Intermediate Algebra

# Chapter 2

Intermediate AlgebraChapter 2

## Try It

2.1

no yes

2.2

yes no

2.3

$m = 2 m = 2$

2.4

$a = 0 a = 0$

2.5

$u = 2 u = 2$

2.6

$x = 4 x = 4$

2.7

$p = −2 p = −2$

2.8

$q = −8 q = −8$

2.9

$y = − 17 5 y = − 17 5$

2.10

$z = 0 z = 0$

2.11

identity; all real numbers

2.12

identity; all real numbers

2.13

conditional equation; $q=−911q=−911$

2.14

conditional equation; $k=20114k=20114$

2.15

2.16

2.17

$x = 1 2 x = 1 2$

2.18

$x = −2 x = −2$

2.19

$x = 12 x = 12$

2.20

$u = −12 u = −12$

2.21

$n = 2 n = 2$

2.22

$m = −1 m = −1$

2.23

$r = 1 r = 1$

2.24

$s = −8 s = −8$

2.25

$n = 9 n = 9$

2.26

$d = 16 d = 16$

2.27

He bought two notebooks.

2.28

He did seven crosswords puzzles.

2.29

$3 3$

2.30

$6 6$

2.31

$−15 , −8 −15 , −8$

2.32

$−29 , 11 −29 , 11$

2.33

$−33 , −32 , −31 −33 , −32 , −31$

2.34

$−13 , −12 , −11 −13 , −12 , −11$

2.35

32, 34, 36

2.36

$−10 , −8 , −6 −10 , −8 , −6$

2.37

The average cost was $5,000. 2.38 The median price was$19,300.

2.39

36 $26 $125%125%$ 2.40 33$36 $175%175%$

2.41

25 grams

2.42

2,375 mg

2.43

50%

2.44

40%

2.45

$8.8 % 8.8 %$

2.46

50%

2.47

$600$1,800

2.48

$2,975$11,475

2.49

He will earn $2,500. 2.50 She earned$7,020.

2.51

The rate of simple interest was 6%.

2.52

The rate of simple interest was 5.5%.

2.53

He paid $17,590. 2.54 She deposited$9,600.

2.55

$b = 2 A h b = 2 A h$

2.56

$h = 2 A b h = 2 A b$

2.57

$C = 5 9 ( F − 32 ) C = 5 9 ( F − 32 )$

2.58

$b = 2 A − B h h b = 2 A − B h h$

2.59

$t = A − P P r t = A − P P r$

2.60

$r = A − P P t r = A − P P t$

2.61

$y = 9 − 4 x 7 y = 9 − 4 x 7$

2.62

$y = 1 − 5 x 8 y = 1 − 5 x 8$

2.63

The window’s height is 12 meters.

2.64

The length of the base is 6 feet.

2.65

The measures of the angles are 20°, 70°, and 90°.

2.66

The measures of the angles are 30°, 60°, and 90°.

2.67

The length of the leg is 8.

2.68

The length of the leg is 12.

2.69

The length is 16 inches and the width is 39 inches.

2.70

The length is 17 yards and the width is 26 yards.

2.71

The lengths of the sides of the triangle are 5, 11 and 12 inches.

2.72

The lengths of the sides of the triangle are 4, 7 and 9 feet.

2.73

The length of the swimming pool is 70 feet and the width is 30 feet.

2.74

The length of the garden is 90 yards and the width is 60 yards.

2.75

2.76

He should attach the lights 8 feet from the base of the mast.

2.77

Jess has 41 nickels and 18 quarters.

2.78

Elane has 22 nickels and 59 dimes.

2.79

Eric bought thirty-two 49-cent stamps and twelve 35-cent stamps.

2.80

Kailee bought twenty-six 49-cent stamps and ten 20-cent stamps.

2.81

84 adult tickets, 31 student tickets

2.82

615 children’s tickets and 195 adult tickets

2.83

Orlando mixed five pounds of cereal squares and 25 pounds of nuts.

2.84

Becca mixed 21 gallons of fruit punch and seven gallons of soda.

2.85

The speed of the local train is 48 mph and the speed of the express train is 60 mph.

2.86

Jeromy drove at a speed of 80 mph and his mother drove 60 mph.

2.87

Christopher’s speed was 50 mph and his parents’ speed was 40 mph.

2.88

Ashley’s parents drove 55 mph and Ashley drove 62 mph.

2.89

Pierre and Monique will be 429 miles apart in 3 hours.

2.90

Thanh and Nhat will be 330 miles apart in 2.2 hours.

2.91

Suzy’s speed uphill is $1.81.8$ mph and downhill is three mph.

2.92

The boat’s speed upstream is eight mph and downstream is12 mph.

2.93

Hamilton drove 40 mph in the city and 70 mph in the desert.

2.94

Phuong rode uphill at a speed of 12 mph and on the flat street at 20 mph.

2.95

2.96

2.97

2.98

2.99

2.100

2.101

2.102

2.113

Angie can buy 7 packs of juice.

2.114

Daniel can have 11 people at the party.

2.115

Sergio and Lizeth can travel no more than 500 miles.

2.116

Rameen can use no more than 76 therms.

2.117

Caleb must work at least 96 hours.

2.118

Elliot must work at least 85 jobs.

2.119

Brenda must babysit at least 27 hours.

2.120

Josue must shovel at least 20 driveways.

2.133

The homeowner can use 5–20 hcf and still fall within the “conservation usage” billing range.

2.134

The homeowner can use 16–40 hcf and still fall within the “normal usage” billing range.

2.135

$±2±2$ no solution 0

2.136

$±11±11$ no solution 0

2.137

$x = 4 , x = − 2 3 x = 4 , x = − 2 3$

2.138

$x = −1 , x = 5 2 x = −1 , x = 5 2$

2.139

$x = 8 , x = 0 x = 8 , x = 0$

2.140

$x = 8 , x = 2 x = 8 , x = 2$

2.141

No solution

2.142

No solution

2.143

$x=−25,x=−25,$ $x=52x=52$

2.144

$x=3,x=3,$ $x=19x=19$

2.153

The diameter of the rod can be between 79.991 and 80.009 mm.

2.154

The diameter of the rod can be between 74.95 and 75.05 mm.

## Section 2.1 Exercises

1.

yes no

3.

no yes

5.

$y = 5 y = 5$

7.

$w = −18 w = −18$

9.

$q = 3 q = 3$

11.

$x = 14 x = 14$

13.

$c = 4 c = 4$

15.

$c = 5 2 c = 5 2$

17.

$n = 2 n = 2$

19.

$y = −5 y = −5$

21.

$s = 10 s = 10$

23.

$p = −4 p = −4$

25.

$c = −4 c = −4$

27.

$h = 3 4 h = 3 4$

29.

$m = 6 m = 6$

31.

identity; all real numbers

33.

conditional equation;$j=25j=25$

35.

conditional equation; $m=165m=165$

37.

39.

41.

identity; all real numbers

43.

$x = −1 x = −1$

45.

$y = −1 y = −1$

47.

$a = 3 4 a = 3 4$

49.

$x = 4 x = 4$

51.

$w = 9 4 w = 9 4$

53.

$b = 12 b = 12$

55.

$p = −41 p = −41$

57.

$x = − 5 2 x = − 5 2$

59.

$n = −3 n = −3$

61.

$x = −2 x = −2$

63.

$u = 3 u = 3$

65.

$x = 18 x = 18$

67.

$x = 20 x = 20$

69.

$n = 9 n = 9$

71.

$d = 8 d = 8$

73.

$L=19.75L=19.75$ feet

75.

77.

79.

## Section 2.2 Exercises

81.

83.

six boys

85.

58 hardback books

87.

15

89.

5

91.

12

93.

$−5 −5$

95.

18, 24

97.

8, 12

99.

32, 46

101.

4, 10

103.

38, 39

105.

25, 26, 27

107.

$−11 , −12 , −13 −11 , −12 , −13$

109.

84, 86, 88

111.

$−69 , −71 , −73 −69 , −71 , −73$

113.

$750 115.$13,500

117.

54 108 30%

119.

$162.5162.5$ $35 150% 121. $11.88 11.88$ 123. 24.2 g 125. 2407 mg 127. 45% 129. 25% 131. 12% 133. 200% 135. $−2.5 % −2.5 %$ 137. $−11 % −11 %$ 139. $26.9726.97$ $17.9817.98$ 141.$576 30%

143.

$7.207.20$ $23.2023.20$

145.

$0.200.20$ $0.800.80$

147.

$116 149.$4836

151.

3%

153.

$3.75 % 3.75 %$

155.

$35,000 157.$3345

159.

$17.5 % 17.5 %$

161.

163.

## Section 2.3 Exercises

165.

$d = C π d = C π$

167.

$L = V W H L = V W H$

169.

$b = 2 A h b = 2 A h$

171.

$d 1 = 2 A d 2 d 1 = 2 A d 2$

173.

$b 1 = 2 A h − b 2 b 1 = 2 A h − b 2$

175.

$a = 2 h − 108 t t 2 a = 2 h − 108 t t 2$

177.

$a = 180 − b − c a = 180 − b − c$

179.

$p = 2 A − 2 B l p = 2 A − 2 B l$

181.

$L = P − 2 W 2 L = P − 2 W 2$

183.

$y = 15 − 8 x y = 15 − 8 x$

185.

$y = −6 + 4 x y = −6 + 4 x$

187.

$y = 4 + x y = 4 + x$

189.

$y = 7 − 4 x 3 y = 7 − 4 x 3$

191.

$y = 12 − 2 x 3 y = 12 − 2 x 3$

193.

$y = 18 − 3 x −2 y = 18 − 3 x −2$

195.

1 foot

197.

23 inches

199.

$45 ° , 45 ° , 90 ° 45 ° , 45 ° , 90 °$

201.

$30 ° , 60 ° , 90 ° 30 ° , 60 ° , 90 °$

203.

15

205.

25

207.

8

209.

12

211.

$10.2 10.2$

213.

$9.8 9.8$

215.

18 meters, 11 meters

217.

$13.513.5$ m, $12.812.8$ m

219.

25 ft, 50 ft

221.

7 m, 11 m

223.

12 ft, 13 ft, 14 ft

225.

3 ft, 6 ft, 8 ft

227.

120 yd, 160 yd

229.

40 ft, 85 ft

231.

5 feet

233.

14.1 feet

235.

$104 ° F 104 ° F$

237.

24 ft

239.

241.

Answers will vary. The areas are the same. The $2×82×8$ rectangle has a larger perimeter than the $4×44×4$ square.

## Section 2.4 Exercises

243.

nine nickels, 16 dimes

245.

ten $10 bills, five$5 bills

247.

63 dimes, 20 quarters

249.

16 nickels, 12 dimes, seven quarters

251.

330 day passes, 367 tournament passes

253.

40 postcards, 100 stamps

255.

15 $10 shares, five$12 shares

257.

34 general, 61 youth

259.

114 general, 246 student

261.

Four pounds of macadamia nuts, eight pounds almonds

263.

$3.63.6$ lbs Bermuda seed, $5.45.4$ lbs Fescue seed

265.

$33,000 in Fund A,$22,000 in Fund B

267.

$5.9 % 5.9 %$

269.

Kathy 5 mph, Cheryl 3 mph

271.

commercial 540 mph, private plane 330 mph

273.

Violet 65 mph, Charlie 55 mph

275.

Ethan 22 mph, Leo 16 mph

277.

DaMarcus 16 mph, Fabian 22 mph

279.

four hours

281.

4.5 hours

283.

uphill $1.61.6$ mph, downhill $4.84.8$ mph

285.

light traffic 54 mph, heavy traffic 30 mph

287.

freeway 72 mph, mountain road 24 mph

289.

running eight mph, walking three mph

291.

15 minutes 20 minutes one hour (d) 1:25

293.

295.

## Section 2.5 Exercises

297.

299.

301.

303.

305.

307.

309.

311.

313.

315.

317.

319.

321.

323.

325.

327.

329.

331.

333.

335.

337.

339.

341.

343.

345.

347.

A maximum of 14 people can safely ride in the elevator.

349.

five drinks

351.

86 cars

353.

$16,875 355.$110,000

357.

260 messages

359.

35 people

361.

32 jobs

363.

62 necklaces

365.

seven lawns

367.

20 hours

369.

20 people

371.

42 guests

373.

375.

## Section 2.6 Exercises

377.
379.
381.
383.
385.
387.
389.
391.
393.
395.
397.
399.
401.
403.
405.
407.
409.
411.
413.
415.
417.
419.
421.
423.
425.
427.

$5 ≤ n ≤ 24 5 ≤ n ≤ 24$

429.

$6 ≤ w ≤ 12 6 ≤ w ≤ 12$

431.

433.

## Section 2.7 Exercises

435.

$x=4,x=−4x=4,x=−4$ no solution $z=0z=0$

437.

$x=3,x=−3x=3,x=−3$ no solution $z=0z=0$

439.

$x = 1 , x = − 1 2 x = 1 , x = − 1 2$

441.

$x = −1 , x = − 5 2 x = −1 , x = − 5 2$

443.

$x = 7 , x = 1 x = 7 , x = 1$

445.

$x = 1 , x = −5 x = 1 , x = −5$

447.

$x = 7 , x = 1 x = 7 , x = 1$

449.

no solution

451.

no solution

453.

$x = −1 , x = − 2 3 x = −1 , x = − 2 3$

455.

$x = −3 , x = 3 x = −3 , x = 3$

457.
459.
461.
463.
465.
467.
469.
471.
473.
475.
477.
479.
481.

$x = 4 , x = 2 7 x = 4 , x = 2 7$

483.

$x = 3 , x = 2 x = 3 , x = 2$

485.

$x = 3 , x = − 11 3 x = 3 , x = − 11 3$

487.

$x = 3 2 , x = − 1 2 x = 3 2 , x = − 1 2$

489.
491.

The minimum to maximum expected production is 207,500 to 2,225,000 bottles

493.

The acceptable weight is 22.5 to 25.5 ounces.

495.

## Review Exercises

497.

no

499.

$s = −22 s = −22$

501.

$m = −14 m = −14$

503.

$q = 18 q = 18$

505.

$x = −1 x = −1$

507.

$k = 3 4 k = 3 4$

509.

511.

$n = 2 n = 2$

513.

$k = 23 k = 23$

515.

$x = 5 x = 5$

517.

There are 116 people.

519.

38

521.

$−3 , −10 −3 , −10$

523.

76, 78, 80

525.

$922 527. 160 529. $3.89 3.89$ 531. 35% 533. 32% 535.$105 $52.5%52.5%$

537.

$428.22 539.$1,900

541.

$d 2 = 2 A d 1 d 2 = 2 A d 1$

543.

$y = 4 x 3 − 4 y = 4 x 3 − 4$

545.

$22.5 ° , 67.5 ° , 90 ° 22.5 ° , 67.5 ° , 90 °$

547.

26

549.

6 feet

551.

$24.524.5$ cm, $12.512.5$ cm

553.

9 ft, 14 ft, 12 ft

555.

nine pennies, six dimes, 12 quarters

557.

559.

$2.22.2$ lbs of raisins, $7.87.8$ lbs of nuts

561.

$9.7 % 9.7 %$

563.

Louellen 65 mph, Tracy 66 mph

565.

upstream 3 mph, downstream 5 mph

567.

heavy traffic 32 mph, light traffic 66 mph

569.
571.
573.
575.
577.
579.
581.
583.
585.
587.

$33 per day 589. at least$300,000

591.

at least 112 jobs

593.
595.
597.
599.
601.
603.
605.

$6 ≤ w ≤ 12 6 ≤ w ≤ 12$

607.

no solution

609.

$x = 2 , x = 2 3 x = 2 , x = 2 3$

611.

$x = 9 , x = −3 x = 9 , x = −3$

613.

$x = 2 , x = 1 4 x = 2 , x = 1 4$

615.
617.
619.
621.
623.

The minimum to maximum expected usage is 210,000 to 220,000 bottles

## Practice Test

625.

$x = −5 x = −5$

627.

$a = 41 a = 41$

629.

631.

$x = 6 x = 6$

633.

$x = −2 , x = − 1 3 x = −2 , x = − 1 3$

635.
637.
639.
641.
643.
645.

$10.8 10.8$

647.

$−57 , −55 −57 , −55$

649.

12 dimes, seven quarters

651.

$30 ° , 60 ° , 90 ° 30 ° , 60 ° , 90 °$

653.

$2.52.5$ hours

655.

At most \$55.56 per costume.

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