Chapter 1 Sec 1 Answers: Page 7 – 9

11)

1) 16d

2) 196

3) 3136 sunrises

32. 72m

33. q – 1

34. r + 13

35. n + 9.4

36. s/3

37. n/41

38. “ The difference of a number and 31” means p – 31, not 31 – p.

40. a) t + I b) A: 70; B:60; C:80 c) 46 points

43. 52.5

44. 6

45. 6

46. 1

54. The cost with tax is 1.05 times the cost of the item; 1.05n

56. 4ph; 19,200; the factory uses 19,200 aglets each day.

63. 7.6

64. 27.95

65. 7.8, 7.98, 8.79, 8.9, 9.78, 9.87

66. B

Chapter 1 Sec 2 Answers: Page 12 – 13

17.

18.

19.

20.

23. 10 to the sixth power; ; 1,000,000

26. 4 to the fourth power; ; 256

27. 0.2 squared; (0.2)(0.2); 0.04

28. 0.6 to the fourth power; (0.6)(0.6)(0.6)(0.6); 0.1296

29. a)Stage 3: E-mails sent: Value of power: 64 Stage 4: E-mails sent: Value of power: 256 b)262,144 e-mails

32. 2401; 0.0256

33. 16,807; 0.01024

36. a) 3375 b)121.5 lb

38. x =8; y =4; z=2

39. 17.75

41. 0.5

48. B

Chapter 1 Section 3 Answers: Page 19 – 20

10. 11.7

12. 11

14. 3

16. 60

18. 14

23. 9.1

25. 7

26. 45.4

27. 20

29. ; 552in

30. 4(1) + 7(2) + 2(3); 24points

32. 86

33. 7

34. 5

35. 4.3

36. a) or 19.5 + 0.15m b) $38.25

Chapter 1 Sec 4 Answers pg 24 – 26

18. <

19. >

20. >

21. <

25. -30, -25, -22, -16

26. 22

28. 21

30. 38

32. 73

34. -6

36. 2

38. 31

40. -81

47. 40

48. 5

49. 13

50. 18

53. a) increase b) decrease c) Wednesday; Saturday d) The high temperature consistently rose from Sunday through Wednesday and consistently fell from Wednesday through Saturday.

54. 15

56. 15

58. -13

65. x, -x

Chapter1 Section5 Page 31 – 33

  1. absolute value
  2. │-71│>│43│, so the sum will have the same sign as -71
  3. 2
  4. -15
  5. 8
  6. 8
  7. -12
  8. -13
  9. -6
  10. -15
  11. -12
  12. 90°C
  13. The arrow should start at -2 and go 5 units in the positive direction; -2 + 5 = 3
  14. A
  15. -16
  16. 9
  17. -10
  18. 10
  19. -14
  20. -13
  21. 6
  22. 3
  23. -9
  24. -14
  25. -52
  26. 50
  27. -26
  28. -15
  29. -102
  30. 13
  31. 5
  32. 21
  33. 7
  34. -71
  35. -24
  36. -4
  37. -13
  38. -1
  39. See Margin for Art, The length of the arrow is the absolute value of the second number. The direction of the arrow is right if the second number is positive and left if the second number is negative.
  40. a) 2 b) -3 c) -1 d) Game 1; the greater the plus-minus rating, the better the rating
  41. $63
  42. -1323
  43. -1915
  44. -578
  45. a) -3743 m b) -4943 m
  46. Sample answer: 1 and -25; 2 and -26, 3 and -27
  47. -24
  48. 10
  49. 65
  50. -2
  51. -17
  52. -18
  53. -18
  54. Even; the sum of two even numbers is even
  55. Even; the sum of two odd numbers is even
  56. Odd; the sum of an even number and an odd number is odd
  57. x ≤ 0; if x < 0, then │x│ and x are opposites so their sum is 0; if x = 0, then │x│ and x are both 0 so their sum is 0
  58. 7
  59. If a and b have the same sign or if a or b is 0
  60. If a and b have different signs and neither a nor b is 0
  61. n + 14.5
  62. m – 2.75
  63. 4900 yd²
  64. =
  65. C
  66. x > 10 or x < -10; if x > 10 or x < -10, then │x│ > 10 and -10 + │x│ > 0

Chapter 1 Section 6 Page 36 – 38

  1. -15 – x
  2. Add the opposite of -60 to -45 to obtain -45 + 60 = 15
  3. -5
  4. 8
  5. -13
  6. -4
  7. -10
  8. -22
  9. 13
  10. -1
  11. 1) -110 2) -90 3) -20 ft
  12. -1
  13. 9
  14. -16
  15. 12
  16. -15
  17. 39
  18. -24
  19. 52
  20. -17
  21. -71
  22. 177
  23. -52
  24. 23
  25. 10
  26. -13
  27. -10
  28. -25
  29. -19
  30. 21
  31. -10
  32. To subtract a number, add the opposite number; so -2 – (-5) = -2 + 5 = 3.
  33. 41°C
  34. a) pasteurization to aging: -85°C, aging to hardening: -35°C, hardening to storage: 25°C; 85°C, 35°C, 25°C b) pasteurization to aging c) Estimates may vary; about 52°C
  35. 25°C
  36. -8°F
  37. 30 ft
  38. -100 m
  39. -190
  40. -609
  41. 235
  42. -195
  43. -12
  44. 30
  45. -16
  46. -12
  47. solution B; 24°C lower
  48. 29°C, 282°C; regular lab; 253°C
  49. No; if b = 0, then a + b = a – b and if b < 0, then a + b < a – b
  50. 19
  51. 6
  52. -1
  53. -2
  54. a) Negative; a < 0 and b > 0, so – b < 0 and a – b = a + (-b) is the sum of two negative integers. b) Positive; b > 0 and a < 0, so – a > 0 and b – a = b + (-a) is the sum of two positive integers. c) Positive; │a│ and │b│ are both positive. d) Negative; - │a│ and -│b│ are both negative, and -│a│ - │b│ = -│a│ + (-│b│) is the sum of two negative integers.
  55. 6:40 A.M.
  56. 18
  57. 30
  58. 54
  59. 6
  60. 10
  61. 29
  62. 75
  63. -51
  64. -370
  65. A
  66. F

Chapter 1 Section 7 Page 44 – 46

  1. The mean of a data set is the sum of the values divided by the number of values
  2. The signs ate the same
  3. Positive
  4. negative
  5. negative
  6. positive
  7. negative
  8. negative
  9. positive
  10. positive
  11. 1) -3 2) 9(- 3); - 27 3) -5°C
  12. 60
  13. 2
  14. -13
  15. -132
  16. -350
  17. -2
  18. 2
  19. -360
  20. -7
  21. 17
  22. 340
  23. -120
  24. The numerator should be positive; -5(-12)/-4 = 60/-4 = -15
  25. Sample answer: The rules are alike in that if the two signs are alike the product or quotient is positive and if the two signs are different the product or quotient is negative. The rules are different for zero: for multiplication, if either factor is zero then the product is zero, but for division you have to check that the divisor is not zero.
  26. Table

2 / 2 / +
3 / -6 / -
4 / 24 / +
5 / -120 / -

b) If the number of negative signs is even, then the product is positive; if the number of negative signs is odd, then the product is negative.

c) No; the sign of the product depends on whether the number of negative signs is even or odd.

  1. a) -20,000 ft b) 10 min
  2. a) – 49 m b) – 48 m c) mean
  3. -1250
  4. 512
  5. 5
  6. -2
  7. -4
  8. 100
  9. 67 ft
  10. -160
  11. 4.5
  12. -96
  13. -6.4
  14. 1
  15. No; the product of an odd number of negative factors is negative, while the product of an even number of negative factors is positive, so (-1)ⁿ = -1 is true for any odd positive integer. Example (-1)³ = -1 but (-1)4 = 1.
  16. a) Sometimes; if k = 5 and n = -2, then nk = -10 and -10 < -2. If k = -5 and n = -2, then nk = 10 and 10 > -2 b) Sometimes; if k = 5 and n = 2, then nk = 10 and 10 > 2. If k = -5 and n = 2, then nk = -10 and -10 < 2.
  17. -21, -12, -5, 0, 13, 31
  18. -70, -54, -45, -22, -16
  19. 24
  20. -29
  21. -51
  22. -32
  23. C
  24. -4°F; Step 1: Add the values to get -24°F. Step 2: Count the values to get 6. Step 3: Divide -24°F by 6 to get -4°F.

Chapter 1 Section 8 Page 49 – 51

  1. -12; 7
  2. No; you can only determine that the point is either in Quadrant II or in Quadrant IV
  3. Quadrant I
  4. Quadrant III
  5. y- axis
  6. Quadrant IV
  7. 1) (8, 19), (24, 13), (31, 17), (71, 14), (88, 11), (103, 7), (119, 7), (127, 5), (134, 3) 2) graph 3) The points generally fall from left to right. We can conclude that as the depth increases the speed tends to decrease.
  8. (-4, 2)
  9. (0, 3)
  10. (0, 0)
  11. (4, 0)
  12. (-2, -4)
  13. (3, -3)
  14. (4, 4)
  15. (-3, -2)
  16. Begin at the origin and move 6 units to the right and 3 units down.
  17. Quadrant I
  18. x-axis
  19. Quadrant IV
  20. Quadrant IV
  21. Quadrant III
  22. y-axis
  23. Quadrant III
  24. Quadrant IV
  25. The first number refers to left/right and the second number refers to up/down; the point (2, -8) is 2 units to the right of the origin and 8 units down.
  26. If an ordered pair contains one zero and that zero is the second number, the point is on the x-axis; if that zero is the first number, the point is on the y-axis. If both numbers are zero, the point is the origin, and would be on both the x-axis and y-axis.
  27. a) graph b)The points generally fall from left to right, so we can conclude that as the engine size increases the mileage tends to decrease.
  28. a)graph b) Square; all four sides are the same length and all four angles are right angles.
  29. a) -5, -3, -1, 1, 3, 5, 7 b) (-3, -5), (-2, -3), (-1, -1), (0, 1), (1, 3), (2, 5), (3, 7) c) graph d) The points lie on a line
  30. a) B: (3, 2) W:(2, 2), (3, 1), (3, 3), (4, 2) b) (-4, 2), (-3, 1), (-3, 3), (-2, 2)
  31. Sample answer: P(5, 0), Q(5, 5), R(0, 5); the distance from O to P is 5 units, the distance from P to Q is 5 units, the distance from Q to R is 5 units, the distance from R to O is 5 units.
  32. Quadrant IV
  33. Quadrant III
  34. Quadrant I
  35. 20 – 2c
  36. always
  37. never
  38. sometimes
  39. -45
  40. -21
  41. 21
  42. -153
  43. B
  44. G