\left(x-2\right), x\ne -5\hbox{ and }x\ne 4\)

12.2.5.77.

Answer.
\(\frac{y^{2}}{\left(y+2\right)\mathopen{}\left(y+9\right)}, y\ne 2\hbox{ and }y\ne 4\)

12.2.5.79.

Answer.
\(-\frac{3\mathopen{}\left(r-1\right)}{7r\mathopen{}\left(r+5\right)}, r\ne 4\hbox{ and }r\ne 1\)

12.2.5.81.

Answer.
\(-\frac{t-1}{2\mathopen{}\left(9t-8\right)}, t\ne -0.888889\hbox{ and }t\ne 0.571429\hbox{ and }t\ne 0\)

12.2.5.83.

Answer.
\(\frac{1}{4x^{3}\mathopen{}\left(x+8\right)}, \left(-\infty ,\infty \right)\)

12.2.5.85.

Answer.
\(4y^{5}, y\ne 0\)

12.2.5.87.

Answer.
\(\frac{1}{5}, y\ne -\left(-2\right)\)

12.2.5.89.

Answer.
\(-\frac{1}{r-3}, r\ne 2.66667\hbox{ and }r\ne -2.66667\)

12.2.5.91.

Answer.
\(t^{2}\mathopen{}\left(t-3\right), t\ne 0\hbox{ and }t\ne -2\hbox{ and }t\ne 3\)

12.2.5.93.

Answer.
\(\frac{4x+9}{x-8}, x\ne 0\)

12.2.5.95.

Answer.
\(\frac{c+6}{8\mathopen{}\left(c-6\right)}, c\ne 0\hbox{ and }c\ne -6\)

12.2.5.97.

Answer.
\(\frac{x\mathopen{}\left(x+1\right)}{\left(x-2\right)\mathopen{}\left(x-4\right)}, x\ne -2\hbox{ and }x\ne -4\hbox{ and }x\ne -1\)

12.2.5.99.

Answer.
\(\frac{4\mathopen{}\left(t+x\right)}{3t+x}\)

12.2.5.101.

Answer.
\(\frac{2x^{5}}{3y}\)

12.2.5.103.

Answer.
\(3\mathopen{}\left(y+5t\right)\)

12.2.5.105.

Answer.
\(2x^{5}\)

12.2.5.107.

Answer.
\(\frac{r+3y}{r^{2}}\)

12.2.5.109.

Answer.
\(\frac{1}{t^{2}\mathopen{}\left(t-6r\right)}\)

12.2.5.111.

Answer.
\(x^{3}\mathopen{}\left(xt-3\right)\)

12.2.5.113.

Answer.
\(\frac{3x^{2}\mathopen{}\left(y-3x\right)}{y}\)

12.2.5.115.

Answer.
\(\frac{4t}{5}\)

12.2.5.117.

Answer.
\(\frac{9n^{3}}{10}\)

12.2.5.119.

Answer.
\(\frac{1}{x+25}\)

12.3 Addition and Subtraction of Rational Expressions
12.3.5 Exercises

12.3.5.1.

Answer.
\({\frac{4}{3}}\)

12.3.5.3.

Answer.
\({\frac{26}{15}}\)

12.3.5.5.

Answer.
\({\frac{3}{8}}\)

12.3.5.7.

Answer.
\(-{\frac{5}{36}}\)

12.3.5.9.

Answer.
\(\left(x+1\right)\mathopen{}\left(x-1\right)\)

12.3.5.11.

Answer.
\(\left(y+4\right)\mathopen{}\left(y+3\right)\)

12.3.5.13.

Answer.
\(\left(y-7\right)\mathopen{}\left(y-2\right)\)

12.3.5.15.

Answer.
\(2\mathopen{}\left(r-5\right)\mathopen{}\left(r-1\right)\)

12.3.5.17.

Answer.
\(6, t\ne -4\)

12.3.5.19.

Answer.
\(5, x\ne -1\)

12.3.5.21.

Answer.
\(-\frac{1}{y+5}, y\ne 7\)

12.3.5.23.

Answer.
\(-\frac{1}{r+4}, r\ne 6\)

12.3.5.25.

Answer.
\(\frac{3t}{4}, \left(-\infty ,\infty \right)\)

12.3.5.27.

Answer.
\(\frac{-x-16}{\left(x+6\right)\mathopen{}\left(x+4\right)}, \left(-\infty ,\infty \right)\)

12.3.5.29.

Answer.
\(\frac{5x-9}{\left(x-3\right)\mathopen{}\left(x+3\right)}, \left(-\infty ,\infty \right)\)

12.3.5.31.

Answer.
\(\frac{1}{y+1}, y\ne 1\)

12.3.5.33.

Answer.
\(\frac{1}{r-2}, r\ne -2\)

12.3.5.35.

Answer.
\(-\frac{4}{t-2}, t\ne -2\)

12.3.5.37.

Answer.
\(-\frac{4}{x+1}, x\ne 1\)

12.3.5.39.

Answer.
\(\frac{y-6}{y}, y\ne 9\)

12.3.5.41.

Answer.
\(\frac{r+6}{r}, r\ne 8\)

12.3.5.43.

Answer.
\(\frac{3}{t+1}, t\ne 1\)

12.3.5.45.

Answer.
\(-\frac{6x}{x+4}, x\ne -5\)

12.3.5.47.

Answer.
\(-\frac{6x}{x-2}, x\ne 5\)

12.3.5.49.

Answer.
\(\frac{2}{y-5}, y\ne 0\)

12.3.5.51.

Answer.
\(\frac{-5r+23}{r-4}, \left(-\infty ,\infty \right)\)

12.3.5.53.

Answer.
\(-\frac{18\mathopen{}\left(t-10\right)}{\left(t+6\right)\mathopen{}\left(t-6\right)}, \left(-\infty ,\infty \right)\)

12.3.5.55.

Answer.
\(2x-5r\)

12.3.5.57.

Answer.
\(-\frac{5y}{8t}\)

12.3.5.59.

Answer.
\(\frac{-6r^{2}-20y}{15ry^{2}}\hbox{, }\frac{2\mathopen{}\left(-3r^{2}-10y\right)}{15ry^{2}}\hbox{, or }-\frac{2\mathopen{}\left(3r^{2}+10y\right)}{15ry^{2}}\)

12.3.5.61.

Answer.
\(-\frac{5}{tx+3}\)

12.3.5.63.

Answer.
\(-\frac{2x}{x-3y}\)

12.4 Complex Fractions
12.4.3 Exercises

12.4.3.1.

Answer 1.
\({\frac{45}{4}}\)
Answer 2.
\(\frac{xy}{rt}\)

12.4.3.3.

Answer 1.
\({\frac{45}{4}}\)
Answer 2.
\({\frac{5}{36}}\)

12.4.3.5.

Answer.
\({\frac{64}{45}}\)

12.4.3.7.

Answer.
\(3\)

12.4.3.9.

Answer.
\(\frac{9x-2}{x+7}, x\ne 0\)

12.4.3.11.

Answer.
\(\frac{c+2}{10\mathopen{}\left(c-2\right)}, c\ne 0\hbox{ and }c\ne -2\)

12.4.3.13.

Answer.
\(\frac{5s+1}{s\mathopen{}\left(s+9\right)}, \left(-\infty ,\infty \right)\)

12.4.3.15.

Answer.
\(\frac{4t\mathopen{}\left(t-1\right)}{6t-1}, t\ne 0\hbox{ and }t\ne 1\)

12.4.3.17.

Answer.
\(\frac{9\mathopen{}\left(2y-9\right)}{-y+14}, y\ne 5\)

12.4.3.19.

Answer.
\(-\frac{c-6}{\left(2c+3\right)\mathopen{}\left(c-2\right)}, c\ne -2\)

12.4.3.21.

Answer.
\(\frac{3\mathopen{}\left(s+4\right)}{\left(4s+15\right)\mathopen{}\left(s-4\right)}, s\ne -4\)

12.4.3.23.

Answer.
\(-\frac{10\mathopen{}\left(q-2\right)\mathopen{}\left(q-2\right)}{2q-3}, q\ne 1\hbox{ and }q\ne 2\)

12.4.3.25.

Answer.
\(\frac{5t^{2}+6t-5}{t-9}, t\ne -1\hbox{ and }t\ne 1\)

12.4.3.27.

Answer.
\(\frac{\left(z-1\right)\mathopen{}\left(z+36\right)}{\left(z+6\right)\mathopen{}\left(z-6\right)}, z\ne -36\)

12.4.3.29.

Answer.
\(\frac{5b}{6}\)

12.4.3.31.

Answer.
\(t^{3}\)

12.4.3.33.

Answer 1.
\(\frac{t}{yx}\)
Answer 2.
\(\frac{tx}{y}\)

12.4.3.35.

Answer.
\(\frac{4}{t\mathopen{}\left(12-x\right)}\hbox{ or }\frac{4}{12t-tx}\)

12.4.3.37.

Answer.
\(\frac{t+4x}{5t+x}\)

12.5 Solving Rational Equations
12.5.5 Exercises

12.5.5.1.

Answer.
\(\{8\}\)

12.5.5.3.

Answer.
\(\{-6\}\)

12.5.5.5.

Answer.
\(\{5\}\)

12.5.5.7.

Answer.
\(\left\{13,3\right\}\)

12.5.5.9.

Answer.
\(\left\{4,-3\right\}\)

12.5.5.11.

Answer.
\(\left\{-1,-10\right\}\)

12.5.5.15.

Answer.
\(\left\{-9\right\}\)

12.5.5.17.

Answer.
\(\left\{6\right\}\)

12.5.5.19.

Answer.
\(\left\{-2\right\}\)

12.5.5.21.

Answer.
\(\left\{63\right\}\)

12.5.5.23.

Answer.
\(\left\{6\right\}\)

12.5.5.25.

Answer.
\(\left\{\frac{-37}{120}\right\}\)

12.5.5.27.

Answer.
\(\left\{6\right\}\)

12.5.5.29.

Answer.
\(\left\{9\right\}\)

12.5.5.31.

Answer.
\({\rm no\ real\ solutions}\)

12.5.5.33.

Answer.
\(\text{no real solutions}\)

12.5.5.35.

Answer.
\(\left\{\frac{15}{4},\frac{3}{2}\right\}\)

12.5.5.37.

Answer.
\(\left\{-\left(-4\right)\right\}\)

12.5.5.39.

Answer.
\(\left\{3,-6\right\}\)

12.5.5.41.

Answer.
\(\left\{-2,-5\right\}\)

12.5.5.43.

Answer.
\(\left\{41\right\}\)

12.5.5.45.

Answer.
\(\left\{30\right\}\)

12.5.5.47.

Answer.
\(\left\{1\right\}\)

12.5.5.49.

Answer.
\(\left\{1,-9\right\}\)

12.5.5.51.

Answer.
\(y = \frac{b}{p}\)

12.5.5.53.

Answer.
\(C = yp\)

12.5.5.55.

Answer.
\(a = \frac{q}{2}\)

12.5.5.57.

Answer.
\(t = 3A-4\)

12.5.5.59.

Answer.
\(\left\{-2.38333,0.457872\right\}\)

12.5.5.61.

Answer.
\(\left\{-1.53677,1.22187\right\}\)

12.5.5.63.

Answer.
\(\left\{-0.607409,0.828675,3.17873\right\}\)

12.5.5.65.

Answer.
\(4.2\)

12.5.5.67.

Answer 1.
\(17\)
Answer 2.
\(127.5\)

12.5.5.69.

Answer 1.
\(15\)
Answer 2.
\(10\)

12.5.5.71.

Answer.
\(18.5\)

12.5.5.73.

Answer.
\(45\)

12.5.5.75.

Answer.
\(22.7283\ {\rm hr}\)

12.5.5.77.

Answer.
\(3.29315\ {\textstyle\frac{\rm\mathstrut mi}{\rm\mathstrut hr}}\)

12.5.5.79.

Answer.
\(255.217\ {\textstyle\frac{\rm\mathstrut mi}{\rm\mathstrut hr}}\)

12.5.5.81.

Answer 1.
\(54.59\ {\rm hr}\)
Answer 2.
\(66.59\ {\rm hr}\)

12.6 Rational Functions and Equations Chapter Review
12.6.6 Exercises

12.6.6.1.

Answer 1.
\(\left(-\infty ,-1\right)\cup \left(-1,\infty \right)\)
Answer 2.
\(\left(-\infty ,1\right)\cup \left(1,\infty \right)\)

12.6.6.3.

Answer 1.
\(350\)
Answer 2.
\(444\)
Answer 3.
\(12\)
Answer 4.
\(450\)

12.6.6.5.

Answer 1.
\(3\)
Answer 2.
\(55\)

12.6.6.7.

Answer 1.
\(2.45\)
Answer 2.
\(1.84\)

12.6.6.9.

Answer.
\(-\frac{x-3t}{x-4t}\)

12.6.6.11.

Answer.
\(\frac{y-3}{5y+1}, y\ne 3\hbox{ and }y\ne 0\)

12.6.6.13.

Answer.
\(\frac{r^{2}}{\left(r+2\right)\mathopen{}\left(r-5\right)}, r\ne 2\hbox{ and }r\ne 4\)

12.6.6.15.

Answer.
\(-\frac{1}{t+1}, t\ne 1.6\hbox{ and }t\ne -1.6\)

12.6.6.17.

Answer.
\(x^{3}\mathopen{}\left(xr+1\right)\)

12.6.6.19.

Answer.
\(\frac{1}{y+2}, y\ne 2\)

12.6.6.21.

Answer.
\(-\frac{3r}{r-6}, r\ne 5\)

12.6.6.23.

Answer.
\(\frac{3}{r-4}, r\ne 0\)

12.6.6.25.

Answer.
\(\frac{18t^{2}-20x^{4}}{15tx^{5}}\hbox{, }\frac{2\mathopen{}\left(9t^{2}-10x^{4}\right)}{15tx^{5}}\hbox{, or }-\frac{2\mathopen{}\left(-9t^{2}+10x^{4}\right)}{15tx^{5}}\)

12.6.6.27.

Answer.
\(-\frac{x}{x+5r}\)

12.6.6.29.

Answer 1.
\({\frac{8}{3}}\)
Answer 2.
\(\frac{yx}{tr}\)

12.6.6.31.

Answer.
\(-\frac{2\mathopen{}\left(3q-4\right)\mathopen{}\left(q-4\right)}{2q-5}, q\ne 1\hbox{ and }q\ne 4\)

12.6.6.33.

Answer.
\(\frac{-2t^{2}+3t+32}{7t+4}, t\ne -4\hbox{ and }t\ne 4\)

12.6.6.35.

Answer.
\(\frac{5y}{6}\)

12.6.6.37.

Answer.
\(\frac{3}{y\mathopen{}\left(12-x\right)}\hbox{ or }\frac{3}{12y-yx}\)

12.6.6.39.

Answer.
\(\left\{-18\right\}\)

12.6.6.41.

Answer.
\(\left\{-\left(-7\right)\right\}\)

12.6.6.43.

Answer.
\(\left\{\frac{8}{3},-1\right\}\)

12.6.6.45.

Answer.
\(\left\{6,-2\right\}\)

12.6.6.47.

Answer.
\(B = 3b-5\)

12.6.6.51.

Answer 1.
\(22\)
Answer 2.
\(99\)

12.6.6.53.

Answer 1.
\(30\)
Answer 2.
\(45\)

13 Graphs and Equations
13.1 Overview of Graphing
13.1.7 Exercises

13.1.7.1.

Answer.
\(x\) \(y=2x+3\) Point
\(-2\) \(-1\) \((-2,-1)\)
\(-1\) \(1\) \((-1,1)\)
\(0\) \(3\) \((0,3)\)
\(1\) \(5\) \((1,5)\)
\(2\) \(7\) \((2,7)\)

13.1.7.3.

Answer.
\(x\) \(y=-\frac{2}{5}x-3\) Point
\(-5\) \(-1\) \((-5,-1)\)
\(0\) \(-3\) \((0,-3)\)
\(5\) \(-5\) \((5,-5)\)

13.1.7.5.

Answer.

13.1.7.7.

Answer.

13.1.7.9.

Answer.

13.1.7.11.

Answer.

13.1.7.13.

Answer.

13.1.7.15.

Answer.
\(x\)-intercept: \((2,0)\)
\(y\)-intercept: \((0,-5)\)

13.1.7.17.

Answer.
\(x\)-intercept: \((-15,0)\)
\(y\)-intercept: \((0,-3)\)

13.1.7.19.

Answer.

13.1.7.21.

Answer.

13.1.7.23.

Answer.
\(x\) \(y=-3x^2\) Point
\(-2\) \(-12\) \((-2,-12)\)
\(-1\) \(-3\) \((-1,3)\)
\(0\) \(0\) \((0,0)\)
\(1\) \(-3\) \((1,-3)\)
\(2\) \(-12\) \((2,-12)\)

13.1.7.25.

Answer.
\(x\) \(y=\frac{1}{2}x^3-x\) Point
\(-2\) \(-2\) \((-2,-2)\)
\(-1\) \(\frac12\) \(\left(-1,\frac12\right)\)
\(0\) \(0\) \((0,0)\)
\(1\) \(-\frac12\) \(\left(1,-\frac12\right)\)
\(2\) \(2\) \((2,2)\)

13.1.7.27.

Answer.
\(x\) \(y=\sqrt{x+5}\) Point
\(-2\) \(1.73\ldots\) \((-2,1.73\ldots)\)
\(-1\) \(2\) \(\left(-1,2\right)\)
\(0\) \(2.23\ldots\) \((0,2.23\ldots)\)
\(1\) \(2.44\ldots\) \(\left(1,2.44\ldots\right)\)
\(2\) \(2.64\ldots\) \((2,2.64\ldots)\)

13.2 Quadratic Graphs and Vertex Form
13.2.6 Exercises

13.2.6.1.

Answer.
\(r^{2}-4r-45\)

13.2.6.3.

Answer.
\(8t^{2}+30t-50\)

13.2.6.5.

Answer.
\(\left(x+1\right)\mathopen{}\left(x+9\right)\)

13.2.6.7.

Answer.
\(2\mathopen{}\left(y+9\right)\mathopen{}\left(y+1\right)\)

13.2.6.9.

Answer 1.
\(\left\{q \mid q\ge 1\right\}\)
Answer 2.
\(\left[1,\infty \right)\)

13.2.6.11.

Answer 1.
\(\left\{y \mid y > 3\right\}\)
Answer 2.
\(\left(3,\infty \right)\)

13.2.6.13.

Answer.
\(-2;\,6;\,-1;\,1;\,0;\,-2;\,1;\,-3;\,2;\,-2;\,3;\,1;\,4;\,6\)

13.2.6.15.

Answer.
\(-2;\,5;\,-1;\,4;\,0;\,1;\,1;\,-4;\,2;\,-11;\,3;\,-20;\,4;\,-31\)

13.2.6.17.

Answer.
\(-2;\,30;\,-1;\,14;\,0;\,4;\,1;\,0;\,2;\,2;\,3;\,10;\,4;\,24\)

13.2.6.19.

Answer.
\(-2;\,24;\,-1;\,23;\,0;\,26;\,1;\,33;\,2;\,44;\,3;\,59;\,4;\,78\)

13.2.6.29.

Answer 1.
\(\left(-0.5,-1.5\right)\)
Answer 2.
\(\left(0,-1\right)\)
Answer 3.
\(\left(-1.36603,0\right), \left(0.366025,0\right)\)
Answer 4.
\(\left(-\infty ,\infty \right)\)
Answer 5.
\(\left[-1.5,\infty \right)\)
Answer 6.
\(-1\)
Answer 7.
\(\left\{-2.15831,1.15831\right\}\)
Answer 8.
\(\left(-\infty ,-2.15831\right)\cup \left(1.15831,\infty \right)\)

13.2.6.31.

Answer 1.
\(\left(0.5,-1.3\right)\)
Answer 2.
\(\left(0,-0.9\right)\)
Answer 3.
\(\left(-0.401388,0\right), \left(1.40139,0\right)\)
Answer 4.
\(\left(-\infty ,\infty \right)\)
Answer 5.
\(\left[-1.3,\infty \right)\)
Answer 6.
\(18.3\)
Answer 7.
\(\left\{-1.13936,2.13936\right\}\)
Answer 8.
\(\left[-1.13936,2.13936\right]\)

13.2.6.33.

Answer 1.
\(\left(3.6,-2.88\right)\)
Answer 2.
\(\left(0,3.6\right)\)
Answer 3.
\(\left(1.2,0\right), \left(6,0\right)\)
Answer 4.
\(\left(-\infty ,\infty \right)\)
Answer 5.
\(\left[-2.88,\infty \right)\)
Answer 6.
\(-2.7\)
Answer 7.
\(\left\{0.4759,6.7241\right\}\)
Answer 8.
\(\left(-\infty ,0.4759\right]\cup \left[6.7241,\infty \right)\)

13.2.6.35.

Answer.
\(150\ {\rm ft}\)

13.2.6.37.

Answer.
\(450\)

13.2.6.39.

Answer.
\(6.16591\)

13.2.6.41.

Answer.
\(13\)

13.2.6.43.

Answer.
\(120, 120\)

13.2.6.45.

Answer.
\(\left(8,-6\right)\)

13.2.6.47.

Answer.
\(\left(-6,-10\right)\)

13.2.6.49.

Answer.
\(\left(0.2,7.4\right)\)

13.2.6.51.

Answer.
\(\left(x-3\right)^{2}-3\)

13.2.6.53.

Answer.
\(-3\mathopen{}\left(x-1\right)^{2}+3\)

13.2.6.55.

Answer.
\(-2\mathopen{}\left(x-4\right)^{2}-1\)

13.2.6.57.

Answer.
\(f\mathopen{}\left(x\right) = -9\mathopen{}\left(x-4\right)^{2}+-6\)

13.2.6.59.

Answer.
\(f\mathopen{}\left(x\right) = -5\mathopen{}\left(x--9\right)^{2}+3\)

13.2.6.61.

Answer 1.
\(\left(-\infty ,\infty \right)\)
Answer 2.
\(\left[7,\infty \right)\)

13.2.6.63.

Answer 1.
\(\left(-\infty ,\infty \right)\)
Answer 2.
\(\left[1,\infty \right)\)

13.2.6.65.

Answer 1.
\(\left(-\infty ,\infty \right)\)
Answer 2.
\(\left[9,\infty \right)\)

13.2.6.67.

Answer 1.
\(\left(-\infty ,\infty \right)\)
Answer 2.
\(\left(-\infty ,\frac{-2}{3}\right]\)

13.2.6.69.

Answer 1.
\(\left(-\infty ,\infty \right)\)
Answer 2.
\(\left(-\infty ,\frac{-4}{9}\right]\)

13.2.6.71.

Answer 1.
\(2;\,\text{right}\)
Answer 2.
\(7;\,\text{up}\)

13.2.6.73.

Answer 1.
\(61;\,\text{right}\)
Answer 2.
\(66;\,\text{down}\)

13.2.6.75.

Answer 1.
\({\frac{3}{8}};\,\text{right}\)
Answer 2.
\({\frac{7}{9}};\,\text{up}\)

13.2.6.77.

Answer 1.
\(x^{2}-4x+3\)
Answer 2.
\(\left(x-1\right)\mathopen{}\left(x-3\right)\)

13.2.6.79.

Answer 1.
\(x^{2}-8x-65\)
Answer 2.
\(\left(x+5\right)\mathopen{}\left(x-13\right)\)

13.2.6.81.

Answer 1.
\(\left(0,-8\right)\)
Answer 2.
\(\left(4,0\right), \left(-2,0\right)\)

13.2.6.83.

Answer 1.
\(\left(0,-288\right)\)
Answer 2.
\(\left(4,0\right), \left(-9,0\right)\)

13.2.6.85.

Answer 1.
\(\left(0,0\right)\)
Answer 2.
\(\left(0,0\right), \left(9,0\right)\)

13.2.6.87.

Answer 1.
\(\left(0,-48\right)\)
Answer 2.
\(\left(-4,0\right)\)

13.2.6.89.

Answer 1.
\(\left(0,18\right)\)
Answer 2.
\(\left(\frac{1}{6},0\right), \left(\frac{9}{4},0\right)\)

13.3 Completing the Square
13.3.6 Exercises

13.3.6.1.

Answer.
\(\left\{7,-9\right\}\)

13.3.6.3.

Answer.
\(\left\{\frac{7}{8},\frac{-11}{8}\right\}\)

13.3.6.5.

Answer.
\(\left\{6+\sqrt{10},6-\sqrt{10}\right\}\)

13.3.6.7.

Answer.
\(\left\{12,-4\right\}\)

13.3.6.9.

Answer.
\(\left\{\frac{11}{8},\frac{3}{8}\right\}\)

13.3.6.11.

Answer.
\(\left\{\frac{-9+\sqrt{14}}{2},\frac{-9-\sqrt{14}}{2}\right\}\)

13.3.6.13.

Answer.
\(\left\{-2,6\right\}\)

13.3.6.15.

Answer.
\(\left\{3,4\right\}\)

13.3.6.17.

Answer.
\(\left\{-5-\sqrt{26},-5+\sqrt{26}\right\}\)

13.3.6.19.

Answer.
\(\left\{7,9\right\}\)

13.3.6.21.

Answer.
\(\left\{-7,2\right\}\)

13.3.6.23.

Answer.
\(\left\{-5-\sqrt{15},-5+\sqrt{15}\right\}\)

13.3.6.25.

Answer.
\(\left\{-2,\frac{-4}{3}\right\}\)

13.3.6.27.

Answer.
\(\left\{\frac{-3}{2}-\frac{1}{2}\sqrt{5},\frac{-3}{2}+\frac{1}{2}\sqrt{5}\right\}\)

13.3.6.29.

Answer 1.
\(f\mathopen{}\left(t\right) = \left(t+2\right)^{2}-3\)
Answer 2.
\(\left(-2,-3\right)\)

13.3.6.31.

Answer 1.
\(g\mathopen{}\left(x\right) = \left(x-\frac{3}{2}\right)^{2}-\frac{21}{4}\)
Answer 2.
\(\left(\frac{3}{2},\frac{-21}{4}\right)\)

13.3.6.33.

Answer 1.
\(F\mathopen{}\left(y\right) = 3\mathopen{}\left(y+\frac{3}{2}\right)^{2}-\frac{23}{4}\)
Answer 2.
\(\left(\frac{-3}{2},\frac{-23}{4}\right)\)

13.3.6.35.

Answer 1.
\(\left(-\infty ,\infty \right)\)
Answer 2.
\(\left[5,\infty \right)\)

13.3.6.37.

Answer 1.
\(\left(-\infty ,\infty \right)\)
Answer 2.
\(\left(-\infty ,-10\right]\)

13.3.6.39.

Answer 1.
\(\left(-\infty ,\infty \right)\)
Answer 2.
\(\left[-3,\infty \right)\)

13.3.6.41.

Answer 1.
\(\left(-\infty ,\infty \right)\)
Answer 2.
\(\left(-\infty ,3\right]\)

13.3.6.63.

Answer.
\(-{\frac{49}{6}}\)

13.3.6.65.

Answer.
\(-{\frac{231}{32}}\)

13.3.6.67.

Answer.
\(\left(-\infty ,\frac{41}{4}\right]\)

13.3.6.69.

Answer.
\(\left[\frac{2}{3},\infty \right)\)

13.3.6.71.

Answer.
\(110.781\ {\rm ft}\)

13.4 Absolute Value Equations
13.4.5 Exercises

13.4.5.1.

Answer.
\(\{90\}\)

13.4.5.3.

Answer.
\(\{-5\}\)

13.4.5.5.

Answer.
\(\{(-7/2)\}\)

13.4.5.7.

Answer 1.
\(4x = 8\)
Answer 2.
\(4x = -8\)
Answer 3.
\(\left\{2,-2\right\}\)

13.4.5.9.

Answer 1.
\(0.2r = 3\)
Answer 2.
\(0.2r = 9\)
Answer 3.
\(\left\{15,45\right\}\)

13.4.5.13.

Answer.
\(\left\{\frac{-2}{9},\frac{-4}{9}\right\}\)

13.4.5.15.

Answer.
\(\left\{\frac{-23}{2},\frac{15}{2}\right\}\)

13.4.5.17.

Answer.
\(\left\{-4,4\right\}\)

13.4.5.19.

Answer.
\(\left\{-8,18\right\}\)

13.4.5.21.

Answer.
\(\left\{-9,2\right\}\)

13.4.5.23.

Answer.
\(\left\{-1,2\right\}\)

13.4.5.25.

Answer.
\(\text{no real solutions}\)

13.4.5.27.

Answer.
\(\left\{-4\right\}\)

13.4.5.29.

Answer.
\(\left\{\frac{-10}{3},\frac{14}{3}\right\}\)

13.4.5.31.

Answer.
\(\left\{-12,-8\right\}\)

13.4.5.33.

Answer.
\(\left\{\frac{37}{2},\frac{-23}{2}\right\}\)

13.4.5.35.

Answer.
\(\left\{-9,7\right\}\)

13.4.5.37.

Answer.
\(\left\{1\right\}\)

13.4.5.39.

Answer.
\(\text{no real solutions}\)

13.4.5.41.

Answer.
\(\text{no real solutions}\)

13.4.5.43.

Answer.
\(\left\{-2\right\}\)

13.4.5.45.

Answer.
\(\left\{\frac{3}{2},\frac{1}{4}\right\}\)

13.4.5.47.

Answer.
\(\left\{\frac{-3}{2}\right\}\)

13.4.5.49.

Answer.
\(\left\{\frac{1}{11},1\right\}\)

13.4.5.51.

Answer.
\(\left\{\frac{-1}{3},\frac{-1}{11}\right\}\)

13.4.5.53.

Answer.
\(\left[4,8\right]\)

13.5 Solving Mixed Equations
13.5.4 Exercises

13.5.4.1.

Answer.
\(\left\{49\right\}\)

13.5.4.3.

Answer.
\(\{1\}\)

13.5.4.5.

Answer.
\(\left\{-8,1\right\}\)

13.5.4.7.

Answer.
\(\text{no solution}\)

13.5.4.9.

Answer.
\(\left\{\frac{-1}{2}-\frac{1}{2}\sqrt{3},\frac{-1}{2}+\frac{1}{2}\sqrt{3}\right\}\)

13.5.4.11.

Answer.
\(\left\{1-\sqrt{5},1+\sqrt{5}\right\}\)

13.5.4.13.

Answer.
\(\left\{-1,2\right\}\)

13.5.4.15.

Answer.
\(\left\{-3,2\right\}\)

13.5.4.17.

Answer.
\(\left\{6,0\right\}\)

13.5.4.19.

Answer.
\(\{72\}\)

13.5.4.21.

Answer.
\(\left\{62\right\}\)

13.5.4.23.

Answer.
\(\left\{-8,4\right\}\)

13.5.4.25.

Answer.
\(\left\{-4,0\right\}\)

13.5.4.27.

Answer.
\(\left\{-4,-10\right\}\)

13.5.4.29.

Answer.
\(\left\{-8\right\}\)

13.5.4.31.

Answer.
\(\left\{0,-5\right\}\)

13.5.4.33.

Answer.
\(\text{no real solutions}\)

13.5.4.35.

Answer.
\(\text{no real solutions}\)

13.5.4.37.

Answer.
\(\left\{-2,16\right\}\)

13.5.4.39.

Answer.
\(\left\{\frac{-3}{4},-10\right\}\)

13.5.4.41.

Answer.
\(\left\{2\right\}\)

13.5.4.43.

Answer.
\(\left\{-68\right\}\)

13.5.4.45.

Answer.
\(\left\{-7,9\right\}\)

13.6 Compound Inequalities
13.6.7 Exercises

13.6.7.1.

Answer 1.
\(\left\{k \mid k > 0\right\}\)
Answer 2.
\(\left(0,\infty \right)\)

13.6.7.3.

Answer 1.
\(\left\{t \mid t\ge 2\right\}\)
Answer 2.
\(\left[2,\infty \right)\)

13.6.7.5.

Answer 1.
\(\left\{x \mid x < -1\right\}\)
Answer 2.
\(\left(-\infty ,-1\right)\)

13.6.7.7.

Answer 1.
\(\left\{x \mid x\le -2\right\}\)
Answer 2.
\(\left(-\infty ,-2\right]\)

13.6.7.9.

Answer 1.
\(\left\{x \mid x\ge 0\right\}\)
Answer 2.
\(\left[0,\infty \right)\)

13.6.7.11.

Answer 1.
\(\left\{t \mid t < 3\right\}\)
Answer 2.
\(\left(-\infty ,3\right)\)

13.6.7.13.

Answer 1.
\(\text{is not}\)
Answer 2.
\(\text{is}\)
Answer 3.
\(\text{is}\)
Answer 4.
\(\text{is not}\)

13.6.7.15.

Answer.
\(\left(-10,6\right]\)

13.6.7.17.

Answer.
\(\left(-\infty ,-8\right)\cup \left[9,\infty \right)\)

13.6.7.19.

Answer.
\(\left(-\infty ,2\right]\)

13.6.7.21.

Answer.
\(\left[5,\infty \right)\)

13.6.7.23.

Answer.
\(\left[-1,8\right)\)

13.6.7.25.

Answer.
\(\left[1,6\right)\)

13.6.7.27.

Answer.
\(\left[0,5\right)\)

13.6.7.29.

Answer.
\(\left[66.2,111.2\right]\)

13.6.7.31.

Answer.
\(\left(-\infty ,-1.9\right)\cup \left(0.6875,\infty \right)\)

13.6.7.33.

Answer.
\(\left(-\infty ,0.666667\right]\)

13.6.7.35.

Answer.
\(\left(0.714286,\infty \right)\)

13.6.7.37.

Answer.
\(\left(-\infty ,-15\right]\cup \left(0,\infty \right)\)

13.6.7.39.

Answer 1.
\(\left\{x \mid 3 < x < 21\right\}\)
Answer 2.
\(\left(3,21\right)\)

13.6.7.41.

Answer 1.
\(\left\{x \mid -12 < x\le 12\right\}\)
Answer 2.
\(\left(-12,12\right]\)

13.6.7.43.

Answer 1.
\(16-10x\)
Answer 2.
\(\left[-74,16\right]\)

13.7 Solving Inequalities Graphically
13.7.5 Exercises

13.7.5.1.

Answer 1.
\(\left\{c \mid c > -1\right\}\)
Answer 2.
\(\left(-1,\infty \right)\)

13.7.5.3.

Answer 1.
\(\left\{k \mid k\ge 1\right\}\)
Answer 2.
\(\left[1,\infty \right)\)

13.7.5.5.

Answer 1.
\(\left(0,4\right)\)
Answer 2.
\(\left(-0.00166667,3.99167\right)\)
Answer 3.
\(\left(-\infty ,\infty \right)\)
Answer 4.
\(\left[3.99167,\infty \right)\)

13.7.5.7.

Answer 1.
\(\left(0.0035,0\right), \left(0,1.1025\right)\)
Answer 2.
\(\left(0.0035,0\right)\)
Answer 3.
\(\left(-\infty ,\infty \right)\)
Answer 4.
\(\left[0,\infty \right)\)

13.7.5.13.

Answer 1.
\(\left(-6,5\right), \left(2,5\right)\)
Answer 2.
\(\left\{-6,2\right\}\)
Answer 3.
\(\left(-\infty ,-6\right)\cup \left(2,\infty \right)\)

13.7.5.15.

Answer 1.
\(\left(-2.5,-5\right), \left(4,-5\right)\)
Answer 2.
\(\left\{-2.5,4\right\}\)
Answer 3.
\(\left(-2.5,4\right)\)

13.7.5.17.

Answer 1.
\(\left(-2,3\right), \left(2,-1\right)\)
Answer 2.
\(\left\{-2,2\right\}\)
Answer 3.
\(\left(-\infty ,-2\right)\cup \left(2,\infty \right)\)

13.7.5.19.

Answer 1.
\(\left(-2,-2\right), \left(0,0\right), \left(2,2\right)\)
Answer 2.
\(\left\{-2,0,2\right\}\)
Answer 3.
\(\left(-2,0\right)\cup \left(2,\infty \right)\)

13.7.5.21.

Answer 1.
\(\left(-3,1\right), \left(5,3\right)\)
Answer 2.
\(\left\{-3,5\right\}\)
Answer 3.
\(\left(-3,5\right)\)

13.7.5.23.

Answer 1.
\(\left(-2,-2\right), \left(0,0\right)\)
Answer 2.
\(\left\{-2,0\right\}\)
Answer 3.
\(\left(-\infty ,-2\right)\cup \left(0,\infty \right)\)

13.7.5.25.

Answer 1.
\(\left(-10,50\right), \left(15,25\right)\)
Answer 2.
\(\left\{-10,15\right\}\)
Answer 3.
\(\left(-\infty ,-10\right)\cup \left(15,\infty \right)\)
Answer 4.
\(\left[-10,15\right]\)

13.7.5.27.

Answer 1.
\(\left(-2,5\right), \left(0.75,5\right)\)
Answer 2.
\(\left\{-2,0.75\right\}\)
Answer 3.
\(\left(-2,0.75\right)\)
Answer 4.
\(\left(-\infty ,-2\right]\cup \left[0.75,\infty \right)\)

13.7.5.29.

Answer 1.
\(\left(-6,10\right), \left(-0.5,21\right)\)
Answer 2.
\(\left\{-6,-0.5\right\}\)
Answer 3.
\(\left(-6,-0.5\right)\)
Answer 4.
\(\left(-\infty ,-6\right]\cup \left[-0.5,\infty \right)\)

13.7.5.31.

Answer.
\(\left(-\infty ,-2\right)\cup \left(-0.5,\infty \right)\)

13.7.5.33.

Answer.
\(\left[0,1.1\right]\)

13.7.5.35.

Answer.
\(\left(-6.37228,-0.627719\right)\)

13.7.5.37.

Answer.
\(\left(-\infty ,0.090098\right]\cup \left[1.1099,\infty \right)\hbox{ or }\left(-\infty ,0.09\right]\cup \left[1.1099,\infty \right)\)

13.7.5.39.

Answer.
\(\left(-\infty ,\infty \right)\)

13.8 Graphs and Equations Chapter Review
13.8.8 Exercises

13.8.8.1.

Answer.
\(x\) \(y=-\frac{2}{5}x-3\) Point
\(-5\) \(-1\) \((-5,-1)\)
\(0\) \(-3\) \((0,-3)\)
\(5\) \(-5\) \((5,-5)\)

13.8.8.3.

Answer.

13.8.8.5.

Answer.

13.8.8.7.

Answer.

13.8.8.9.

Answer.
\(x\) \(y=-3x^2\) Point
\(-2\) \(-12\) \((-2,-12)\)
\(-1\) \(-3\) \((-1,3)\)
\(0\) \(0\) \((0,0)\)
\(1\) \(-3\) \((1,-3)\)
\(2\) \(-12\) \((2,-12)\)

13.8.8.11.

Answer 1.
\(\left(0.25,-1.125\right)\)
Answer 2.
\(\left(0,-1\right)\)
Answer 3.
\(\left(-0.5,0\right), \left(1,0\right)\)
Answer 4.
\(\left(-\infty ,\infty \right)\)
Answer 5.
\(\left[-1.125,\infty \right)\)
Answer 6.
\(9\)
Answer 7.
\(\left\{-1.5,2\right\}\)
Answer 8.
\(\left(-1.5,2\right)\)

13.8.8.13.

Answer 1.
\(4.375\)
Answer 2.
\(606.25\)

13.8.8.15.

Answer 1.
\(7;\,\text{right}\)
Answer 2.
\(8;\,\text{down}\)

13.8.8.17.

Answer 1.
\(x^{2}-2x-3\)
Answer 2.
\(\left(x-3\right)\mathopen{}\left(x+1\right)\)

13.8.8.19.

Answer 1.
\(\left(0,-24\right)\)
Answer 2.
\(\left(-4,0\right), \left(6,0\right)\)

13.8.8.21.

Answer.
\(\left\{-2,1\right\}\)

13.8.8.23.

Answer.
\(\left\{-1,4\right\}\)

13.8.8.25.

Answer 1.
\(\left(-\infty ,\infty \right)\)
Answer 2.
\(\left(-\infty ,5\right]\)

13.8.8.31.

Answer.
\(\left\{7,3\right\}\)

13.8.8.33.

Answer.
\(\left\{-3,6\right\}\)

13.8.8.35.

Answer.
\(\left\{-16,-8\right\}\)

13.8.8.37.

Answer.
\(\left\{5\right\}\)

13.8.8.39.

Answer.
\(\left\{\frac{-7}{5},\frac{1}{9}\right\}\)

13.8.8.41.

Answer.
\(\left\{\frac{-1}{6},\frac{-3}{10}\right\}\)

13.8.8.43.

Answer.
\(\text{no real solutions}\)

13.8.8.45.

Answer.
\(\left\{-8,10\right\}\)

13.8.8.47.

Answer.
\(\left\{\frac{-6}{5},-2\right\}\)

13.8.8.49.

Answer.
\(\left\{3\right\}\)

13.8.8.51.

Answer.
\(\left\{-2\right\}\)

13.8.8.53.

Answer.
\(\left\{-1,9\right\}\)

13.8.8.55.

Answer.
\(\left(-\infty ,0.0526316\right)\cup \left[0.470588,\infty \right)\)

13.8.8.57.

Answer.
\(\left(-\infty ,-0.1\right]\)

13.8.8.59.

Answer.
\(\left(0,\infty \right)\)

13.8.8.61.

Answer.
\(\left(-\infty ,-8.5\right]\)

13.8.8.63.

Answer.
\(\left[-5,0\right)\)

13.8.8.65.

Answer.
\(\left[82.4,95\right]\)

13.8.8.69.

Answer 1.
\(\left(-6,5\right), \left(2,5\right)\)
Answer 2.
\(\left\{-6,2\right\}\)
Answer 3.
\(\left(-\infty ,-6\right)\cup \left(2,\infty \right)\)

13.8.8.71.

Answer 1.
\(\left(-2,3\right), \left(2,-1\right)\)
Answer 2.
\(\left\{-2,2\right\}\)
Answer 3.
\(\left(-\infty ,-2\right)\cup \left(2,\infty \right)\)

13.8.8.73.

Answer 1.
\(\left(3,1\right), \left(5,3\right)\)
Answer 2.
\(\left\{3,5\right\}\)
Answer 3.
\(\left(3,5\right)\)

13.8.8.75.

Answer 1.
\(\left(-\infty ,0\right)\cup \left(6,\infty \right)\)
Answer 2.
\(\left[0,6\right]\)
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