13.1.1: Chapter 1

Last updated

Feb 19, 2024
Save as PDF
- 13.1: Answer Key
- 13.1.2: Chapter 2

$\newcommand{\vecs}[1]{\overset { \scriptstyle \rightharpoonup} {\mathbf{#1}} }$

$\newcommand{\vecd}[1]{\overset{-\!-\!\rightharpoonup}{\vphantom{a}\smash {#1}}}$

$\newcommand{\id}{\mathrm{id}}$ $\newcommand{\Span}{\mathrm{span}}$

( \newcommand{\kernel}{\mathrm{null}\,}\) $\newcommand{\range}{\mathrm{range}\,}$

$\newcommand{\RealPart}{\mathrm{Re}}$ $\newcommand{\ImaginaryPart}{\mathrm{Im}}$

$\newcommand{\Argument}{\mathrm{Arg}}$ $\newcommand{\norm}[1]{\| #1 \|}$

$\newcommand{\inner}[2]{\langle #1, #2 \rangle}$

$\newcommand{\Span}{\mathrm{span}}$

$\newcommand{\id}{\mathrm{id}}$

$\newcommand{\Span}{\mathrm{span}}$

$\newcommand{\kernel}{\mathrm{null}\,}$

$\newcommand{\range}{\mathrm{range}\,}$

$\newcommand{\RealPart}{\mathrm{Re}}$

$\newcommand{\ImaginaryPart}{\mathrm{Im}}$

$\newcommand{\Argument}{\mathrm{Arg}}$

$\newcommand{\norm}[1]{\| #1 \|}$

$\newcommand{\inner}[2]{\langle #1, #2 \rangle}$

$\newcommand{\Span}{\mathrm{span}}$ $\newcommand{\AA}{\unicode[.8,0]{x212B}}$

$\newcommand{\vectorA}[1]{\vec{#1}} % arrow$

$\newcommand{\vectorAt}[1]{\vec{\text{#1}}} % arrow$

$\newcommand{\vectorB}[1]{\overset { \scriptstyle \rightharpoonup} {\mathbf{#1}} }$

$\newcommand{\vectorC}[1]{\textbf{#1}}$

$\newcommand{\vectorD}[1]{\overrightarrow{#1}}$

$\newcommand{\vectorDt}[1]{\overrightarrow{\text{#1}}}$

$\newcommand{\vectE}[1]{\overset{-\!-\!\rightharpoonup}{\vphantom{a}\smash{\mathbf {#1}}}}$

$\newcommand{\vecs}[1]{\overset { \scriptstyle \rightharpoonup} {\mathbf{#1}} }$

$\newcommand{\vecd}[1]{\overset{-\!-\!\rightharpoonup}{\vphantom{a}\smash {#1}}}$

$\newcommand{\avec}{\mathbf a}$

$\newcommand{\bvec}{\mathbf b}$

$\newcommand{\cvec}{\mathbf c}$

$\newcommand{\dvec}{\mathbf d}$

$\newcommand{\dtil}{\widetilde{\mathbf d}}$

$\newcommand{\evec}{\mathbf e}$

$\newcommand{\fvec}{\mathbf f}$

$\newcommand{\nvec}{\mathbf n}$

$\newcommand{\pvec}{\mathbf p}$

$\newcommand{\qvec}{\mathbf q}$

$\newcommand{\svec}{\mathbf s}$

$\newcommand{\tvec}{\mathbf t}$

$\newcommand{\uvec}{\mathbf u}$

$\newcommand{\vvec}{\mathbf v}$

$\newcommand{\wvec}{\mathbf w}$

$\newcommand{\xvec}{\mathbf x}$

$\newcommand{\yvec}{\mathbf y}$

$\newcommand{\zvec}{\mathbf z}$

$\newcommand{\rvec}{\mathbf r}$

$\newcommand{\mvec}{\mathbf m}$

$\newcommand{\zerovec}{\mathbf 0}$

$\newcommand{\onevec}{\mathbf 1}$

$\newcommand{\real}{\mathbb R}$

$\newcommand{\twovec}[2]{\left[\begin{array}{r}#1 \\ #2 \end{array}\right]}$

$\newcommand{\ctwovec}[2]{\left[\begin{array}{c}#1 \\ #2 \end{array}\right]}$

$\newcommand{\threevec}[3]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \end{array}\right]}$

$\newcommand{\cthreevec}[3]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \end{array}\right]}$

$\newcommand{\fourvec}[4]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \\ #4 \end{array}\right]}$

$\newcommand{\cfourvec}[4]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \\ #4 \end{array}\right]}$

$\newcommand{\fivevec}[5]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \\ #4 \\ #5 \\ \end{array}\right]}$

$\newcommand{\cfivevec}[5]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \\ #4 \\ #5 \\ \end{array}\right]}$

$\newcommand{\mattwo}[4]{\left[\begin{array}{rr}#1 \amp #2 \\ #3 \amp #4 \\ \end{array}\right]}$

$\newcommand{\laspan}[1]{\text{Span}\{#1\}}$

$\newcommand{\bcal}{\cal B}$

$\newcommand{\ccal}{\cal C}$

$\newcommand{\scal}{\cal S}$

$\newcommand{\wcal}{\cal W}$

$\newcommand{\ecal}{\cal E}$

$\newcommand{\coords}[2]{\left\{#1\right\}_{#2}}$

$\newcommand{\gray}[1]{\color{gray}{#1}}$

$\newcommand{\lgray}[1]{\color{lightgray}{#1}}$

$\newcommand{\rank}{\operatorname{rank}}$

$\newcommand{\row}{\text{Row}}$

$\newcommand{\col}{\text{Col}}$

$\renewcommand{\row}{\text{Row}}$

$\newcommand{\nul}{\text{Nul}}$

$\newcommand{\var}{\text{Var}}$

$\newcommand{\corr}{\text{corr}}$

$\newcommand{\len}[1]{\left|#1\right|}$

$\newcommand{\bbar}{\overline{\bvec}}$

$\newcommand{\bhat}{\widehat{\bvec}}$

$\newcommand{\bperp}{\bvec^\perp}$

$\newcommand{\xhat}{\widehat{\xvec}}$

$\newcommand{\vhat}{\widehat{\vvec}}$

$\newcommand{\uhat}{\widehat{\uvec}}$

$\newcommand{\what}{\widehat{\wvec}}$

$\newcommand{\Sighat}{\widehat{\Sigma}}$

$\newcommand{\lt}{<}$

$\newcommand{\gt}{>}$

$\newcommand{\amp}{&}$

$\definecolor{fillinmathshade}{gray}{0.9}$

Try It

1.1

ⓐ yes ⓑ yes ⓒ no ⓓ yes
ⓔ no

1.2

ⓐ no ⓑ yes ⓒ yes ⓓ no
ⓔ no

1.3

$2 \cdot 2 \cdot 2 \cdot 2 \cdot 5$

1.4

$2 \cdot 2 \cdot 3 \cdot 5$

1.5

$36$

1.6

$72$

1.7

1.8

1.9

1.10

1.11

ⓐ 9 ⓑ 64 ⓒ40

1.12

ⓐ 216 ⓑ 64 ⓒ 185

1.13

$10 x^{2} + 16 x + 17$

1.14

$12 y^{2} + 9 y + 7$

1.15

ⓐ $14 x^{2} - 13$ ⓑ $12 x \div 2$
ⓒ $z + 13$ ⓓ $8 x - 18$

1.16

ⓐ $17 y^{2} + 19$ ⓑ $7 y$
ⓒ $x + 11$ ⓓ $11 a - 14$

1.17

ⓐ $4 (p + q)$ ⓑ $4 p + q$

1.18

ⓐ $2 x - 8$ ⓑ $2 (x - 8)$

1.19

$w - 7$

1.20

$l - 6$

1.21

$4 q - 8$

1.22

$7 n + 3$

1.23

ⓐ $=$ ⓑ $>$ ⓒ $<$
ⓓ $=$

1.24

ⓐ $>$ ⓑ $=$ ⓒ $>$
ⓓ $<$

1.25

1.26

1.27

ⓐ $−6$ ⓑ 2 ⓒ $−2$

1.28

ⓐ $−7$ ⓑ 3 ⓒ $−3$

1.29

ⓐ 2 ⓑ $−2$ ⓒ $−10$ ⓓ 10

1.30

ⓐ 3 ⓑ $−3$ ⓒ $−11$ ⓓ 11

1.31

ⓐ $8, 8$ ⓑ $−18,$ $−18$
ⓒ $19, 19$ ⓓ $−4,$ $−4$

1.32

ⓐ $8, 8$ ⓑ $−22,$ $−22$
ⓒ $23, 23$ ⓓ $3, 3$

1.33

1.34

1.35

ⓐ 23 ⓑ 60 ⓒ $−63$ ⓓ $−9$

1.36

ⓐ 39 ⓑ 39 ⓒ −28 ⓓ −7

1.37

ⓐ 81 ⓑ $−81$

1.38

ⓐ 49 ⓑ $−49$

1.39

ⓐ 4 ⓑ 21

1.40

ⓐ 9 ⓑ 6

1.41

1.42

1.43

$(9 + (−16)) + 4; - 3$

1.44

$(−8 + (−12)) + 7; - 13$

1.45

The difference in temperatures was 45 degrees.

1.46

The difference in temperatures was 9 degrees.

1.47

$- \frac{23}{40}$

1.48

$- \frac{5}{8}$

1.49

$−33 a$

1.50

$−26 b$

1.51

$\frac{4}{15}$

1.52

$\frac{2}{3}$

1.53

$\frac{3}{4 b}$

1.54

$\frac{4}{q}$

1.55

$\frac{79}{60}$

1.56

$\frac{103}{60}$

1.57

ⓐ $\frac{27 a - 32}{36}$ ⓑ $\frac{2 a}{3}$

1.58

ⓐ $\frac{24 k - 5}{30}$ ⓑ $\frac{2 k}{15}$

1.59

1.60

1.61

$\frac{1}{90}$

1.62

272

1.63

1.64

$\frac{2}{7}$

1.65

$- \frac{1}{2}$

1.66

$\frac{2}{3}$

1.67

ⓐ $6.58$ ⓑ $6.6$ ⓒ 7

1.68

ⓐ $15.218$ ⓑ $15.22$
ⓒ $15.2$

1.69

ⓐ $−16.49$ ⓑ $−0.42$

1.70

ⓐ $−23.593$ ⓑ $−12.58$

1.71

$−27.4815$

1.72

$−87.6148$

1.73

ⓐ 25.8 ⓑ 258 ⓒ 2,580

1.74

ⓐ 142 ⓑ 1,420 ⓒ 14,200

1.75

$587.3$

1.76

$34.25$

1.77

ⓐ $\frac{117}{500}$ ⓑ $−0.875$

1.78

ⓐ $\frac{3}{125}$ ⓑ $−0.375$

1.79

ⓐ 0.09, 0.87, 0.039 ⓑ 17%, 175%, 8.25%

1.80

ⓐ 0.03, 0.91, 0.083 ⓑ 41%, 225%, 9.25%

1.81

ⓐ 6 ⓑ 13 ⓒ $−15$

1.82

ⓐ 4 ⓑ 14 ⓒ $−10$

1.83

ⓐ $4, \sqrt{49}$ ⓑ $−3, 4, \sqrt{49}$
ⓒ $−3, 0. \bar{3}, \frac{9}{5}, 4, \sqrt{49}$ ⓓ $− \sqrt{2}$
ⓔ $−3, − \sqrt{2}, 0. \bar{3}, \frac{9}{5}, 4, \sqrt{49}$

1.84

ⓐ $6, \sqrt{121}$
ⓑ $− \sqrt{25}, −1, 6, \sqrt{121}$
ⓒ $− \sqrt{25}, - \frac{3}{8}, −1, 6, \sqrt{121}$
ⓓ $2.041975.. .$
ⓔ $− \sqrt{25}, - \frac{3}{8}, −1, 6, \sqrt{121}, 2.041975.. .$

1.85

$Figure shows a number line with numbers ranging from minus 4 to 5. Various points on the line are highlighted. From left to right, these are: minus 8 by 3, minus 7 by 4, minus 1, 1 by 3, 6 by 5, 9 by 2 and 5.$

1.86

$Figure shows a number line with numbers ranging from minus 4 to 5. Various points on the line are highlighted. From left to right, these are: minus 7 by 3, minus 2, minus 7 by 4, 2 by 3, 7 by 5, 3 and 7 by 2.$

1.87

ⓐ

$Figure shows a number line with numbers ranging from 0 to 1. 0.6 is highlighted.$

ⓑ

$Figure shows a number line with numbers ranging from minus 1.00 to 0.00. Minus 0.74 is highlighted, minus 0.25 is highlighted.$

1.88

ⓐ

$Figure shows a number line with numbers ranging from 0 to 1. 0.9 is highlighted.$

ⓑ

$Figure shows a number line with numbers ranging from minus 1.00 to 0.00. Minus 0.74 is highlighted.$

1.89

$32 r + 29 s$

1.90

$41 m + 6 n$

1.91

$1 \frac{7}{15}$

1.92

$1 \frac{2}{9}$

1.93

$−48 a$

1.94

$−92 x$

1.95

$\frac{5}{49}$

1.96

$\frac{11}{25}$

1.97

ⓐ 0 ⓑ undefined

1.98

ⓐ 0 ⓑ undefined

1.99

$4 x + 8$

1.100

$6 x + 42$

1.101

$5 y + 3$

1.102

$4 n + 9$

1.103

$70 + 15 p$

1.104

$4 + 35 d$

1.105

$−10 + 15 a$

1.106

$−56 + 105 y$

1.107

$− z + 11$

1.108

$− x + 4$

1.109

$3 - 3 x$

1.110

$2 x - 20$

1.111

$5 x - 66$

1.112

$7 x - 13$

Section 1.1 Exercises

Divisible by 2, 3, 6

Divisible by 2

Divisible by 3, 5

$2 \cdot 43$

$5 \cdot 7 \cdot 13$

11.

$2 \cdot 2 \cdot 2 \cdot 2 \cdot 3 \cdot 3 \cdot 3$

13.

15.

280

17.

440

19.

21.

23.

25.

149

27.

29.

31.

ⓐ 64 ⓑ 16 ⓒ 7

33.

35.

37.

$10 x + 6$

39.

$22 a + 1$

41.

$17 x^{2} + 20 x + 16$

43.

ⓐ $5 x^{2} - 6 x y$ ⓑ $\frac{6 y^{2}}{5 x}$
ⓒ $y^{2} + 21$ ⓓ $81 x^{2} - 6 x$

45.

ⓐ $4 a b^{2} + 3 a^{2} b$ ⓑ $20 x y^{2}$
ⓒ $m + 15$ ⓓ $121 x^{2} - 9 x$

47.

ⓐ $8 (y - 9)$ ⓑ $8 y - 9$

49.

ⓐ $5 (3 x + y)$ ⓑ $15 x + y$

51.

$2 c + 14$

53.

$3 n - 7$

55.

Answers will vary.

57.

Answers will vary.

Section 1.2 Exercises

59.

ⓐ $>$ ⓑ $>$ ⓒ $>$ ⓓ $>$

61.

ⓐ $=$ ⓑ $=$ ⓒ $>$ ⓓ $=$

63.

65.

67.

69.

71.

ⓐ $−11$ ⓑ $−3$ ⓒ $3$

73.

75.

$−22$

77.

$29$

79.

ⓐ 6 ⓑ $−6$ ⓒ $−20$ ⓓ $20$

81.

$−59$

83.

85.

ⓐ 16 ⓑ16

87.

ⓐ 45 ⓑ45

89.

91.

93.

95.

ⓐ $−32$ ⓑ $−65$ ⓒ $−4$
ⓓ $13$

97.

ⓐ $−4$ ⓑ $−12$ ⓒ $−39$
ⓓ $14$

99.

ⓐ $64$ ⓑ $−64$

101.

$−47$

103.

$90$

105.

$9$

107.

$41$

109.

$−9$

111.

$−29$

113.

$1$

115.

$−3$

117.

$5$

119.

ⓐ $−47$ ⓑ $16$

121.

$121$

123.

$−56$

125.

$6$

127.

$(3 + (−15)) + 7; - 5$

129.

ⓐ $10 - (−18); 28$
ⓑ $−25 - 11; - 36$

131.

$\frac{−6}{a + b}$

133.

$96 °$

135.

21 yards

137.

$− $ 28$

139.

Answers will vary.

141.

Answers will vary.

Section 1.3 Exercises

143.

$- \frac{12}{7}$

145.

$\frac{10}{21}$

147.

$\frac{2 x^{2}}{3 y}$

149.

$- \frac{21 a^{2}}{11 b^{2}}$

151.

$\frac{1}{3}$

153.

$- \frac{21}{50}$

155.

$\frac{11}{30}$

157.

$9 n$

159.

$\frac{33}{4 x}$

161.

$- \frac{4}{9}$

163.

$\frac{10 u}{9 v}$

165.

$- \frac{1}{16}$

167.

$- \frac{10}{9}$

169.

$- \frac{2}{5}$

171.

$\frac{2 m}{3 n}$

173.

$\frac{29}{24}$

175.

$\frac{1}{48}$

177.

$\frac{17}{105}$

179.

$- \frac{53}{40}$

181.

$\frac{1}{12}$

183.

$\frac{4 x + 3}{12}$

185.

ⓐ $\frac{5}{6}$ ⓑ $4$

187.

ⓐ $\frac{25 n}{16}$ ⓑ $\frac{25 n - 16}{30}$

189.

ⓐ $\frac{−8 x - 15}{18}$ ⓑ $- \frac{10 k}{27}$

191.

ⓐ $\frac{−5 (a + 1)}{3}$ ⓑ $a$

193.

$\frac{9}{7}$

195.

$−8$

197.

$\frac{11}{6}$

199.

$\frac{5}{2}$

201.

$54$

203.

$\frac{49}{25}$

205.

$\frac{15}{4}$

207.

$\frac{5}{21}$

209.

$\frac{5}{4}$

211.

$\frac{1}{24}$

213.

$\frac{−28 - 15 y}{60}$

215.

$\frac{33}{64}$

217.

$\frac{7}{9}$

219.

$−5$

221.

$\frac{23}{24}$

223.

$\frac{11}{5}$

225.

$1$

227.

$\frac{13}{3}$

229.

ⓐ $\frac{1}{5}$ ⓑ $\frac{6}{5}$

231.

$- \frac{1}{9}$

233.

$- \frac{5}{11}$

235.

Answers will vary.

237.

Answers will vary.

Section 1.4 Exercises

239.

ⓐ 5.78 ⓑ 5.8 ⓒ 6

241.

ⓐ 0.30 ⓑ 0.3 ⓒ 0

243.

ⓐ 63.48 ⓑ 63.5 ⓒ 63

245.

$−40.91$

247.

$−7.22$

249.

$−27.5$

251.

$102.212$

253.

$51.31$

255.

$−4.89$

257.

$−1200.47982$

259.

$337.8914$

261.

$1.305$

263.

$92.4$

265.

2.5

267.

55200

269.

$$ 2.44$

271.

$−4.8$

273.

$2.08$

275.

$\frac{1}{25}$

277.

$\frac{19}{200}$

279.

$0.85$

281.

$−12.4$

283.

$0.71$

285.

$0.393$

287.

$156 %$

289.

$6.25 %$

291.

293.

295.

$−10$

297.

ⓐ $0, \sqrt{36}, 9$ ⓑ $−8, 0, \sqrt{36}, 9$ ⓒ $−8, 0, \frac{12}{5}, \sqrt{36}, 9$ ⓓ $1.95286...,$ ⓔ $−8, 0, 1.95286..., \frac{12}{5}, \sqrt{36}, 9$

299.

ⓐ none ⓑ $− \sqrt{100}, −7, −1$
ⓒ $− \sqrt{100}, −7, - \frac{8}{3}, −1, 0.77, 3 \frac{1}{4}$
ⓓ none
ⓔ $− \sqrt{100}, −7, - \frac{8}{3}, −1, 0.77, 3 \frac{1}{4}$

301.

$Figure shows a number line with numbers ranging from 0 to 6. Some values are highlighted. From left to right, these are: 3 by 10, 11 by 6, 7 by 2 and 4.$

303.

$Figure shows a number line with numbers ranging from minus 4 to 4. Some values are highlighted. From left to right, these are: minus 5 by 2, minus 1 and two thirds, minus 3 by 4, 3 by 4, 1 and two thirds, and 5 by 2.$

305.

$Figure shows a number line with numbers ranging from minus 4 to 4. Two values are highlighted. One is between minus 2 and minus 1. The other is between 0 and 1.$

307.

$Figure shows a number line with numbers ranging from minus 4 to 4. Two values are highlighted. One is between minus 2 and minus 1. The other is between 3 and 4.$

309.

Answers will vary.

311.

Answers will vary.

Section 1.5 Exercises

313.

$27 m + (−21 n)$

315.

$\frac{5}{4} g + \frac{1}{2} h$

317.

$2.43 p + 8.26 q$

319.

$−63$

321.

$1 \frac{5}{6}$

323.

$17$

325.

$14.88$

327.

$10 p$

329.

$44$

331.

$\frac{7}{8}$

333.

$d$

335.

$\frac{49}{11}$

337.

339.

undefined

341.

undefined

343.

$32 y + 72$

345.

$6 c - 78$

347.

$\frac{3}{4} q + 3$

349.

$5 y - 3$

351.

$3 + 8 r$

353.

$36 d + 90$

355.

$r s - 18 r$

357.

$y p + 4 p$

359.

$−28 p - 7$

361.

$−3 x + 18$

363.

$−3 x + 7$

365.

$−3 y - 8$

367.

$−33 c + 26$

369.

$− a + 19$

371.

$4 m - 10$

373.

$72 x - 25$

375.

$22 n + 9$

377.

$6 c + 34$

379.

$12 y + 63$

381.

Answers will vary.

383.

Answers will vary.

Review Exercises

385.

Divisible by $2, 3, 5, 6, 10$

387.

120

389.

391.

393.

$6 x^{2} - x + 5$

395.

ⓐ $11 (y - 2)$ ⓑ $11 y - 2$

397.

399.

$−9$

401.

403.

ⓐ 40 ⓑ 40

405.

407.

409.

$−12$

411.

413.

$(−4 + (−9)) + 23; 10$

415.

$46^{°}$

417.

$- \frac{15 x^{3}}{11 y^{2}}$

419.

$\frac{8 x}{15 y}$

421.

$\frac{31}{36}$

423.

ⓐ $\frac{11}{8}$ ⓑ $\frac{5}{6}$

425.

$- \frac{1}{6}$

427.

429.

$- \frac{1}{5}$

431.

$6.17$

433.

$96.978$

435.

488.1813

437.

$56.3$

439.

$−2.3$

441.

$- \frac{48}{5}$

443.

$1. \bar{27}$

445.

$4.75 %$

447.

no real number

449.

$Figure shows a number line with numbers ranging from minus 4 to 4. Some values are highlighted.$

451.

$\frac{3}{4} x + y$

453.

$1 \frac{11}{15}$

455.

$\frac{9}{17}$

457.

undefined

459.

$8 b + 10$

461.

$x p - 5 p$

463.

$−6 x - 6$

465.

$6 y + 16$

Practice Test

467.

$7 n + 7$

469.

$−8 - 11; - 19$

$(−8 - (−3)) + 5; 0$

471.

ⓐ $28.15$ ⓑ $28.146$

473.

$Figure shows a number line with numbers ranging from minus 4 to 4. Some values are highlighted.$

475.

477.

$−8$

479.

$\frac{15}{17}$

481.

$- \frac{5}{3}$

483.

$3$

485.

$- \frac{7}{6}$

487.

$−65.4$

489.

−160

491.

$1 \frac{8}{13}$

493.

ⓐ 0 ⓑ undefined

495.

$13 y - 3$

Search

Text Color

Text Size

Margin Size

Font Type

Try It

Section 1.1 Exercises

Section 1.2 Exercises

Section 1.3 Exercises

Section 1.4 Exercises

Section 1.5 Exercises

Review Exercises

Practice Test

Try It

Section 1.1 Exercises

Section 1.2 Exercises

Section 1.3 Exercises

Section 1.4 Exercises

Section 1.5 Exercises

Review Exercises

Practice Test

Support Center

How can we help?