Chapter 4 Test an Introduction to Functions Review

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4.6

$\left(\mathrm{v},\mathrm{-iv}\right)$

4.9

infinitely many solutions

4.10

infinitely many solutions

four.11

ⓐ no solution, inconsistent, contained ⓑ 1 solution, consequent, independent

4.12

ⓐ no solution, inconsistent, contained ⓑ one solution, consistent, independent

4.14

$\left(\mathrm{-3},5\right)$

4.15

$\left(2,\frac{3}{2}\right)$

4.16

$\left(-\frac{\mathrm{ane}}{2},\mathrm{-2}\right)$

4.17

$\left(2,\mathrm{-1}\right)$

4.18

$\left(\mathrm{-ii},3\right)$

four.20

$\left(4,\mathrm{-3}\right)$

four.22

$\left(\mathrm{ane},\mathrm{-ii}\right)$

4.23

infinitely many solutions

four.24

infinitely many solutions

4.25

ⓐ Since both equations are in standard grade, using emptying will be about user-friendly. ⓑ Since 1 equation is already solved for x, using commutation will be most convenient.

iv.26

ⓐ Since 1 equation is already solved for y, using exchange volition be almost convenient. ⓑ Since both equations are in standard course, using emptying volition exist virtually convenient.

four.31

Mark burned xi calories for each minute of yoga and 7 calories for each infinitesimal of jumping jacks.

four.32

Erin burned 11 calories for each minute on the rowing machine and 5 calories for each minute of weight lifting.

4.33

The angle measures are 55 and 35.

4.34

The bending measures are 5 and 85.

4.35

The bending measures are 42 and 138.

4.36

The angle measures are 66 and 114.

four.39

The length is 60 anxiety and the width is 35 feet.

4.40

The length is 60 feet and the width is 38 feet.

4.41

It will accept Clark four hours to catch Mitchell.

four.42

It will accept Sally $\mathrm{i}\frac{\mathrm{one}}{\mathrm{ii}}$ hours to catch upwardly to Charlie.

four.43

The rate of the boat is xi mph and the rate of the electric current is 1 mph.

four.44

The speed of the canoe is 7 mph and the speed of the current is 1 mph.

4.45

The speed of the jet is 235 mph and the speed of the air current is thirty mph.

4.46

The speed of the jet is 408 mph and the speed of the current of air is 24 mph.

4.47

206 adults, 347 children

4.48

42 adults, 105 children

4.49

13 dimes and 29 quarters

4.50

19 quarters and 51 nickels

4.51

three pounds peanuts and two pounds cashews

4.52

10 pounds of beans, 10 pounds of basis beef

4.53

120 ml of 25% solution and 30 ml of 50% solution

4.54

125 ml of 10% solution and 125 ml of forty% solution

iv.55

$42,000 in the stock fund and $8000 in the savings account

4.56

$1750 at 11% and $5250 at thirteen%

4.57

Depository financial institution $4,000; Federal $14,000

4.58

$41,200 at 4.5%, $24,000 at seven.two%

iv.59

ⓐ $C(\mathrm{10})=\mathrm{xv}x+25,500$

ⓑ $R(\mathrm{10})=32x$

ⓒ

ⓓ $\mathrm{1,500}$ ; when 1,500 benches are sold, the cost and acquirement will exist both 48,000

four.60

ⓐ $C(x)=120x+\mathrm{150,000}$

ⓑ $R(x)=170\mathrm{10}$

ⓒ

ⓓ $\mathrm{iii,000}$ ; when 3,000 benches are sold, the revenue and costs are both $510,000

4.63

$\left(2,\mathrm{-1},\mathrm{three}\right)$

4.64

$\left(\mathrm{-2},3,\mathrm{four}\right)$

4.65

$\left(\mathrm{-iii},4,\mathrm{-2}\right)$

four.66

$\left(\mathrm{-2},\mathrm{three},\mathrm{-1}\right)$

4.69

infinitely many solutions $\left(x,\mathrm{iii},z\right)$ where $x=z-\mathrm{three};y=3;z$ is any real number

iv.seventy

infinitely many solutions $\left(\mathrm{10},y,z\right)$ where $x=5z-2;y=4z-3;z$ is whatever real number

iv.71

The fine arts section sold 75 adult tickets, 200 student tickets, and 75 kid tickets.

4.72

The soccer squad sold 200 adult tickets, 300 educatee tickets, and 100 child tickets.

4.73

ⓐ $\left[\begin{array}{ccccccc}3\hfill & & & 8\hfill & & & \hfill \mathrm{-3}\\ 2\hfill & & & 5\hfill & & & \hfill \mathrm{-3}\end{array}\right]$
ⓑ $\left[\begin{array}{cccccccccc}2\hfill & & & \hfill \mathrm{-5}& & & \mathrm{three}\hfill & & & \hfill 8\\ \mathrm{three}\hfill & & & \hfill \mathrm{-one}& & & 4\hfill & & & \hfill 7\\ 1\hfill & & & \hfill 3& & & \mathrm{ii}\hfill & & & \hfill \mathrm{-3}\end{array}\right]$

iv.74

ⓐ $\left[\begin{array}{ccccccc}11\hfill & & & 9\hfill & & & \hfill \mathrm{-5}\\ \mathrm{seven}\hfill & & & \mathrm{v}\hfill & & & \hfill \mathrm{-1}\end{array}\right]$
ⓑ $\left[\begin{array}{cccccccccc}\mathrm{v}\hfill & & & \hfill \mathrm{-3}& & & \hfill 2& & & \hfill \mathrm{-5}\\ 2\hfill & & & \hfill \mathrm{-i}& & & \hfill \mathrm{-1}& & & \hfill \mathrm{iv}\\ \mathrm{iii}\hfill & & & \hfill \mathrm{-two}& & & \hfill 2& & & \hfill \mathrm{-7}\end{array}\right]$

iv.75

$\{\begin{array}{c}x-y+\mathrm{ii}z=3\hfill \\ \mathrm{two}\mathrm{ten}+y-\mathrm{two}z=1\hfill \\ \mathrm{iv}x-y+2z=0\hfill \end{array}$

4.76

$\{\begin{array}{c}\mathrm{10}+y+z=\mathrm{four}\hfill \\ \mathrm{ii}\mathrm{ten}+3y-z=8\hfill \\ \mathrm{ten}+y-z=3\hfill \end{array}$

4.77

ⓐ $\left[\begin{array}{cccccccccc}\hfill \mathrm{-2}& & & \hfill \mathrm{three}& & & \hfill 0& & & \hfill \mathrm{-2}\\ \hfill 4& & & \hfill \mathrm{-1}& & & \hfill \mathrm{-four}& & & \hfill 4\\ \hfill \mathrm{five}& & & \hfill \mathrm{-2}& & & \hfill \mathrm{-2}& & & \hfill \mathrm{-2}\end{array}\right]$
ⓑ $\left[\begin{array}{cccccccccc}\hfill \mathrm{-two}& & & \hfill 3& & & \hfill 0& & & \hfill \mathrm{-ii}\\ \hfill \mathrm{four}& & & \hfill \mathrm{-1}& & & \hfill \mathrm{-4}& & & \hfill 4\\ 15\hfill & & & \hfill \mathrm{-6}& & & \hfill \mathrm{-6}& & & \hfill \mathrm{-6}\end{array}\right]$
ⓒ $\left[\begin{array}{ccccccccccccc}\hfill \mathrm{-2}& & & \hfill 3& & & \hfill 0& & & \hfill \mathrm{-2}& & & \\ \hfill \mathrm{three}& & & \hfill 4& & & \hfill \mathrm{-13}& & & \hfill \mathrm{-16}& & & \hfill \mathrm{-8}\\ \hfill 15& & & \hfill \mathrm{-6}& & & \hfill \mathrm{-6}& & & \hfill \mathrm{-half\; dozen}& & & \end{array}\right]$

4.78

ⓐ $\left[\begin{array}{cccccccccc}\mathrm{four}\hfill & & & \hfill \mathrm{ane}& & & \hfill \mathrm{-three}& & & \hfill 2\\ \mathrm{two}\hfill & & & \hfill \mathrm{-3}& & & \hfill \mathrm{-ii}& & & \hfill \mathrm{-4}\\ 5\hfill & & & \hfill 0& & & \hfill 4& & & \hfill \mathrm{-one}\end{array}\right]$
ⓑ $\left[\begin{array}{cccccccccc}8\hfill & & & \hfill 2& & & \hfill \mathrm{-6}& & & \hfill 4\\ \mathrm{two}\hfill & & & \hfill \mathrm{-3}& & & \hfill \mathrm{-2}& & & \hfill \mathrm{-4}\\ \mathrm{v}\hfill & & & \hfill 0& & & \hfill 4& & & \hfill \mathrm{-1}\end{array}\right]$
ⓒ $\left[\begin{array}{cccccccccc}14\hfill & & & \hfill \mathrm{-seven}& & & \hfill \mathrm{-12}& & & \hfill \mathrm{-8}\\ \mathrm{two}\hfill & & & \hfill \mathrm{-3}& & & \hfill \mathrm{-2}& & & \hfill \mathrm{-4}\\ 5\hfill & & & \hfill 0& & & \hfill \mathrm{four}& & & \hfill \mathrm{-1}\end{array}\right]$

4.79

$\left[\begin{array}{ccccccc}1\hfill & & & \hfill \mathrm{-1}& & & \hfill \mathrm{ii}\\ 0\hfill & & & \hfill \mathrm{-iii}& & & \hfill \mathrm{-4}\end{array}\right]$

iv.fourscore

$\left[\begin{array}{ccccccc}1\hfill & & & \hfill \mathrm{-1}& & & \hfill \mathrm{iii}\\ 0\hfill & & & \hfill \mathrm{-5}& & & \hfill \mathrm{viii}\end{array}\right]$

4.81

The solution is $\left(4,\mathrm{-ane}\right).$

iv.82

The solution is $\left(\mathrm{-2},0\right).$

4.83

$\left(\mathrm{vi},\mathrm{-1},\mathrm{-3}\right)$

4.84

$(\mathrm{v},7,4)$

four.87

infinitely many solutions $\left(x,y,z\right)\text{,}$ where $x=z-3;y=3;z$ is whatever existent number.

iv.88

infinitely many solutions $\left(\mathrm{ten},y,z\right)\text{,}$ where $x=5z-2;y=4z-3;z$ is any real number.

4.97

$(-\frac{15}{\mathrm{vii}},\frac{24}{7})$

4.98

$(\mathrm{-2},0)$

iv.99

$\left(\mathrm{-ix},\mathrm{iii},\mathrm{-1}\right)$

4.100

$\left(\mathrm{-6},\mathrm{iii},\mathrm{-2}\right)$

4.107

The solution is the grey region.

4.108

The solution is the grayness region.

4.109

The solution is the grey region.

iv.110

The solution is the grey region.

4.111

The solution is the gray region.

iv.112

The solution is the grey region.

four.115

The solution is the grey region.

four.116

The solution is the gray region.

4.117

ⓐ $\{\begin{array}{c}\mathrm{thirty}m+20p\le 160\hfill \\ \mathrm{two}m+\mathrm{three}p\le 15\hfill \end{array}$
ⓑ

ⓒ aye
ⓓ no

iv.118

ⓐ $\{\begin{array}{c}a\ge p+5\hfill \\ a+\mathrm{two}p\le 400\hfill \end{array}$
ⓑ

ⓒ no
ⓓ no

4.119

ⓐ $\{\begin{array}{c}0.75d+\mathrm{ii}e\le 25\hfill \\ 360d+110e\ge \mathrm{m}\hfill \end{array}$
ⓑ

ⓒ yes
ⓓ no

4.120

ⓐ $\{\begin{array}{c}140p+125j\ge 1000\hfill \\ \mathrm{1.eighty}p+\mathrm{ane.25}j\le 12\hfill \end{array}$
ⓑ

ⓒ aye
ⓓ no

Section 4.1 Exercises

5 .

$(\mathrm{-2},\mathrm{iii})$

11 .

$(\mathrm{-2},2)$

15 .

$(6,\mathrm{-iv})$

25 .

No solutions, inconsistent, independent

27 .

one point, consistent and independent

29 .

space solutions, consistent, dependent

31 .

$\left(1,\mathrm{-4}\right)$

33 .

$\left(\mathrm{-3},2\right)$

35 .

$\left(\mathrm{-1}\text{/}2,5\text{/}\mathrm{two}\right)$

37 .

$\left(\mathrm{-5},\mathrm{four}\right)$

39 .

$\left(0,\mathrm{ten}\right)$

41 .

$\left(\mathrm{iv},\mathrm{-2}\right)$

49 .

$\left(7,12\right)$

51 .

$\left(\mathrm{-3},\mathrm{-5}\right)$

53 .

$\left(2,\mathrm{-iii}\right)$

55 .

$\left(\mathrm{-11},\mathrm{ii}\right)$

57 .

$\left(6\text{/}\mathrm{-nine},24\text{/}7\right)$

59 .

$\left(\mathrm{-three},2\right)$

65 .

ⓐ commutation ⓑ emptying

67 .

ⓐ elimination ⓑ substituion

Section iv.2 Exercises

81 .

Eighty cable packages would need to be sold to brand the full pay the same.

83 .

Mitchell would need to sell 120 stoves for the companies to be equal.

87 .

1000 calories playing basketball game and 400 calories canoeing

89 .

Oranges cost $2 per pound and bananas cost $ane per pound

91 .

Package of paper $4, stapler $7

93 .

Hot dog 150 calories, cup of cottage cheese 220 calories

95 .

Owen volition need 80 quarts of h2o and 20 quarts of concentrate to make 100 quarts of lemonade.

97 .

$53.5$ degrees and $36.5$ degrees

99 .

16 degrees and 74 degrees

101 .

134 degrees and 46 degrees

103 .

37 degrees and 143 degrees

109 .

Width is 41 feet and length is 118 feet.

111 .

Width is 10 feet and length is twoscore feet.

117 .

Boat rate is sixteen mph and electric current charge per unit is 4 mph.

119 .

Gunkhole rate is xviii mph and current rate is 2 mph.

121 .

Jet rate is 265 mph and air current speed is 22 mph.

123 .

Jet rate is 415 mph and wind speed is 25 mph.

Section four.iii Exercises

127 .

110 adult tickets, 190 child tickets

129 .

half-dozen skillful seats, 10 inexpensive seats

131 .

92 adult tickets, 220 children tickets

133 .

xiii nickels, 3 dimes

135 .

42 dimes, 8 quarters

137 .

17 $x bills, 37 $20 bills

139 .

80 pounds basics and forty pounds raisins

141 .

9 pounds of Chicory coffee, 3 pounds of Jamaican Blue Mountain coffee

143 .

10 bags of Chiliad&M'south, 15 bags of Reese's Pieces

145 .

$\mathrm{7.v}$ liters of each solution

147 .

fourscore liters of the 25% solution and twoscore liters of the 10% solution

149 .

240 liters of the 90% solution and 120 liters of the 75% solution

151 .

$1600 at viii%, 960 at half dozen%

153 .

$28,000 at 9%, $36,000 at $5.5\text{\%}$

155 .

$8500 CD, $1500 savings account

157 .

$55,000 on loan at 6% and $30,000 on loan at $4.5\text{\%}$

159 .

ⓐ $C(\mathrm{ten})=5\mathrm{10}+6500$

ⓑ $R(x)=10\mathrm{ten}$

ⓒ

ⓓ one,500; when 1,500 h2o bottles are sold, the toll and the acquirement equal $fifteen,000

Section 4.4 Exercises

167 .

$\left(4,5,\mathrm{two}\right)$

169 .

$\left(\mathrm{seven},12,\mathrm{-2}\right)$

171 .

$\left(\mathrm{-3},\mathrm{-five},4\right)$

173 .

$\left(\mathrm{two},\mathrm{-3},\mathrm{-2}\right)$

175 .

$\left(6,\mathrm{-nine},\mathrm{-iii}\right)$

177 .

$\left(3,\mathrm{-4},\mathrm{-two}\right)$

179 .

$\left(\mathrm{-three},2,3\right)$

181 .

$\left(\mathrm{-2},0,\mathrm{-3}\right)$

185 .

$x=\frac{203}{\mathrm{sixteen}};y=\frac{\mathrm{–25}}{\mathrm{xvi}};z=\frac{\mathrm{–231}}{\mathrm{sixteen}};$

187 .

$\left(x,y,z\right)$ where $x=5z+2;y=\mathrm{-iii}z+1;z$ is any real number

189 .

$\left(\mathrm{ten},y,z\right)$ where $x=5z-\mathrm{ii};y=\mathrm{four}z-3;z$ is any real number

Section four.5 Exercises

197 .

ⓐ $\left[\begin{array}{ccccccc}2\hfill & & & \hfill \mathrm{iv}& & & \hfill \mathrm{-5}\\ \mathrm{three}\hfill & & & \hfill \mathrm{-2}& & & \hfill 2\end{array}\right]$
ⓑ $\left[\begin{array}{cccccccccc}\hfill 3& & & \hfill \mathrm{-2}& & & \hfill \mathrm{-one}& & & \hfill \mathrm{-ii}\\ \hfill \mathrm{-2}& & & \hfill 1& & & \hfill 0& & & \hfill 5\\ \hfill 5& & & \hfill 4& & & \hfill \mathrm{ane}& & & \hfill \mathrm{-one}\end{array}\right]$

199 .

ⓐ $\left[\begin{array}{ccccccc}2\hfill & & & \hfill \mathrm{-5}& & & \hfill \mathrm{-3}\\ \mathrm{four}\hfill & & & \hfill \mathrm{-3}& & & \hfill \mathrm{-i}\end{array}\right]$
ⓑ $\left[\begin{array}{cccccccccc}4\hfill & & & \hfill 3& & & \hfill \mathrm{-2}& & & \hfill \mathrm{-3}\\ \hfill \mathrm{-2}& & & \hfill 1& & & \hfill \mathrm{-3}& & & \hfill \mathrm{four}\\ \mathrm{-i}\hfill & & & \hfill \mathrm{-iv}& & & \hfill 5& & & \hfill \mathrm{-two}\end{array}\right]$

201 .

$\{\begin{array}{c}2x-4y=\mathrm{-ii}\hfill \\ \mathrm{iii}x-3y=\mathrm{-one}\hfill \end{array}$

203 .

$\{\begin{array}{c}2x-\mathrm{ii}y=\mathrm{-1}\hfill \\ \mathrm{ii}y-z=2\hfill \\ \mathrm{three}x-z=\mathrm{-two}\hfill \end{array}$

205 .

ⓐ $\left[\begin{array}{ccccccc}\mathrm{iii}\hfill & & & \hfill 2& & & \hfill 1\\ \mathrm{iv}\hfill & & & \hfill \mathrm{-6}& & & \hfill \mathrm{-3}\end{array}\right]$
ⓑ $\left[\begin{array}{ccccccc}12\hfill & & & \hfill 8& & & \hfill 4\\ 4\hfill & & & \hfill \mathrm{-half\; dozen}& & & \hfill \mathrm{-3}\end{array}\right]$
ⓒ $\left[\begin{array}{ccccccc}12\hfill & & & \hfill 8& & & \hfill 4\\ 24\hfill & & & \hfill \mathrm{-10}& & & \hfill \mathrm{-five}\end{array}\right]$

207 .

ⓐ $\left[\begin{array}{cccccccccc}\hfill \mathrm{two}& & & \hfill \mathrm{ane}& & & \hfill \mathrm{-four}& & & \hfill 5\\ \hfill \mathrm{vi}& & & \hfill \mathrm{-5}& & & \hfill \mathrm{ii}& & & \hfill \mathrm{iii}\\ \hfill \mathrm{three}& & & \hfill \mathrm{-three}& & & \hfill \mathrm{i}& & & \hfill \mathrm{-i}\end{array}\right]$
ⓑ $\left[\begin{array}{cccccccccc}2\hfill & & & \hfill \mathrm{ane}& & & \hfill \mathrm{-4}& & & \hfill \mathrm{five}\\ 6\hfill & & & \hfill \mathrm{-v}& & & \hfill 2& & & \hfill 3\\ \mathrm{iii}\hfill & & & \hfill \mathrm{-iii}& & & \hfill 1& & & \hfill \mathrm{-1}\end{array}\right]$
ⓒ $\left[\begin{array}{cccccccccc}\hfill \mathrm{two}& & & \hfill 1& & & \hfill \mathrm{-4}& & & \hfill 5\\ \hfill 6& & & \hfill \mathrm{-5}& & & \hfill 2& & & \hfill 3\\ \hfill \mathrm{-4}& & & \hfill \mathrm{vii}& & & \hfill \mathrm{-six}& & & \hfill \mathrm{vii}\end{array}\right]$

209 .

$\left[\begin{array}{cccccccccc}\mathrm{ane}\hfill & & & \hfill \mathrm{-two}& & & \hfill 3& & & \hfill \mathrm{-four}\\ 0\hfill & & & \hfill 5& & & \hfill \mathrm{-xi}& & & \hfill 17\\ 0\hfill & & & \hfill 1& & & \hfill \mathrm{-10}& & & \hfill 7\end{array}\right]$

211 .

$\left(1,\mathrm{-1}\right)$

213 .

$\left(3,3\right)$

215 .

$(\mathrm{-two},\mathrm{five},2)$

217 .

$\left(\mathrm{-3},\mathrm{-5},\mathrm{iv}\right)$

219 .

$\left(\mathrm{-3},2,3\right)$

221 .

$\left(\mathrm{-2},0,\mathrm{-3}\right)$

227 .

infinitely many solutions $\left(x,y,z\right)$ where $x=\frac{\mathrm{i}}{\mathrm{two}}z+4;y=\frac{1}{\mathrm{two}}z-6;z$ is whatever real number

229 .

infinitely many solutions $\left(x,y,z\right)$ where $x=\mathrm{five}z+\mathrm{ii};y=\mathrm{-3}z+1;z$ is whatsoever existent number

Section 4.half-dozen Exercises

237 .

ⓐ half dozen ⓑ $\mathrm{-xiv}$ ⓒ $\mathrm{-6}$

249 .

$(\mathrm{seven},6)$

251 .

$(\mathrm{-2},0)$

253 .

$(\mathrm{-iii},\mathrm{ii})$

255 .

$(\mathrm{-9},3)$

257 .

$\left(\mathrm{-3},\mathrm{-5},\mathrm{four}\right)$

259 .

$\left(2,\mathrm{-iii},\mathrm{-2}\right)$

261 .

$\left(\mathrm{-3},2,\mathrm{three}\right)$

263 .

$\left(\mathrm{-two},0,\mathrm{-3}\right)$

265 .

infinitely many solutions

271 .

infinitely many solutions

Department 4.seven Exercises

287 .

The solution is the grey region.

289 .

The solution is the grey region.

291 .

The solution is the greyness region.

293 .

The solution is the grey region.

295 .

The solution is the greyness region.

297 .

The solution is the grey region.

299 .

The solution is the grey region.

301 .

The solution is the grey region.

303 .

The solution is the grayness region.

305 .

The solution is the grey region.

307 .

The solution is the grayness region.

309 .

No solution.

311 .

No solution.

313 .

The solution is the grey region.

315 .

The solution is the gray region.

317 .

The solution is the grey region.

319 .

ⓐ $\{\begin{array}{c}f\ge 0\hfill \\ p\ge 0\hfill \\ f+p\le \mathrm{xx}\hfill \\ \mathrm{two}f+\mathrm{v}p\le 50\hfill \end{array}$
ⓑ

ⓒ aye
ⓓ no

321 .

ⓐ $\{\begin{array}{c}c\ge 0\hfill \\ a\ge 0\hfill \\ c+a\le 24\hfill \\ a\ge 3c\hfill \end{array}$
ⓑ

ⓒ yeah
ⓓ no

323 .

ⓐ $\{\begin{array}{c}w\ge 0\hfill \\ b\ge 0\hfill \\ 27\mathrm{west}+16b>\mathrm{fourscore}\hfill \\ 3.20\mathrm{due\; west}+1.75b\le 10\hfill \end{array}$
ⓑ

ⓒ no
ⓓ yes

325 .

ⓐ $\{\begin{array}{c}\mathrm{west}\ge 0\hfill \\ r\ge 0\hfill \\ \mathrm{west}+r\ge 4\hfill \\ 270w+650r\ge 1500\hfill \end{array}$
ⓑ

ⓒ no
ⓓ aye

Review Exercises

331 .

$\left(\mathrm{three},\mathrm{-1}\right)$

333 .

no solution

335 .

1 solution, consistent system, independent equations

337 .

$\left(4,5\right)$

339 .

$\left(\mathrm{three},1\right)$

341 .

infinitely many solutions

343 .

$\left(\mathrm{four},\mathrm{-1}\right)$

345 .

$\left(6,2\right)$

349 .

l irises and 150 tulips

351 .

ten calories jogging and x calories cycling

357 .

the length is 450 feet, the width is 264 feet

361 .

the rate of the jet is 395 mph, the rate of the wind is vii mph

363 .

41 dimes and 11 pennies

365 .

$46\frac{\mathrm{ii}}{\mathrm{iii}}$ liters of 30% solution, $23\frac{1}{\mathrm{three}}$ liters of 60% solution

367 .

$29,000 for the federal loan, $14,000 for the private loan

371 .

$\left(\mathrm{-3},2,\mathrm{-4}\right)$

377 .

$\left[\begin{array}{cccccccccc}\hfill \mathrm{iv}& & & \hfill \mathrm{three}& & & \hfill 0& & & \hfill \mathrm{-2}\\ \hfill 1& & & \hfill \mathrm{-2}& & & \hfill \mathrm{-3}& & & \hfill 7\\ \hfill 2& & & \hfill \mathrm{-1}& & & \hfill 2& & & \hfill \mathrm{-6}\end{array}\right]$

379 .

$\{\begin{array}{c}x-\mathrm{iii}z=\mathrm{-1}\hfill \\ \mathrm{10}-\mathrm{ii}y=\mathrm{-27}\hfill \\ \text{−}y+\mathrm{two}z=\mathrm{three}\hfill \end{array}$

381 .

ⓐ $\left[\begin{array}{cccccccccc}\mathrm{ane}\hfill & & & \hfill \mathrm{-three}& & & \hfill \mathrm{-ii}& & & \hfill \mathrm{four}\\ 4\hfill & & & \hfill \mathrm{-ii}& & & \hfill \mathrm{-three}& & & \hfill \mathrm{-ane}\\ \mathrm{ii}\hfill & & & \hfill 2& & & \hfill \mathrm{-i}& & & \hfill \mathrm{-3}\end{array}\right]$
ⓑ $\left[\begin{array}{cccccccccc}2\hfill & & & \hfill \mathrm{-six}& & & \hfill \mathrm{-4}& & & \hfill 8\\ \mathrm{four}\hfill & & & \hfill \mathrm{-2}& & & \hfill \mathrm{-3}& & & \hfill \mathrm{-i}\\ 2\hfill & & & \hfill \mathrm{ii}& & & \hfill \mathrm{-i}& & & \hfill \mathrm{-3}\end{array}\right]$
ⓒ $\left[\begin{array}{cccccccccc}\mathrm{ii}\hfill & & & \hfill \mathrm{-6}& & & \hfill \mathrm{-four}& & & \hfill 8\\ \mathrm{iv}\hfill & & & \hfill \mathrm{-2}& & & \hfill \mathrm{-3}& & & \hfill \mathrm{-ane}\\ 0\hfill & & & \hfill \mathrm{-6}& & & \hfill \mathrm{-i}& & & \hfill 5\end{array}\right]$

383 .

$(\mathrm{-2},\mathrm{v},\mathrm{-2})$

391 .

$(\mathrm{-three},2)$

393 .

$\left(\mathrm{-3},2,3\right)$

399 .

The solution is the grey region.

401 .

The solution is the grayness region.

403 .

No solution.

405 .

ⓐ $\{\begin{array}{c}b\ge 0\hfill \\ \mathrm{due\; north}\ge 0\hfill \\ b+n\le 40\hfill \\ 12b+\mathrm{xviii}n\ge 500\hfill \end{array}$
ⓑ

ⓒ yeah
ⓓ no

Practice Test

407 .

$\left(\mathrm{two},\mathrm{-3}\right)$

409 .

$(2,1)$

411 .

$(\mathrm{ii},\mathrm{-2},1)$

413 .

$(5,\mathrm{seven},4)$

417 .

fifteen liters of 1% solution, 5 liters of 5% solution

419 .

The candy cost $20; the cookies cost $5; and the popcorn toll $10.

421 .

ⓐ $\{\begin{array}{c}C\ge 0\hfill \\ \mathrm{Fifty}\ge 0\hfill \\ C+0.5\mathrm{Fifty}\le 50\hfill \\ L\ge \mathrm{three}C\hfill \end{array}$
ⓑ

ⓒ no
ⓓ yeah

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Source: https://openstax.org/books/intermediate-algebra/pages/chapter-4

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