Unit C Homework Helper Answer Key

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Unit C Homework Helper Answer Key

Lesson 4-1

The Pythagorean Theorem 1. 26 2. 17.464 in. 3. 17.1 ft 4. 28.7 m 5. 68 6. a. 37 ft b. Answers will vary. 7. a. 27.7 cm b. D 8. 708.5 ft 9. "10

10. a. 39.6 ft b. Answers will vary.

11. 306.5 ft 12. a. A

b. 39 13. a. B

b. 34 in. 14. a. 37.0 m

b. go through the park

Lesson 4-2

Finding Unknown Leg Lengths 1. 12 2. 400 ft 3. 17.7 yd 4. a. D b. 9.8 ft 5. 48 in. 6. 92.3 in. 7. 33.6 ft 8. a. 125 ft b. Answers will vary. 9. a. 36.8 ft b. Answers will vary.

10. a. 39.6 ft b. Answers will vary.

11. a. 3.9 cm b. She did not square the length of the given leg.

12. 9.2 ft 13. 36.5 cm 14. a. B

b. 35.0 cm 15. Biking 16. 27.4 mm

Lesson 4-3

The Converse of the Pythagorean Theorem

1. Yes 2. No 3. II only 4. a. A

b. Answers will vary. 5. B 6. a. Student 1 and Student 3 are

incorrect.

b. They used the equation a b c, not a2 b2 c2.

7. Triangle 2 and Triangle 3 are right triangles.

8. Triangle 1, Triangle 3 9. No 10. a. A

b. Answers will vary. 11. D 12. a. Decide which side length to

substitute for the hypotenuse length. b. No 13. a. The sides of the triangle satisfy the equation a2 b2 c2. b. Triangle 1, Triangle 2, Triangle 3 14. a. Triangle 1 and Triangle 2 only b. Answers will vary.

digits Texas 13 Grade 8

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Unit C Homework Helper Answer Key

Lesson 4-4

Distance in the Coordinate Plane 1. 5 mi 2. 3.9 3. scalene 4. a. You are closer to the school. b. Answers will vary. 5. a. The triangle formed by the points H, P, and L is a right triangle. The distance from the library to your home is the length of the hypotenuse, HL. b. 6 miles 6. 5 yd 7. 86.0 ft 8. 6.2 9. a. Find PR by finding the difference of the x-coordinates. Then use the Pythagorean Theorem to find PQ and QR. b. Isosceles

10. B

Lesson 4-5

Additional Problem Solving 1. (10, 10), (10, 8) 2. a. (5, 10), (5, 14) b. (5, 8), (5, 16) 3. 9,680 ft3 4. 19.6 cm 5. a. B, C b. 20.7 cm 6. a. (7, 3), (7, 5) b. D 7. a. 360 in.2 b. Yes 8. (4, 4), (4, 4) 9. a. A b. 8 mm c. 2,400 mm3

10. a. 5,096 in.2 b. Answers will vary.

11. (5, 5) (3, 5) 12. a. A

b. 26.7 in. 13. 1,800 cm2 14. a. 24.7 in.

b. Answers will vary.

Lesson 5-1

Surface Areas of Prisms 1. 368 in.2 2. 666 in.2 3. 297 in.2 4. 5,152 cm2 5. 283.36 m2 6. a. 1,522 cm2 b. Check students' work. Answers will vary. 7. Answers will vary; 2 : 3 8. 4,007.66 cm2 9. a. 335.8 cm2 b. C

10. a. 28.32 cm2 b. Answers will vary.

11. a. B b. 777.12 in.2

12. a. A b. 265.2 cm2

13. a. 2,494.6 in.2 b. 3,136 in.2

digits Texas 14 Grade 8

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Unit C Homework Helper Answer Key

Lesson 5-2

Surface Areas of Cylinders 1. 150.7 cm2 2. 1,758.8 mm2 3. 2,179.5 ft2 4. 950.8 in.2 5. 725.3 cm2 6. a. 228.3 m2 b. Answers will vary. 7. a. 620.7 in.2 b. Answers will vary. 8. a. A b. 432.5 in.2 9. a. 494.6 in.2 b. She forgot to include the lateral area.

10. a. 742.6 ft2 b. 11 gal

11. a. D b. 52.1 in.2

12. 2,628.2 cm2 13. a. 111p in.2

b. 6.25 in.2

Lesson 5-3

Volumes of Cylinders 1. a. 48p in.3 b. 96p in.3 2. 91.4 in.3 3. 1,055.04 in.3 4. 2.0 cm 5. a. 4.9 in. b. Answers will vary. 6. a. 800p m3 b. Answers will vary. 7. a. 36.0 in.3 b. No c. He found the volume of the rectangular container instead of the cylinder.

8. a. 96p ft3 b. 6,144p ft3 c. 64

9. 773.6 cm3 10. 25,143p in.3 11. 4 m 12. a. A

b. 147p yd3 13. a. Use the height of the original can

to find the height of the new can. b. 261.0 cm3 14. 34.0 lb 15. 1.8 in.

Lesson 5-4

Volumes of Cones 1. 12p 2. Cone 1, Cone 3, Cone 2 3. 759.88 m3 4. a. B b. 190.76 5. $12,057.60 6. 7 yd 7. 3.9 feet 8. 7 feet 9. a. B, C b. 2.17 yd

10. a. 75p b. Answers will vary.

11. a. 16 b. Answers will vary.

12. a. 4 b. C

13. a. 871.87 m3 b. A

14. a. 508.68 in.3 b. 1,526.04 in.3

15. 3 cm

digits Texas 15 Grade 8

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Unit C Homework Helper Answer Key

16. 296 packages

17. a. Cone 1: 3,072p

Cone 2: 6,000p

b.

64 125

or

125 64

Lesson 5-5

Volumes of Spheres 1. 2,143.57 in.3 2. 113 ft3 3. 268 in.3 4. 4,187 ft3 5. a. 0.47 in.3

b. Answers will vary.

6. 16 cm

7. 12 cm

8. Radius: 7 mm

Diameter: 14 mm

9. a. B b. 33 in.3

10. a. 44,579.63 in.3

b. Answers will vary.

11. a. 4.4 in.

b. Answers will vary. 12. a. 82.41 m3

b. B 13. 9,412.01 in.3 14. a. 7,234.56 cm3

b. 24 minutes 15. 163 yd3

16. a. 7.6 cm b. 229.73 cm3

17. a. B b. 555.36 cm3

18. 575 in.3 19. a. 8513p in.3

b. 4223p in.3 c. 3 in.

Lesson 5-6

Additional Problem Solving 1. 523 cm3 2. a. 1,611 in.3 b. A 3. 46 cm3 4. a. 54,937 m3 b. Check students' drawings. 5. 910 gallons 6. a. B 8,574 in.3 7. 915.8 in.3

Lesson 6-1

Solving Two-Step Equations 1. 84 2. 4018 3. a. D b. 123.32 mi 4. a. B b. 8 5. a. D b. $5.38 6. x 8 7. z 3114 8. $30 per ft2 9. a. y 15 b. Answers will vary.

10. a. D b. 227

11. a. D b. 8 mi

12. a. D b. B; 1

13. a. C b. y 60

14. a. B b. A c. 255.01

15. h 29156

digits Texas 16 Grade 8

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Unit C Homework Helper Answer Key

Lesson 6-2

Writing and Solving Equations with Variables on Both Sides

1. 4 2. 8 3. a. Answers will vary.

b. 1 4. 2 5. 4 6. a. 43,425 125x 200x

45,000 150x b. 7 months 7. a. 2 b. Answers will vary. 8. a. D b. Answers will vary. 9. a. x; all real numbers b. Answers will vary. 10. 20 11. a. 6 b. C 12. a. D b. 2 13. 2.9 hours 14. a. A b. Answers will vary.

Lesson 6-3

Writing and Solving Inequalities with Variables on Both Sides

1. x 6 2. After 1.5 hours. 3. a. B

b. Answers will vary. 4. After 11 months. 5. x 16 6. a. C

b. A; x 4.5 c. B 7. a. C b. After 2 hours.

8. a. A b. Answers will vary. c. x 3; answers will vary.

9. a. A b. D; x 1.1

10. a. A b. Answers will vary.

11. D; 2

Lesson 6-4

Additional Problem Solving 1. 520 2. 27 in. 3. $643.51 4. a. 50 hr b. Answers will vary. 5. a. 9 lb b. Answers will vary. 6. 3 hr 7. 15 8. a. D b. 10 9. a. 12 yd b. 24 yd

10. a. B b. 28

11. a. C b. 9 months

12. 3 hr 13. 27 14. a. 90

b. 280 c. 560

Lesson 7-1

Angles, Lines, and Transversals 1. B 2. mu 32 3. m2 157 4. 75.8

digits Texas 17 Grade 8

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Unit C Homework Helper Answer Key

5. a. 3 and 6, 2 and 7 b. Answers will vary.

6. a. mw 79 b. Jacob thought that w and y are corresponding angles, when actually w and t are corresponding angles and have the same measure.

7. m1 27 8. a. m12 127

b. Answers will vary. 9. 148? 10. a. Find the measure of the

corresponding angle, 2, by subtracting m1 from 180. b. 101 11. a. D b. 32 12. a. m3 86 and m6 129 b. Ball A

Lesson 7-2

Reasoning and Parallel Lines 1. D 2. 142 3. a. Yes, because corresponding angles are 27 each. b. Yes, because alternate interior angles are 81 each. 4. D 5. m 7 n 6. a. 72 b. Your friend found the supplement of 72. 7. a. C b. Answers will vary. 8. D 9. a. 2x 54 86 b. 16 c. Answers will vary.

10. a. 2x 20 86 b. 53

11. a. The value of x must equal the value of y.

b. 73

Lesson 7-3

Interior Angles of Triangles 1. 37 2. 50 3. 41 4. 30 5. 50 6. x 36, mQ 126 7. a. 61 b. Answers will vary. 8. a. 51 b. Answers will vary. 9. a. 35 b. D

10. 45 11. a. D

b. 52.8 12. mA 40 13. mB 93.5 14. a. D

b. 36.2 15. a. C

b. mA 19.3 mB 77.2 mC 83.5

16. mA 93 mB 31 mC 56

Lesson 7-4

Exterior Angles of Triangles 1. B 2. a. D b. B, D 3. a. C b. A, C 4. m1 62

digits Texas 18 Grade 8

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Unit C Homework Helper Answer Key

5. m1 32 m2 36

6. a. m1 116 b. Answers will vary.

7. a. m1 58 b. Answers will vary.

8. a. m1 54 m2 68

b. B 9. m1 30 10. m1 145 11. m1 120

m2 35 12. a. A

b. 73 13. a. C

b. 97

Lesson 7-5

Angle-Angle Triangle Similarity 1. Yes 2. No 3. B, C 4. a. Yes b. Answers will vary. 5. a. A, B, C b. Anchil did not give all the similar triangles. 6. No 7. Yes 8. A, B, C 9. a. If two angles of WSR are congruent to two angles of ZSP b. No

10. a. A, C, D b. A, B, D

11. B, D, E, F

Lesson 7-6

Additional Problem Solving 1. m3 49 2. m3 150

3. B 4. a. First use vertical angles to find

m5. Then use corresponding angles to find m3. Finally, use alternate interior angles to find m2. b. m2 55 c. Answers will vary. 5. a. m4 129 b. A 6. m4 136, m3 44 7. m2 78 8. a. Yes b. Each triangle has angle measures of 30, 59, and 91. 9. a. C b. 117 10. a. m1 m2 m3 b. 36 11. m1 23 m2 49 m3 108 m4 72 12. A

Lesson 8-1

What Are Simultaneous Linear Equations in Two Variables?

1. C, D, F 2. Answers will vary. 3. Yes 4. B 5. a. C

b. Answers will vary. 6. a. A

b. Answers will vary. 7. a. n 16 4w

n 42 11w b. Answers will vary. 8. a. d 58

d 3t 53 b. Lake 2

digits Texas 19 Grade 8

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Unit C Homework Helper Answer Key

9. a. Answers will vary. b. No

10. C 11. C, E 12. B 13. a. C

b. c 25 0.35m c 13 0.4m

14. a. c 42 c 10 8t

b. Shop N

Lesson 8-2

Estimating Solutions of Simultaneous Linear Equations by Inspection

1. one solution 2. one solution 3. no solution 4. one solution 5. infinitely many solutions 6. a. no solution

b. Answers will vary. 7. A 8. C 9. a. one solution

b. D 10. a. infinitely many solutions

b. Answers will vary. 11. a. A

b. one solution 12. infinitely many solutions 13. a. A

b. A 14. a. A

b. infinitely many solutions 15. a. infinitely many solutions

b. Answers will vary. 16. no solution

Lesson 8-3

Solving Simultaneous Linear Equations by Graphing

1. a. Check students' graphs. b. (4, 3)

2. a. Check students' graphs. b. A

3. a. A b. Check students' graphs. c. 4 hours

4. a. c 10 c 0.6n 1

b. Check students' graphs. c. 15 5. a. Check students' graphs. b. (3, 3) c. Answers will vary. 6. a. c 5

c 2 0.2n b. Check students' graphs. c. 15 copies d. Store Z; Store W; answers will vary. 7. a. Answers will vary. b. (3, 3) 8. a. Check students' graphs. b. D c. Answers will vary. 9. a. A b. Answers will vary. 10. a. Check students' graphs. b. (7, 3) 11. a. c 12.75n 12

c 15.75n b. Check students' graphs. 12. a. Check students' graphs. b. (0.5, 3.75) c. Answers will vary.

digits Texas 20 Grade 8

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