–3, –6, –9, –12 6

4.1 Prime and Composite Numbers

1. 2, 4, 6, 8 2. 9, 18, 27, 36 3. 12, 24, 36, 48 4. 90, 180, 270, 360 5. –3, –6, –9, –12 6. –10, –20, –30, –40 7. yes

8. no 9. no

10. yes 11. yes 12. no 13. yes 14. no 15. yes

16. 2, 4, 5, 10

17. 2, 3, 5, 6, 9, 10 18. none

Section 4.1 19. 2, 3, 4, 6

20. 1, 2, 7, 14

21. 1, 2, 4, 5, 10, 20 22. 1, 7, 49

23. 1, 2, 4, 8, 16, 32 24. 1, 3, 7, 9, 21, 63 25. 1, 3, 5, 15, 25, 75 26. neither

27. prime 28. prime

29. prime

30. composite 31. prime

32. composite 33. prime

34. composite 35. prime

36. prime

37. composite 38. composite

Section 4.1 39. prime

40. composite

41. 2, 3, 5, 7, 11, 13, 17, 19, 23, 29

42. 2 + 5 + 7

43. 5 + 13 + 17; 3 + 13 + 19;

5 + 11 + 19; 7 + 11 + 17 44. 1 (mod 7)

45. 2 (mod 7) 46. 6 (mod 7) 47. 3 (mod 7)

48. 4 (mod 7) 49. 2 (mod 7) 50. 5 (mod 7)

51. {0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10}

52. 7 (mod 11) 53. 8 (mod 11) 54. 0 (mod 11) 55. 9 (mod 11) 56. 4 (mod 11)

Section 4.1 57. 7 (mod 11)

58. 6 (mod 11) 59. 2 (mod 11) 60. yes

61. yes; 0

62. 2, since 1 + 2 = 0 (mod 3).

63. –32 64. 14

65. –8 66. 2 67. –8 68. 3 69. 5 70. –2 71. –6 72. 7

4.2 Prime Factorization

1. 42 2. 60 3. 18 4. 110 5. 100 6. 315 7. 3 · 11 8. 2² · 7 9. 2 · 3 · 11

10. 2 · 3² · 5 11. 2² · 3² 12. 2⁶

13. 3² · 7 14. 2³ · 5 15. 72 16. 675 17. 5,488 18. 588

Section 4.2 19. 12,375

20. 5,915 21. 5² · 7

22. 2² · 7 · 11 23. 3² · 31 24. 3³ · 5 25. 3 · 7 · 11 26. 2 · 3³ · 11 27. 2 · 3² · 11 28. 2 · 3 · 7²

29. 2 · 13² 30. 3 · 5² · 7 31. s = 3 32. n = 7 33. c = 11 34. y = 17 35. t = 7 36. y = 5

37. no; check sum = 240 [ 0 (mod 11)

Section 4.2 38. yes; check sum = 242 K 0

(mod 11)

39. yes; check sum = 132 K 0 (mod 11)

40. 10 41. 7

42. It’s invalid; the check sum now = 138 [ 0 (mod 11) 43. Identity Property of

Multiplication

44. Distributive Property

45. Commutative Property of Multiplication

46. Identity Property of Addition

47. –19 48. 8 49. 16 50. –9 51. –4 52. –1

4.3 Greatest Common Factor

1. 2 2. 4 3. 14 4. 5 5. 1 6. 9 7. 10 8. 7 9. 6

10. 12 11. 7 12. 20 13. 14 14. 12 15. 2 16. 27 17. 5 18. 6

Section 4.3 19. 4

20. 9 21. 14 22. a²b 23. 3c³d⁴ 24. 2j⁴ 25. m¹⁵ 26. 5s² 27. 4x³y 28. yes

29. no 30. yes 31. 36 32. 33 33. 100 34. 1 35. 6 36. 20

37. invalid; 44 [ 0 (mod 10) 38. no; 46 [ 0 (mod 10)

Section 4.3 39. yes; 50 K 0 (mod 10)

40. yes; 40 K 0 (mod 10) 41. 1,100

42. –600 43. 4,900 44. –6,200

45. n – 16 = 52 46. –28n = 252 47. n + 97 = 26 48. n – 319 = 498 49. 19n = 456 50. n – 38 = 63

4.4 Least Common Multiple

1. 15 2. 12 3. 30 4. 20 5. 30 6. 24 7. 450 8. 2,205 9. 588

10. 525 11. 1,615 12. 96 13. 646 14. 144 15. 8,575 16. 11,628 17. 28

18. 60

Section 4.4 19. 75

20. 252 21. 294 22. 1,260 23. 20 24. 24 25. 80 26. 300 27. 360 28. 324

29. a³b⁵ 30. 36c⁴d⁷ 31. 12g³h³j⁵ 32. m¹⁸n²p⁶ 33. 200r³s³t² 34. 576x⁵y⁷z⁴

35. GCF: 12; LCM: 144 36. GCF: 6; LCM: 72 37. 1

Section 4.4 38. There is none; both lists of

multiples are infinite.

39. GCF; divide the numerator and the denominator by 50, the GCF.

40. LCM; the least common denominator, 24, is the LCM of 6 and 8.

41. UMMB UM IB 17 XU IB BPM KTCJPWCAM WV 13 11 ABMMT ZWIL 42. KPWKWTIBM KPQX

KWWSQMA IVL UQTS QV ZWWU 11 14 12.

43. Bring 36 doughnuts to the meeting.

44. Sir Bean is the Green Knight of Camelot.

45. no 46. yes; 2 47. yes; 61 48. no

49. yes 50. yes 51. yes

Section 4.4 52. yes

53. x ≤ –24 54. x < 15 55. x < –18 56. y < 40

4.5 Arithmetic Sequences

1. arithmetic

2. common difference 3. recursive

4. explicit 5. 2

6. 7 7. 23 8. 44

9. 6, 13, 20, 27, 34

10. –8, –5, –2, 1, 4 11. –10, –6, –2, 2, 6 12. 20, 12, 4, –4, –12 13. 2, 7, 12, 17, 22 14. –1, 7, 15, 23, 31 15. –3, 2, 7, 12, 17 16. 6, 1, –4, –9, –14 17. –1, 4, 9, 14, 19

18. –1, –6, –11, –16, –21

Section 4.5 19. 3, 34, 65, 96, 127

20. a₁ = 3; an = a_{n – 1} + 4 21. a₁ = –6; an = a_{n – 1} + 6 22. a₁ = –2; an = a_{n – 1} – 4 23. a₁ = 30; a_n = a_{n – 1} – 12 24. a₁ = –2; a_n = a_{n – 1} + 8 25. a₁ = 4; a_n = a_{n – 1} – 2 26. a_n = 4n + 3

27. a_n = 10n – 13 28. an = –3n + 14

29. an = –5n + 1 30. an = 6n – 14 31. an = 9n + 10

32. a₁ = –16; d = 13;

a₅₀ = 621; a₈₉ = 1,128 33. a₁ = 2; d = 7;

a₅₀ = 345; a₈₉ = 618 34. a₁ = 8; d = –5;

a₅₀ = –237; a₈₉ = –432 35. a₁ = 10; d = –6;

a₅₀ = –284; a₈₉ = –518

Section 4.5 36. a₁ = –25; d = 4;

a₅₀ = 171; a₈₉ = 327 37. a₁ = 60; d = –15;

a₅₀ = –675; a₈₉ = –1,260

38. 19 39. 34 40. 3 41.

42. I love popcorn and peanut butter.

43. JM VJZKNZ VNAN KDAZNZ, QNLLRAZ VDXGO AJON

Section 4.5 44. 84

45. ³⁶

5

− 46. 75 47. –25 48. –37

49. 3 50. 125 51. –13 52. 8 53. –6

4.6 Geometric Sequences

1. geometric

2. common ratio 3. 2

4. 4 5. 128 6. 2,048 7. –6 8. 2 9. –48

10. –192

11. 3, 6, 12, 24, 48

12. –2, –6, –18, –54, –162 13. 6, 24, 96, 384, 1,536 14. –10, 30, –90, 270, –810 15. recursive

16. 2, 8, 32, 128, 512 17. –1, 3, –9, 27, –81 18. –3, 6, –12, 24, –48

Section 4.6 19. 6, 30, 150, 750, 3,750

20. –20, –10, –5, –2.5, –1.25 21. –1, 5, –25, 125, –625 22. 3, 18, 108, 648, 3,888 23. a₁ = 3; a_n = 2a_{n – 1}

24. a₁ = –6; a_n = 3a_{n – 1} 25. a₁ = –2; a_n = –4a_{n – 1} 26. a₁ = 60; a_n = 0.5a_{n – 1} 27. a₁ = –2; a_n = 5a_{n – 1} 28. a₁ = 4; an = –2a_{n – 1}

29. geometric; r = 2 30. arithmetic; d = 2 31. neither

32. arithmetic; d = 10 33. neither

34. geometric; r = ¹

2

35. 9 ft.; 6.75 ft.; 5.0625 ft.

36. r = 0.75 37. 43.5 ft.

Section 4.6 38. Theoretically, never;

practically, when you can no longer see the bounce.

39. 3.8 × 10¹ 40. 1.42 × 10⁵ 41. –2.9 × 10^–4 42. 8.45 × 10⁶

43. 540 adult tickets, 560 children's tickets

44. 3 lb of each type of candy 45. prime

46. composite 47. composite 48. prime

Problem Solving 4—Find a Pattern

1. 1, 4, 9, 16; n² 2. 1 + 3 + 5 + 7 + 9 + 11

= 36

1 + 3 + 5 + 7 + 9 + 11 + 13

= 49

1 + 3 + 5 + 7 + 9 + 11 + 13 + 15 = 64

1 + 3 + 5 + 7 + 9 + 11 + 13 + 15 + 17 = 81

1 + 3 + … + (2n – 1) = n²; if n = 20, n² = 400

Problem Solving 4 3. 512 problems; 2^{(n – 1)}

4. 15, 21, 28, 36; ( ₁)

2 n n +

5. 11 + 22 + 33 + 44 + 55 + 66 + 77 + 88 = 396;

99; 4; it is half the number of addends; multiply them:

4(99) = 396

6. 55; 5,050; ( ₁)

2 n n +

7. 15; yes

8. add the two prior terms;

34, 55, 89

4.7 Bases

1. 19 2. 30 3. 8 4. 38 5. 366 6. 25 7. 15 8. 10 9. 6

10. 19 11. 477 12. 22 13. 300 14. 39 15. 215

16. 1, 10, 11, 100, 101, 110, 111, 1000, 1001, 1010, 1011, 1100, 1101, 1110, 1111, 10000

Section 4.7 17. 1, 2, 3, 10, 11, 12, 13, 20,

21, 22, 23, 30, 31, 32, 33, 100

18. 1, 2, 3, 4, 5, 6, 7, 8, 9, A, B, C, D, E, F, 10

19. 224₅ 20. 403₅ 21. 2132₅ 22. 3132₅ 23. 31010₅ 24. 211443₅

25. 10000₂ 26. 100011₂ 27. 1000₂ 28. 110011₂ 29. 1100111₂ 30. 110₂

31. 1000₃ 32. 213₆ 33. 240₇ 34. 332₈

Section 4.7 35. 30₄

36. 2725₈ 37. 415 38. 112 39. 3,013 40. 504 41. 75₁₂ 42. 202₁₂ 43. 37C₁₆ 44. 31E₁₆

45. 1,200 46. 13,000 47. 2,100 48. 3,100 49. 8

50. –36 51. 8 52. 2

4.8 Operations in Bases

1. 443₅ 2. 11₅ 3. 42₅ 4. 120₅ 5. 1003₅ 6. 205₆ 7. 4₇ 8. 4₈ 9. 10₂

10. 24₅ 11. 110₈ 12. 32₆ 13. 101₈ 14. 1100₂ 15. 100010₂ 16. 1102₃ 17. 101110₂ 18. 6002₇

Section 4.8 19. 41₅

20. 342₈ 21. 176₈ 22. 211₅ 23. 11₂ 24. 1050₆ 25. 125A₁₅ 26. 9D₁₄ 27. 1540₁₂ 28. A1₁₁

29. 1273₁₂ 30. 1BB₁₂ 31. 150E₁₆ 32. 223₁₆

33. Answers will vary; possible answer: Change both

numbers to base 10 and then add.

34. 91 35. 324 36. 804

Section 4.8 37. 607

38. at least $1.43/lb.

39. not more than 27 spools 40. Dale: at least 15;

Lance: at least 21

41. at least $1.31 per pair

42. 2, 4

43. 2, 3, 5, 6, 9, 10 44. 2

45. 2, 4 46. none

47. 2, 3, 5, 6, 10

Math and Scripture 4

1. 483 yr.

2. Jerusalem 3. house of God 4. house of God

5. allow volunteers to return to Jerusalem and take a

freewill offering to use to buy animals, meal, and wine for the offerings

6. build the walls and gates 7. Messiah is cut off (killed) 8. 38 AD (actually AD 37

since there is no year 0) 9. 31 AD (actually AD 30) 10. within one year

Chapter 4 Review

1. 1, 2, 3, 4, 6, 12 2. 1, 3, 9, 27

3. 1, 2, 4, 7, 8, 14, 28, 56 4. 1, 2, 3, 4, 6, 7, 12, 14, 21,

42, 84 5. prime

6. composite 7. composite 8. prime

9. 2, 4, 5, 8, 10

10. 2, 3, 6 11. 5

12. none

13. Every composite integer greater than one can be written as a product of

prime factors in exactly one way (though the order of the factors may vary).

14. 2 · 29 15. 2² · 3 · 5

Chapter 4 Review 16. 2² · 3² · 7

17. 2³ · 11

18. 3² · 5² · 13 19. 3² · 5 · 7 20. 2

21. 18 22. 15 23. 1 24. no 25. yes

26. 165 27. 2,952 28. 18 29. 600

30. LCM: 1,890; GCF:

6; 270 · 42 = 11,340;

LCM · GCF = 11,340;

they are equal

31. a sequence in which the consecutive terms differ by a constant value called the common difference

Chapter 4 Review 32. a sequence in which the

consecutive terms differ by a constant multiplier called the common ratio

33. A recursive definition defines the terms of a sequence based on the previous terms, but an explicit definition defines the terms of a sequence based on the number of the term.

34. 6, 9, 12, 15, 18

35. –8, 16, –32, 64, –128

36. –4, –7, –10, –13, –16 37. 1, 2, 4, 8, 16

38. 6, 10, 14, 18, 22 39. 2, –6, 18, –54, 162 40. a₁ = 2; a_n = a_{n – 1} + 4 41. a₁ = 9; a_n = 2a_{n – 1} 42. a_n = 4n

43. a_n = 9(2)^{n – 1} 44. 8

45. 1111₂

Chapter 4 Review 46. AD8₁₆

47. 11001₂ 48. 40₅ 49. 464₈

50. God used multiplication in His representation of 490 years as 70 weeks of years.