CHAPTER 5 – Algebra 2 – Selected Answers “Evens”p.1
Section 5.1 (p.213)
Oral Ex/ 1. 36 2. 27 3. -8 4. 1/25 5. t3 6. 1/x3 7. 1/yn 8. s2 9. 2xy 10. b2/2 11. x 12. p
Written Exercises
2. 4. 6. 8. 10. 12. 3x2 14. 16. 18. 20. 22.
24. 26. xy 28. z2n – 3 30. 32a. b., yes
34. (1) Definition of exponent (2) Multiplication Rule for fractions 36. *This looks like a strange exercise! Rewrite the Laws of Exponents (see page 212) replacing am with ma?!
I. ma + na = (m+n)a, true II. m(a + b) = ma + mb, true III. n(ma)= mn(a), true (hmm…)
IVa. If m > n, (ma) – (na) = (m – n)a, true IVb. If n > m, (ma) – (na) = 1 - (n – m)a, false
(unless, we get to write 1 as a0 and then replace 1 or a0 with 0(a) = 0… then true, again!)
V. m(a – b) = ma – mb, true. (Am I the only one in the world doing this problem?!)
Section 5.2 (p.218)
Oral Ex/ 1. 8 2. 15 3. 100 4. 9 5. c2 6. 1/a 7. y2 8. 1/y3 9. 1 10. 5 11. p2/q2
12. 13. 14. 2ab2 15. 16.
Written Exercises
2. 1/15 4. -4 6. 1/5 8. ¾ 10. 12. 14. 0.238 16. .0145 18. 6.25
20. .0025 22. p2/q2 24. -3x3 26. 28. 30. 5s2t5 32. 34. 3 36. a 38. 1
40. 42. 44. Let x = 2 and y = 3, then 46. Let x = -1, then
(1 – (-1))-2 = ¼ 1 – (-1)-2 = 0 48. -3x2 + x + 2 50. x2 – 9 52. x2 – 1
54. Step (1) (am)-n = Definition of negative exponents (2) = 3rd Law of Exponents (3) = Definition of negative exponents (4) = Substitution using properties of multiplying negatives (5) (am)-n = Transitive, =
56. = a-ma-n (Definition of negative exponents) = a-m + (-n) (1st Law of Exponents)
= a-m - n (Definition of subtraction) 58.= (Def. of negative exponents) = an – m (2nd Law of Exponents) = a-(m – n) (Substitution since m – n = -(n – m)) = a-m + n = a-m –(-n)
Section 5.3 (p.223)
Oral Ex/ 1. 4 2. 5 3. 2 4. 3 5. 2 6. 3 7. 4 8. 2 9. < 10. < 11. < 12. >
Written Exercises
2. 1.06105 4. 3.810-3 6. 7.6220102 8. 4.6010-5 10. 2.510-4 12. 4.775101
14. .0001 16. 10,000,000 18. .0620 20. 400.0 22. > 24. < 26. 40,000 28. 300
30. 2.510-2 32. 2.6103
CHAPTER 5 – Selected Answers “Evens”p.2
Problems (Section 5.3 continued)
2a. 6.28% b. 6.44% c. .202% 4a. 26.1 persons/km2 b. 110 persons/km2
c. 191persons/km2 d. 33.8persons/km2 6. 2.5 nanoseconds 8. 1830 to 1
10. 1.49108 km, 3.081013 km 12. 48.4 g 14. $10,000,000
Section 5.4 (p.228)
Oral Ex/ 1. 5x/y 2. 5xy/3 3. 4. x – 1 5. x 6. -1 7a. {x | x0} b. 2
8a.{x | x2} b. 0 9a. {x | x1} b. -1 10a. {x | x-1} b. no zeros 11a. Reals b. -3
12a. {x | x2} b. 1,3 13a. {x | x1,-1} b. no zeros 14a. Reals b. 2, -2
15a. {x | x-2,2} b. 4
Written Exercises
2. 4. 6. 8. 10. 12. 14. 16. 1
18. 20. 22a. {x | x2,-2} b. 0 24a. {x | x-2} b. 2
26a. {x | x1/2} b. ¼ ,-4 28a. {x | x1} b. 4,-1 30. t – 1 32.
34. 36. 38. 40. 42.
Section 5.5 (p.233)
Oral Ex/1. 8/5 2. 2/5 3. 8/5 4. 2/5 5. ab 6. a3/b3 7. 8.
Written Exercises
2. -8/15 4. 6. 8. ½ 10. 12. 14. x(x + 1) 16. 18.
20. x 22. 1 24. 1
Section 5.6 (p.236)
Oral Ex/ 1. 4/5 2. 3/7 3. 2/3 4. 5/8 5. 6. 7. 8.
Written Exercises
2. 4/5 4. 1/3 6. 8/15 8. ½ 10. 12. 14. 16.
18. 20. 22. 24. 26. 28.
30. 32. 34. 36. 38. 40. A = -3/4 B = 13/5
CHAPTER 5 – Selected Answers “Evens”p.3
Section 5.7 (p.239)
Written Exercises
2. 1 4. -3/10 6. z + 1 8. x 10. 12. 14. 16. 18. 20. 2x + 1
22. 24. 26. u2 + 2u 28. 30. 32. 34. -1/x
Section 5.8 (p.244)
Oral Ex/ 1. 3x – 6 = 5 2. y + 12 = 4 3. 2t – 3 > 6 4. 5x – 6 30 5. 10u = 4 – 5u
6. 2t + 5 = 9 7. 27 + 5s = 12 8. 14x – 6 = 15 9. 4z – 9 = 10
Written Exercises
2. 5/3 4. 7/2 6. 8. 10. 4,-1 12. 3/2,1/2 14. -1/2,3 16. ¾,1 18. -2/3,3/4
20. 2/3 22. 24.
Problems
2. 42 4. 80 6. 8. 180 L 10. 10 km 12. $9000@8%, $15,% 14. 600 mL
16. 5:24 PM 18. 400 m 20. 3 L
Section 5.9 (p.249)
Written Exercises
2. -4 4. 4 6. 2 8. 6 10. 1 12. 2 14. -4 16. no solution 18. 0,-3 20. 1,3 22. -1
24. no solution 26. 5,-5 28. -1,5 30. -2,2,-1,1
Problems
2. 15 and 10 4. 8 6. 18 h 8. 800 km/h 10. 32 km 12. 30 14. 800 km/h 16. 60 mi/h
18. 96 km/h 20. 4 m/s 22. 3 and 15
Chapter 5 Review (p.255)
2. d 4. d 6. b 8. a 10. c 12. c 14. a 16. c 18. b
Chapter 5 Test (p.257)
1. 2. 3. p3 4. 5. 3.410-2 6. 4.3106 7a.{x|x4,-3} b. 2/3 8a.{x|x} b. 4,-3
9. 10. (u – 3)(u – 2) 11. 5/6 12. 13. a/b 14. 15. 16. -3/2, 6
17. 8/5 days 18. -3 19. 20