Answers
1 Arithmetic to algebra
1·1 1. Rationals, Reals
2. Integers, Rationals, Reals
3. Rationals, Reals
4. Whole, Integers, Rationals, Reals
5. Irrationals, Reals
6. Natural, Whole, Integers, Rationals, Reals
7. Rationals, Reals
8. Rationals, Reals
9. Rationals, Reals
10. Irrationals, Reals
11–20. 
1·2 1. Commutative Property for Addition
2. Associative Property for Multiplication
3. Identity for Addition
4. Inverse for Multiplication
5. Distributive Property
6. Zero Product Property
7. Associative Property for Addition
8. Identity for Multiplication
9. Commutative Property for Multiplication
10. Multiplication Property of Zero
11. Inverse for Addition
12. Distributive Property
13. Identity for Multiplication
14. Associative Property for Addition
15. Inverse for Addition
1·3 1. 2
2. −17
3. −54
4. 4
5. 3
6. 14
7. 24
8. −3
9. −8
10. 18
11. 2
12. 7
13. −32
14. −10
15. −40
16. −12
17. −1
18. −48
19. 16
20. 5
1·4 1. 9
2. 225
3. 10
4. 4
5. 23
6. 21
7. 3
8. 15
9. 20
10. −2
1·5 1. 11t
2. 4x
3. 3x + 3y
4. x + 10y − 3
5. −1 + 2x − 2x2
6. 13t − 3r − 10
7. 7x2 − 6x + 19
8. 8x − 6y − 19
9. 2x2 + 2x + 1
10. 10y − 9x
11. 2 + 3x
12. 3y − 7
13. 
14. 9n − 8
15. w + (−w)
16. 
17. r2 − 4r
18. 
19. (3z + 2)(4z − 6)
20. 
1·6 1. 14
2. −16
3. 1
4. 2
5. 15
6. 1
7. 85
8. 230
9. −3
10. −26
2 Linear equations
2·1 1. x = 4
2. y = 16
3. t = 3
4. w = 37
5. x = 2
6. z = 13.1
7. 
8. x = −6
9. y = 3
10. t = −7
2·2 1. x = 4
2. z = 63
3. 
4. t = −36
5. x = 30
6. w = 15.4
7. 
8. m = −12.4
9. x = −3
10. z = 175
2·3 1. x = 13
2. t = −3
3. x = 5
4. 
5. x = 12
6. x = 7
7. x = 16
8. x = 0.5
9. x = 25
10. x = −8
2·4 1. x = 5
2. x = −4
3. 17 = x
4. −1 = x
5. 
6. x = 5.8
7. x = 2.5
8. x = 31
9. 
10. 
2·5 1. x = 6
2. x = 10
3. 11 = x
4. x = 0
5. 11 = x
6. 2 = x
7. x = 6
8. 
9. 
10. x = 3
2·6 1. 
2. 
3. x = 9 x = −9.8
4. x = 5 x = −6
5. x = 5.5 x = −7.25
6. x = 2 Reject 
because it will make the 18x negative,
7. x = 5 (Reject x = −10)
8. x = 9.5 x = 0.75
9. x = 4 x = −2
10. 
2·7 1. 5 nickels
2. 
h, or 4 h and 10 min, later
3. 
lb of peanuts and
lbs of raisins
4. 23 dimes
5. 5:00 p.m.
6. 250 pennies
7. 481 students
8. 12 ounces of Sweet Rose Tulsi tea and 4 ounces of Orange Blossom green tea
9. 1:15 p.m.
10. 2:30 p.m.
3 Linear inequalities
3·1 1. 
2. 
3. 
4. 
5. 
6. 
7. 
8. 
9. 
10. 
3·2 1. 
2. 
3. 
4. 
5. 
6. 
7. 
8. 
9. x −1 or x > 10, which is equivalent to x > −1
10. y > 3 y ≥ 7, which is equivalent to y ≥ 7
3·3 1. 
2. 
3. 
4. 
5. 
6. 
7. 
8. 
9. 
10. 
4 Coordinate graphing
4·1 1–5. 
6. Quadrant II
7. Quadrant I
8. Quadrant IV
9. Quadrant III
10. Quadrant IV
4·2 1. 
2. 
3. 
4. 
5. d = 7
6. a = 4, a = 10
7. d = 15, d = −9
8. c = 15, c = 1
9. b = −, b = 8
10. a = ±4
4·3 1. (3.5, 5.5)
2. (−2, 4.5)
3. (−3, −2)
4. (4, 4)
5. (2, −3)
6. x = 2
7. x = 7
8. y = 9
9. x = −5
10. x = 16
4·4 1. 
2. 
3. m = 0
4. 
5. Undefined
6. y = −2
7. x = 4
8. y = 4.5
9. x = −8
10. y = 3
4·5 1. 
2. 
3. 
4. 
5. 
6. 
7. 
8. 
9. 
10. 
4·6 1. 
2. 
3. 
4. 
5. 
6. 
7. 
8. 
9. 
10. 
4·7 1. Vertical
2. Horizontal
3. Vertical
4. Oblique
5. Horizontal
6. 
7. 
8. 
9. 
10. 
4·8 1. 
2. 
3. 
4. 
5. 
6. 
7. 
8. 
9. 
10. 
4·9 1. 
2. 
3. 
4. 
5. 
6. 
7. 
8. 
9. 
10. 
4·10 1. y = 3x + 8
2. y = − 5x + 2
3. 
4. y = 4x − 5
5. 
6. 
7. y = 2x + 3
8. 
9. 
10. 
4·11 1. Perpendicular
2. Parallel
3. Neither
4. Parallel
5. Perpendicular
6. y = 5x − 16
7. 
8. 
9. 
10. y = 2x − 16
5 Systems of linear equations and inequalities
5·1 1. 
2. 
3. 
4. 
5. 
6. 
7. 
8. 
9. 
10. 
5·2 1. 
2. 
3. 
4. 
5. 
6. 
7. 
8. 
9. 
10. 
5·3 1. x = 5, y = 5
2. x = 4, y = 8
3. x = 3, y = 9
4. x = 30, y = 27
5. x = 19, y = 23
6. x = 54, y = 8
7. x = 3, y = 1
8. x = 9, y = 4
9. x = 11, y = 2
10. x = −1, y = 5
5·4 1. x = 6, y = 2
2. x = 10, y = 7
3. x = 4, y = 1
4. x = 7, y = 1
5. 
6. x = 2, y = 3
7. x = 3, y = 0
8. x = 3, y = 10
9. x = 8, y = −7
10. 
5·5 1. a = 1, b = 6
2. x = 1, y = 10
3. x = 2.5, y = −2
4. x = 7, y = 3
5. x = 5, y = 2
6. 
7. x = 3, y = −3
8. x = −2, y = −5
9. 
10. x = 0.6, y = 6.6
5·6 1. Dependent
2. Inconsistent
3. Consistent
4. Inconsistent
5. Dependent
6. Consistent
7. Consistent
8. Inconsistent
9. Consistent
10. Dependent
6 Powers and polynomials
6·1 1. x11
2. y6
3. 6x6
4. 21x10
5. x6
6. 
7. y7
8. 
9. x2
10. y21
11. x0 = 1
12. x10
13. x2
14. 
15. x6
6·2 1. 4x10
2. −8x9
3. 20a8
4. −27x5y15
5. 72b11
6. 
7. 
8. 
9. 
10. 
6·3 1. 2x3 + 3x2 + 5x − 7; degree 3
2. 5t12 + t7 + 8t2 − 9t − 1; degree 12
3. −12y11 + 5y6 − 2y3 + 8; degree 11
4. Not a polynomial; variable under radical
5. 2x5 − 4x3 + 3x; degree 5
6. −3z7 − 4z2 + 8z + 4; degree 7
7. w5 − 9w3 − 3w + 7; degree 5
8. −b4 + b2 − 3b − 4; degree 4
9. Not a polynomial; variable in denominator
10. −7y3 + 8y2 − 4y + 6; degree 3
6·4 1. 14w2 − 9w − 1
2. 2a2 − 5a − 4
3. −9x2 + 41x − 24
4. −4y2 − 3y + 32
5. 4 − b + 4b2
6. 4b2 − 3b + 3
7. 11x2 − 13x + 2
8. −2x2 − 7x + 2
9. −3x2 + x + 2
10. 2x2 − 16x + 3
6·5 1. −6b7
2. 30x4 y4
3. −36x5 y2z10
4. −3a2b2c3
5. 40a3b
6. 18x6 y3
7. −36w5x6
8. 4x6
9. 20b8
10. −27r3t9
11. (2x3)(−3x2)= −6x5
12. (−3b2)(−4b5) = 12b7
13. (−5x4 y2)(3x2 y) = −15x6 y3
14. (−3x2z)(−2z4) = 6x2z5
15. 
6·6 1. 10a3 +15a2
2. − 2x4 + 6x3 + 4x2
3. 22y4 − 6y3 + 10y2
4. − 6b5 + 9b4 − 12b3
5. 3x3y + 5x2y2 − 2xy3
6. 25x4y − 35x3y2 +5x2y3
7. 8x2 + 16xy − 24xz
8. -5a3b + 5ab4
9. 4x10 − 3x8 + 5x7 − x5 + 7x4 − 10x3
10. 9a6b4c2 − 6a4b4c3 + 21a9b3c6
11. 3(x +1)= 3x + 3
12. a(b − 5)= ab − 5a
13. 4(2x − y)= 8x − 4y
14. 7x(1 + 7x)= 7x + 49x2
15. 2ab(2a + b)= 4a2b + 2ab2
6·7 1. x2 +10x +16
2. y2 - 13y + 36
3. t2 + 4t - 12
4. 2x2 + 2x - 24
5. 3y2 - 26y - 9
6. 15x2 + 2x - 24
7. 6x2 + 29x - 5
8. 5 -13b - 6b2
9. 6x2 + x - 35
10. -10x2 + 29x - 10
11. x2 - 16
12. x2 - 9
13. 4x2 - 1
14. 9x2 - 25
15. 49 - 9x2
16. (x + 3)(x + 2)= x2 +5x + 6
17. (x - 7)(x - 2)= x2 - 9x + 14
18. (2a +1)(a + 4)= 2a2 + 9a + 4
19. (3x - 2)(x - 5)= 3x2 -17x +10
20. (2t + 3)(3t - 5)= 6t2 - t - 15
6·8 
6·9 
6·10 
7 Factoring
7·1 
7·2 
7·3 
7·4 
7·5 
7·6 
8 Radicals
8·1 1. 6
2. −9
3. ±5
4. 3
5. −5
6. 12
7. −2
8. −2
9. 10
10. No Real Root
8·2 
8·3 
8·4 
8·5 
8·6 
8·7 1. x = 5
2. x = 5
3. x = 4
4. x = -1.25
5. x = 3
6. 
7. x = 9
8. x = 25
9. x = -1.75
10. x = 11
8·8 1. 
2. 
3. 
4. 
5. 
6. 
7. 
8. 
9. 
10. 
9 Quadratic equations and their graphs
9·1 1. x = ±8
2. x = ±4
3. x = ±5
4. 
5. x = ±4
6. 
7. 
8. 
9. 
10. 
9·2 1. x = 7, x = -3
2. x = 2, x = -4
3. 
4. 
5. 
6. 
7. x = 7, x = 2
8. 
9. 
10. 
9·3 1. x = 3, x = -7
2. t = 2, t = -5
3. y = 8, y = -4
4. x = 3, x = -2
5. 
6. 
7. 
8. 
9. 
10. 
11. b2 - 4ac = 61, two irrational solutions
12. b2 - 4ac = -11, no real solutions
13. b2 - 4ac = 25, two rational solutions
14. b2 - 4ac = 0, one rational solution
15. b2 - 4ac = 24, two irrational solutions
16. b2 - 4ac = 1, two rational solutions
17. b2 - 4ac = 44, two irrational solutions
18. b2 - 4ac = -31, no real solutions
19. b2 - 4ac = 0, one rational solution
20. b2 - 4ac = 69, two irrational solutions
9·4 1. x = -2, x = -3
2. x = 4, x = 3
3. y = 2, y = -4
4. a = 5, a = -2
5. x = 4, x = -5
6. x = 5, x = 1
7. x = 0, x = -3
8. x = 0, x = 5
9. 
10. 
9·5 1. (3, 0), (1, 0), (0, 3)
2. (5, 0), (−1, 0), (0, −5)
3. (−2, 0), (0, 0)
4. (3, 0), (4, 0), (0, 12)
5. (−1, 0), 
6. x = 4, (4, −1)
7. x = −2, (−2, −6)
8. x = 1, (1, 1)
9. x = 3, (3, 2)
10. x = 2, (2, 11)
9·6 1. 
2. 
3. 
4. 
5. 
6. 
7. 
8. 
9. 
10. 
10 Proportion and variation
10·1 1. 45°, 60°, 75°
2. 8 ft. and 12 ft.
3. 104 and 39
4. 20 oz
5. 24, 32, and 64
6. 20 and 24
7. 6 and 14
8. 51
9. 8 and 20
10. 6 and 20
10·2 1. x = 4.2
2. w = 15
3. x = 25
4. 
5. x = 15
6. x = 29
7. x = ±8
8. x = ±5
9. x = ±13
10. x = 7, x = -4
10·3 1. 42
2. 100
3. 312
4. 1275
5. 700
6. 0.009 V
7. 143 mi
8. 0.6 mi
9. 304 cm3
10. 70 mi
10·4 1. k = 3, y = 3
2. k = 32, x = 16
3. k = 72, y = 8
4. k = 132, t = 44
5. k = 540, a = 12
6. 
7. k = 88, w = 4
8. k = 24, 
9. k = 234, x = 13
10. k = 288, a = 24
10·5 1. y = 180
2. x = 8
3. z = 7
4. y = 5
5. x = 21
6. z = 42
7. 20 cm
8. Approximately 683 N
9. Approximately 7.8 ft3
10. 0.1875, or 
ohm
11 Rational equations and their graphs
11·1 1. 2
2. 
3. 
4. 
5. 
6. 
7. 
8. 
9. 
10. 
11·2 1. 1
2. 
3. 
4. 
5. (5 - y)2 = 25 - 10y + y2
6. 
7. x − 9
8. 2
9. 
10. 
11·3 1. 
2. 
3. 
4. 
5. 2
6. 
7. 
8. 
9. 
10. 
11·4 1. 
2. 
3. 
4. 
5. 
6. 
7. 
8. 
9. 
10. 
11. 
12. 
13. 
14. 
15. 
11·5 1. 
2. y + x
3. 
4. 
5. 
6. 
7. 
8. 
9. 
10. 
11·6 1. 
2. x = 3
3. x = 24
4. a = 8
5. 
6. x = 10
7. x = 5
8. 
9. t = 2
10. x = 5
11·7 1. 
2. x = -0.9
3. x = 6
4. 
5. 
6. y = -5
7. x = 3
8. x = 8
9. x = -9
10. x = 4
11·8 1. 
2. 
3. 
4. 
5. 
6. 
7. 
8. 
9. 
10. 
12 Exponential growth and decay
12·1 1. Exponential
2. Linear
3. Quadratic
4. Exponential
5. Quadratic
6. a = 2, b = 3
7. a = 3, b = 2
8. 
, b = 3
9. a = −2, 
10. a = 2, b = 10
12·2 1. y = 162
2. y = 8
3. y = −125
4. y = 9
5. y = 3,000,000
6. y = −0.02
7. x = 2
8. x = 2
9. x = 3
10. x = 4
12·3 1. $5304.50
2. $14802.44
3. $2977.73
4. $3052.24
5. $327,148.96
6. $6204.59
7. $8492.03
8. $5977.69
9. $30,491.91
10. $59,913.95
12·4 1. Growth
2. Decay
3. Decay
4. Growth
5. Decay
6. Growth, 3,355,443,200 bacteria
7. Decay, 102.4 mg
8. Growth, approximately 379,518
9. Decay, $16,355.33
10. Decay, 36,652.78 acres
12·5 1. 
2. 
3. 
4, 
5. 
6. 
7. 
8. 
9. 
10. 
13 Matrix algebra
13·1 1. 2 × 4
4. 2 × 1
2. 1 × 4
5. 3 × 3
3. 3 × 2
6. 
13·2 1. 
2. 
3. [10 6 8 3 2 10 3]
4. Cannot be added
5. 
6. 
7. 
8. Cannot be subtracted
9. 
10. 
13·3 1. 
2. 
3. 
4. 
5. 
6. 
7. 
8. Cannot be added
9. 
10. 
11. 
12. 
13. 
14. 
13·4 1. 2 × 3
2. Not possible
3. Not possible
4. 3 × 2
5. 2 × 2
6. 3 × 3
7. Not possible
8. Not possible
9. 2 × 1
10. Not possible
11. 1 × 1
12. 3 × 3
13. Not possible
14. [10]
15. [−5]
16. Cannot be multiplied
17. [48 9]
18. 
13·5 1. −4
2. −22
3. Not possible
4. 71
5. Not possible
6. 1
7. 7
8. 0
9. 3
10. 5
11. 0
13·6 1. Inverses
2. Not inverses
3. Not inverses
4. Yes
5. No, not square
6. Yes
7. No, determinant = 0
8. Yes
9. 
10. 
13·7 1. x = 6, y = -1
2. x = 4, y = 1
3. x = -0.5, y = 1.3
13·8 1. x = 6, y = -1
2. x = 4, y = 1
3. x = -0.5, y = 1.3
4. x = 3, y = 1
5. x = 7, y = -3
6. x = -5, y = 2
14 Problem solving
14·1 1. Let N = the number. N – 9 = 75
2. Let x = the number. 3x – 17 = 43
3. Let n = the number. 5x = 28 + x
4. Let y = the number. 8y – 40 = y – 5
5. Let g = the number of games she won, and g – 6 = the number of games she lost. g + (g – 6) = 30
6. Let S = the son’s age, and 5S = the father’s age. 5S – S = 44
7. Let x = the cost of a pen and x − 0.89 = the cost of a pencil. x + (x – 0.89) = 1.25
8. Let J = the number of laps Jaden ran and J + 3 = the number of laps Carlos ran. 
9. Let P = the price of a large bucket of popcorn and 2P = the price of a ticket. 2(2P) + P = 35
10. Let W = the number of weeks and 5W = the number of work days. 5.50(5W) + 8W = 110
14·2 1. 
ounces of 60% cocoa
2. Width = 14.5 feet and length = 35.5 feet
3. k = 8.5, length = 27
4. The number is 60.
5. The numbers are 31, 32, and 33.
6. 30 mg of full strength and 70 mg of 50% strength.
7. The numbers are 88, 89, 90, 91, and 92.
8. The numbers are 28, 30, 32, and 34.
9. An increase of 11.1% would be required.
10. k = 9, the height is 12 cm.
14·3 1. x = 5 or x = 17
2. 
10.5
3. 3, 5, and 7 or −1, 1, and 3
4. The base is 6 meters.
5. Approximately 8.1 seconds.
6. The dimensions of the rectangle are 6 inches by 8 inches.
7. Approximately 1.7 seconds
8. The original rectangle was 2 feet by 6 feet or 3 feet by 9 feet.
9. The two numbers are 7 and −2.
10. Approximately 1.2 seconds
14·4 1. 9 hours
2. 3 months
3. 2.1 days
4. 
hours
5. 12 hours
6. 67.5 minutes
7. 3 cm
8. 5.5 hours
9. 2.6 × 1012 Newtons
10. 3 feet
14·5 1. 7 nickels
2. 1.25 hours
3. $2,600 at 4% and $3,400 at 7%
4. 12 problems correct
5. First number is 16, second is 10.
6. 10 pounds of $1.60 per pound tea and 30 pounds of $2 tea
7. 9 web pages
8. 188 chickens
9. 36 brownies
10. There are a total of 20 coins, 13 nickels, and 7 dimes.