Answer Key - CK-12 Chapter 01 Algebra I Concepts

Chapter
1 – Equations and FunctionsAnswer Key
1.1 Definition of Variable
Answers
1. (2)(11x)

2. 1.35y

3. (3)( 41 )

4. 41 z

5. m = .25q + .10d

6. m = .25q + .10d + .01p

7. (7 + 6)x

8. 20x − 4

9. m = 10.25h − 4

10. i = 2000
c
11.
CK12 Algebra I Concepts 1
Chapter 1 – Equations and FunctionsAnswer Key
1.2 Expressions with One or More Variables
Answers
1. 2(− 3) + 3(2) = 0

2. 4(5) + (− 4) = 16

3. 5(− 3)(5) − 2(2) =− 79

2(−3) −6
4. 2
5 ( 4) = 9 =− 3
−−

3(2)
5. = 6
=− 1 21
−4 −4

(−3)−4(2)
6. 3(5)+2(−4) =− 11
7

7. 1
=− 1
−3+2

(−3)(2) −6 3
8. 5(−4) = −20
= 10

9. C = 2000 + 3(1000) = $5, 000

10. C = 2000 + 3(2000) = $8, 000

11. C = 2000 + 3(2500) = $9, 500
12.
1.3 Algebra Expressions with Exponents
Answers
1. 8(− 1)3 =− 8

5(−1)2 5
2. 6(−3)3
= −162

3. 3(− 3)2 − 5(4)2 = 27 − 80 =− 53

4. (− 1)2 − (2)2 =− 3

(−3)3 +(4)3 37
5. (−3)3 −(4)3
=− 91

6. 2(− 1)3 − 3(− 1)2 + 5(− 1) − 4 =− 14

7. 4(4)3 + 3(4)2 − 4 + 2 = 302

8. 3 + ( 13)2 = 28
9
−

9. V = 4(2)(10 − 2)2 = 512 in3

10. V = 4(3)(10 − 3)2 = 588 in3
11.
1.4 Order of Operations
Answers
1. a) 2(5)2 = 50
b) 3(5)2 + 2(5) + 1 = 86

2. 75

3. (1 − 2)2 = 1

4. 3

5. 3+7
7−12 =− 2

6. (4 − 1)2 + 32 (2) = 27

7. (5 − 2)×(6 − 5) + 2 = 5

8. 12÷4 + 10 − 3×3 + 7 = 11

9. (22 − 32 − 5)×(3 − 5) = 30

10. 12 − [(8 − 4)×5) =− 8

11. (250)2 + 2(250) − (250(− 120)) = 93, 000

2
12. (0.02(− 0.025) − (0.025)4 ) = 0.000000250 = 2.50×10−7
13.
1.5 Algebra Expressions with Fraction Bars
Answers
2(3+(2−1))
1. 4−(6+2) − (3 − 5) = 0

4+7(3) 12−3(2)
2. 9−4 + 2 = 8

2
(22 +5)
3. 52 −42
÷(2 + 1) = 3

6(12)
4. 6+12 = 4

2+32
5. 3−2 = 11

4(2) 8
6. 9(2)2 −3(2)+1
= 31

7. 42 2

1+(−2) + 1−1(−2) =− 47
3

4(3)(2)(5)
8. =− 24
22 −32

(−1)2 −(3)2
9. (−1)(3)−2(−1)(3—1) =− 58

10. 2502 + 2(250) − (250)(− 120) = 93, 000

2
11. (0.02(− 0.025) − (0.025)4 ) = 2.5×10−7

1 3
2 + 2 −(−1)
12. ( 2 )( 2 )+( 23 )(−1)+( 21 )(−1)
1 3 =− 12/5

(3+(−5))2 4
13. 4(32 )−(−5)2
=− 11

4−(−2)3 (4+(−2))2 21
14. 43 −(−2)
+ 4+(−2)4
= 55

1.6 Patterns and Expressions
Answers
1. p = 20d

2. $200
3. $220
4. c = 24 − e
5. c = 24 − 9 = 15
6. c = 24 − 9 − 3 = 12
7. 7x = 35 : x = 5
8. 3x + 15 = 24 : x = 3
9. 2x = 5y − 3 : 3y = 15 : y = 5, x = 11
10. x − 25 = 2y : 5x + 5y = 350 : 5(2y − 25) + 5y = 350 : x = 55, y = 15
11. x + (x + 1) = 35 : 2x + 1 = 35 : x = 17 : 17, 18

p
12. 3 = p − 6 : p = 9
13. s = 5q
14. 70 = 5q : q = 14
15. 83 = 5q : q = 17
16. 80%
17. .25(w + a) = a : a = 1, w = 3
18. .5v + 4 = .75(v + 4) : v = 4
19. s = 2f : f + 9 = 2s : f = 3, s = 6
20.
a. 1:30 pm
b. 6:24pm
c. 24 mins
d. 30 mins

21. .8x = 120 : $150

22. $50

1.7 Words that Describe Patterns
Answers
1. s = square yards 25 = 10 + .2s : s = 75

2. p = number of people 324 = 200 + 4p : p = 31

3. m = number of miles 100 = 55 + .45m : m = 100

4. p = number of blocks Peter has now OR n = number of blocks Nadia gave Peter : p = 11
OR n = 11

5. p = number of passengers : p≤65

6. i = smaller integer : i + (i + 1) < 54

7. n = number : 3n > 30

8. a = amount invested : 0.05a≥250

9. h = number of hamburgers : 0.49h≤3

10. r = number of reports : 2r≥7

1.8 Checking Solutions to Equations
Answers
1. 4(− 3) + 3 =− 9 : Y ES

3 4 1
2. 4(3) + 2 = 23 : Y ES

3. 2.5(2) − 10.0 =− 5.0 : Y ES

4. 2(5 − 2(− 5)) = 20 − 2(− 5 − 1) : N O

5. 5(10) − 7 = 43 : Y ES

6. 3( 32 ) + 5 = 7 : Y ES

7. − 39 (10) =− 30 : Y ES

8. 2( 21 ) = 1.5 − 21 : Y ES

9. 0.5(1 − 2(0.5) = 6 + 6(4(0.5) − 3) : Y ES

10. 0.27l = f : 0.27l = 15, 000 : l = 55, 555.55

1.9 Checking Solutions to Inequalities
Answers
1. 2((12) + 6)≤8(12) : Y ES

2. 1.4(− 9) + 5.2 > 0.4(− 9) : N O

3. − 25 (40) + 1
2 <− 18 : Y ES

4. 80≥10(3(.4) + 2) : Y ES

5. 1000 + 0.06x≥1200 + 0.05(x − 2000) : x ≥10, 000

6.
a. c = 10
b. c = 5 + 0.05(m − 60)
c. c = 0.10m
7. 10 < 5 + 0.05(m − 60) : m > 160

8. 10 < 0.1m : m > 100

9. 5 + 0.05(m − 60) < 0.10m : m > 40

10. m > 160

11. 40 < m≤160

12. m≤40

13. Plan C

14. Plan A: $10, Plan B: $5, Plan C: $3

1.10 Domain and Range of a Function
Answers
1. Domain : 0 < x < ∞ Range : 0 < y < ∞

2. Domain : 0 < x < ∞ Range : 15 < y < ∞

3. Domain : − ∞ < x < ∞ Range : 0 < y < ∞

4. Domain : − ∞ < x < ∞ Range : 5 < y < ∞

5. Domain : − ∞ < x < ∞, x≠0 Range : − ∞ < y < ∞, y≠0

6. Domain : − ∞ < x < ∞ Range : − ∞ < y < ∞

7. Range: y = {− 1, − 4, − 5}

8. Range: y = {− 5 43 , − 3 43 , 9 41 }

9. Domain: x = {3, 4, 5}

10. Range: y = {27, 36, 45}

11.
Hours 5 10 15 20 25 30
Incom $32.5 $65.0 $97.5 $130.0 $162.5 $195.0

e 0 0 0 0 0 0

12.
Heigh 1 2 3 4 5 6
t
Area 4 8 1 1 2 2
2 6 0 4

13.
x 1 0 1 2 3 4 5
f (x) − √2 + 3 3 √2 + 3 2√2 + 3 3√2 + 3 4√2 + 3 5√2 + 3

1.11 Functions that Describe Situations
Answers
1. f (x) = x 2

2. f (x) = 15 + 5x

24
3. f (x) = 2x

4. f (x) = x − 1

x
5. f (x) = 2

6. f (h) = 40 + 25h

7. f (3) = 40 + 25(3) : f (3) = 115

8. 3(f (1)) = 3(40 + 25(1)) = 195

9. f (b) = 12.50b

10. p(b) = 12.50b − 2500

11. 12.50b = 2500 : b = 200

12. 12.50b = 2550 : b = 204

1.12 Functions on a Cartesian Plane
Answers
1. 5.

6.
a. (6, 4)
b. (7, 6)
c. (8, 2)
d. (4, 7)
e. (5, 0)

7.

8.

9.

10.

1.13 Graphs of Functions Based on Rules
Answers
1. Y = 20x

2.

3.

4.

5.
6.

7.
8.

9.
10.

1.14 Function Rules based on Graphs
Answers
1. Apx 62.5 years

2. Apx 69 years

3. Apx 73 years

4. Apx 76 years

5. Apx $19,000

6. Apx $55,500

7. Apx $10,500

8. Apx $30,500

9. y =− 23 x + 9

10. y = ∣ 2x ∣

11. y = √x

1.15 Algebraic Functions
Answers
1. Yes, function

2. No, not a function

3. Yes, function


5. Yes, function

6. Yes, function

7. Yes, function


9. Yes, function


1.16 ProblemSolving Models
Answers
1. $37.71

2. $42,857.14
3. $545
4. $89.29
5. $45.25
6. $750
7. 316 minutes
8.
a. 8 rides
b. $31.50
9. $219.65
10. 86%
11. It is a 306090 triangle
12. $96

13. 7 cups
14.
a. She makes $15 per lawn
b. The bike costs $100
15.
a. Jared collects 3+3(2)+12=21 pieces
b. The three kids together collect 21+23+23=67 pieces

16. 5 blocks are missing
17. 40 minutes
18. The home team wins by 1, Karen owes Chase 9($0.50)=$4.50
19. Kelley scores 37 points
20. 24 people ( $350 1
$15 = 23 3 , but they can’t charge 1/3 of a person)
21.
26(2)
a. 8 = 6.5 halfpound containers (7, assuming the store only sells full containers)
b. 6($4.80) + 7($2.80) = $48.40

1.17 Comparison of ProblemSolving Models
Answers
1. 35 nickels and 5 dimes

2. 4 tenfoot plots and 10 twelvefoot plots

3. 23 squares in the 12 th diagram

4. They need a threebedroom house

5. 7 guests (Jaden + 5 guests = $120, 2 more guests = $180 total)

6. 44 students and 156 general admission

7. 6 weeks

8. $0.50

9.
a. It will hold 6 and burst with 7
b. 4 smoothies

10. $240

11. 5 ½ hours

12. 4 hours

13.
a. 210 visitors
b. 1,110 visitors

14. 36 square feet

15. 18 points

16. Janet is 6, and Mark is 9

17. Jane scored 6 points, and Russell scored 4 points

18.
a. First pod will arrive first, on the 9th
of June
b. Second pod will arrive two days later on the 11 th
c. The second pod will catch the first pod on the second day
d. 30 miles


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Chapter

10. x − 25 = 2y : 5x + 5y = 350 : 5(2y − 25) + 5y = 350 : x = 55, y = 15

11. x + (x + 1) = 35 : 2x + 1 = 35 : x = 17 : 17, 18

18. .5v + 4 = .75(v + 4) : v = 4

1. s = square yards 25 = 10 + .2s : s = 75

1. Domain : 0 < x < ∞ Range : 0 < y < ∞

Incom $32.5 $65.0 $97.5 $130.0 $162.5 $195.0

f (x) − √2 + 3 3 √2 + 3 2√2 + 3 3√2 + 3 4√2 + 3 5√2 + 3

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