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Elementary Algebra

Katherine Yoshiwara

Appendix A Answers to Selected Exercises and Homework Problems

1 Variables
1.1 Variables
Skills Warm-Up
Exercises

1.

Answer.
Subtract 16 from the outside temperature.

2.

Answer.
Multiply the amount of soda by 3.

3.

Answer.
Add 2 feet to the distance between the poles.

4.

Answer.
Divide the weight of the bridge by 8.

5.

Answer.
Subtract the time for math from 4 hours.

6.

Answer.
Multiply the cost of the luxury car by 0.63.

Homework 1.1

1.

Answer.
  1. \(m\) \(g\)
    \(2\) \(5\)
    \(3\) \(6\)
    \(5\) \(8\)
    \(10\) \(13\)
    \(12\) \(15\)
    \(16\) \(19\)
    \(18\) \(21\)
    \(m\) \(m+3\)
  2. \(\displaystyle g=m+3\)

3.

Answer.
  1. \(b\) \(x\)
    \(0\) \(0\)
    \(2\) \(1\)
    \(4\) \(2\)
    \(5\) \(2.5\)
    \(6\) \(3\)
    \(8\) \(4\)
    \(9\) \(4.5\)
    \(b\) \(\dfrac{b}{2}\)
  2. \(\displaystyle x=\dfrac{b}{2}\)

5.

Answer.
Answers will vary. Sample answer:
\(n\) \(0\) \(5\) \(10\) \(15\) \(20\)
\(W\) \(0\) \(6\) \(12\) \(18\) \(24\)

7.

Answer.
a, b, and c:
\(x\) \(y\)
\(4\) \(0.5\)
\(8\) \(1\)
\(10\) \(1.25\)
\(16\) \(2\)
The three tables have identical values.

9.

Answer.
Temperature in Ridgecrest \(70\) \(75\) \(82\) \(86\) \(90\) \(R\)
Calculation \(70+15\) \(75+15\) \(82+15\) \(86+15\) \(90+15\) \(R+15\)
Temperature in Sunnyvale \(85\) \(90\) \(97\) \(101\) \(105\) \(R+15\)
  1. Add \(15\degree\) to Ridgecrest’s temperature to find Sunnyvale’s temperature.
  2. Temperature in Sunnyvale \(=\) Temperature in Ridgecrest \(+15\)
  3. \(\displaystyle S=R+15\)
  4. line

11.

Answer.
Total bill \(15\) \(30\) \(45\) \(75\) \(81\) \(b\)
Calculation \(15\div 3\) \(30\div 3\) \(45\div 3\) \(75\div 3\) \(81\div 3\) \(b\div 3\)
Milton’s share \(5\) \(10\) \(15\) \(20\) \(27\) \(\dfrac{b}{3}\)
  1. Divide the total bill by 3 to get Milton’s share.
  2. Milton’s share \(= \dfrac{\text{total bill}}{3}\)
  3. \(\displaystyle s=\dfrac{b}{3}\)
  4. line

13.

Answer.
  1. Horizontal: Number of years, Vertical: Amount in account
  2. About $3000
  3. Approximately after 13.75 years
  4. About $200
  5. About $400

15.

Answer.
Graph C

17.

Answer.
  1. line and points
  2. triangle

19.

Answer.
  1. \(\displaystyle y=2-x\)
  2. \(x\) \(0\) \(0.2\) \(0.3\) \(0.5\) \(0.6\) \(0.7\)
    \(y\) \(2\) \(1.8\) \(1.7\) \(1.5\) \(1.4\) \(1.3\)
    line and points

1.2 Algebraic Expressions
Homework 1.2

1.

Answer.
\(4y\)

3.

Answer.
\(1.15g\)

5.

Answer.
\(\dfrac{7}{w}\)

7.

Answer.
\(T+20\)

9.

Answer.
\(\dfrac{15}{M}\)

11.

Answer.
\(n-6\)

13.

Answer.
\(6-n\)

15.

Answer.
\(2x\)

17.

Answer.
\(2v\)

19.

Answer.
  1. \(\displaystyle \dfrac{m}{5}\)
  2. Spending money (dollars) \(20\) \(25\) \(60\)
    Amount saved (dollars) \(4\) \(5\) \(12\)

21.

Answer.
  1. \(\displaystyle \dfrac{2}{3}p\)
  2. Members present \(90\) \(96\) \(120\)
    Votes needed \(60\) \(64\) \(80\)

23.

Answer.
\(15p\)

25.

Answer.
\(\dfrac{3}{5}b\)

27.

Answer.
\(\dfrac{w}{16}\)

29.

Answer.
\(c-16\)

31.

Answer.
  1. \(\displaystyle 480-x\)
  2. \(\displaystyle 500-x\)
  3. \(\displaystyle 30-x\)

33.

Answer.
Amount of milk: \(m,~~ 0.70m\)

35.

Answer.
Votes received: \(v,~~ v-432\)

37.

Answer.
  1. \(\displaystyle d=180t\)
  2. 360 miles, 630 miles, 2160 miles

39.

Answer.
  1. \(\displaystyle B=0.085R\)
  2. $8500; $42,500; $170,000

1.3 Equations and Graphs
Homework 1.3

1.

Answer.
  1. no
  2. yes
  3. no
  4. no

3.

Answer.
  1. yes
  2. no
  3. no
  4. yes

5.

Answer.
  1. no
  2. no
  3. yes
  4. yes

7.

Answer.
horizontal: 0.25; vertical: 4

9.

Answer.
  1. \(x\) \(0\) \(2\) \(5\) \(6\) \(10\) \(12\) \(16\)
    \(y\) \(16\) \(14\) \(11\) \(10\) \(6\) \(4\) \(0\)
  2. \(\displaystyle y=16-x\)

11.

Answer.
f

13.

Answer.
c, e

15.

Answer.
  1. $35
  2. \(w\) \(12\) \(16\) \(20\) \(30\) \(36\) \(40\)
    \(p\) \(15\) \(20\) \(25\) \(37.50\) \(45\) \(50\)
  3. line on grid

17.

Answer.
  1. \(\displaystyle S=\dfrac{3600}{m}\)
  2. \(m\) \(20\) \(40\) \(60\) \(100\)
    \(S\) \(180\) \(90\) \(60\) \(36\)
  3. curve on grid

19.

Answer.
  1. \(\displaystyle g \approx 13.9\)
  2. \(\displaystyle g \approx 11.7\)

21.

Answer.
  1. \(\displaystyle (4,16)\)
  2. A 4-inch tall bunny weighs 16 ounces.

23.

Answer.
  1. \(\displaystyle P=6000-C\)
  2. \(C\) $800 $1000 $2500
    \(P\) $5200 $5000 $3500
  3. line on grid

25.

Answer.
  1. \(\displaystyle S=\dfrac{540}{n}\)
  2. \(n\) 20 25 30
    \(S\) 27 21.6 18
  3. line on grid

1.4 Solving Equations
Homework 1.4

1.

Answer.
\(t\) \(2\) \(4\) \(6\) \(9\)
\(q\) \(11\) \(13\) \(15\) \(18\)
To find a value for \(q\text{,}\) add 9 to the value of \(p\text{.}\) To find a value for \(p\text{,}\) subtract 9 from the value of \(q\text{.}\)

3.

Answer.
  1. yes
  2. no
  3. yes

5.

Answer.
\(y=2.8\)

7.

Answer.
\(b=12\)

9.

Answer.
\(x=4\)

11.

Answer.
\(z=\dfrac{10}{3}\)

13.

Answer.
  1. \(\displaystyle I=Prt; ~75=P \cdot 0.03 \cdot 1\)
  2. \(P=2500\text{;}\) Clive loaned his brother $2500.

15.

Answer.
  1. \(\displaystyle d=rt; ~234=13t\)
  2. \(t=18\text{;}\) It takes 18 hours.

17.

Answer.
\(x+7=26\)

19.

Answer.
\(\dfrac{x}{7}=26\)

21.

Answer.
\(\dfrac{x}{26}=7\)

23.

Answer.
  1. \(B=\) amount before Craft Fair
  2. \(\displaystyle B-24=9\)
  3. $63

25.

Answer.
  1. \(w=\) hourly wage
  2. \(\displaystyle 20w=136\)
  3. $6.80

27.

Answer.
\(89=p-26~~~\) Her mother paid $115.

29.

Answer.
\(1978=B-2378~~~\) There was $4356 in her account.

31.

Answer.
  1. Number of pames played: \(p;\)
    number of games won: \(w;~~~ w=0.06p\)
  2. 72
  3. 160

1.5 Order of Operations
Homework 1.5

1.

Answer.
14

3.

Answer.
72

5.

Answer.
\(\dfrac{3}{2}\)

7.

Answer.
0

9.

Answer.
4

11.

Answer.
3

13.

Answer.
0.859

15.

Answer.
42.705

17.

Answer.
  1. 18
  2. 50

19.

Answer.
  1. 2
  2. 8

21.

Answer.
  1. 2
  2. 18

23.

Answer.
\(z\) \(5z\) \(5z-3\)
\(2\) \(10\) \(7\)
\(4\) \(20\) \(17\)
\(5\) \(25\) \(22\)

25.

Answer.
26

27.

Answer.
\(\dfrac{7}{12}\)

29.

Answer.
\(\dfrac{15}{2}\)

31.

Answer.
  1. \(\displaystyle (20-2)\cdot 8+1=145\)
  2. \(\displaystyle 20-2\cdot(8+1)=2\)
  3. \(\displaystyle 20-2\cdot8+1=5\)

33.

Answer.
  1. \(\displaystyle \dfrac{20-8}{6+4+10}\)
  2. \(\displaystyle (20-8)\div(6+4+10)\)

35.

Answer.
\(\dfrac{12}{m-3}\)

37.

Answer.
\(\dfrac{m-3}{12}\)

39.

Answer.
Subtracting \(9-3\) is incorrect. It should be
\begin{equation*} 9-3(2)=9-6=3 \end{equation*}

1.6 Chapter 1 Summary and Review
Review Problems

Exercises

1.
Answer.
  1. Gallons of gas \(3\) \(5\) \(8\) \(10\) \(11\) \(12\)
    Miles driven \(66\) \(110\) \(176\) \(220\) \(242\) \(264\)
  2. Multiply the number of gallons by 22
  3. \(\displaystyle m=22g\)
  4. line
3.
Answer.
\(x\) \(0.5\) \(1.0\) \(1.5\) \(2.0\) \(4.0\) \(6.0\) \(7.5\)
\(y\) \(0.125\) \(0.25\) \(0.375\) \(0.5\) \(1\) \(1.5\) \(1.875\)
\(y=\dfrac{x}{4}\)
5.
Answer.
\(z+5\)
7.
Answer.
\(f-60\)
9.
Answer.
\(y+6\)
11.
Answer.
\(0.08b\)
13.
Answer.
  1. \(\displaystyle d=88t\)
  2. 440 ft; 44 ft; 2640 ft
15.
Answer.
  1. \(\displaystyle I=35t\)
  2. $35; $70; $175
17.
Answer.
  1. \(\displaystyle n=b-60\)
  2. \(n\) \(100\) \(120\) \(150\) \(180\) \(200\)
    \(b\) \(40\) \(60\) \(90\) \(120\) \(140\)
19.
Answer.
  1. \(\displaystyle n=2s\)
  2. \(s\) \(2\) \(3\) \(5\) \(8\)
    \(n\) \(4\) \(6\) \(10\) \(16\)
    line
21.
Answer.
a, c, d
23.
Answer.
  1. yes
  2. no
25.
Answer.
9
27.
Answer.
0.4
29.
Answer.
0
31.
Answer.
  1. 32
  2. 24
33.
Answer.
\(171=0.095P;~~\) $1800
35.
Answer.
\(106,000=0.53W;~~\) 200,000
37.
Answer.
\(\dfrac{w}{85}=0.7;~~\) 59.5 lb
39.
Answer.
3
41.
Answer.
6
43.
Answer.
\(\dfrac{1}{2}d+4\)
45.
Answer.
\(3(l+5.6)\)
47.
Answer.
4
49.
Answer.
5
51.
Answer.
$1300

2 Linear Equations
2.1 Signed Numbers
Homework 2.1

1.

Answer.
  1. \(\displaystyle 2\)
  2. \(\displaystyle -2\)
  3. \(\displaystyle -8\)

3.

Answer.
  1. \(\displaystyle -25\)
  2. \(\displaystyle 4.1\)
  3. \(\displaystyle -\dfrac{-1}{6}\)

5.

Answer.
  1. \(\displaystyle 4+(-8)=-4\)
  2. \(\displaystyle 3+9=12\)
  3. \(\displaystyle -8+6=-2\)
  4. \(\displaystyle -6+(-5)=-11\)

7.

Answer.
  1. \(\displaystyle -11\)
  2. \(\displaystyle -9\)
  3. \(\displaystyle 0\)
  4. \(\displaystyle -8\)

9.

Answer.
  1. \(\displaystyle 10\)
  2. \(\displaystyle 10\)
  3. \(\displaystyle 10\)

11.

Answer.
  1. \(\displaystyle -5\)
  2. \(\displaystyle -9\)
  3. \(\displaystyle 5\)
  4. \(\displaystyle 9\)
  5. \(\displaystyle 5\)

13.

Answer.
  1. \(\displaystyle -6\)
  2. \(\displaystyle -18\)

15.

Answer.
  1. \(\displaystyle -2\)
  2. \(\displaystyle 12\)
  3. \(\displaystyle -39\)

17.

Answer.
  1. \(\displaystyle 32\)
  2. \(\displaystyle -3\)
  3. \(\displaystyle 4\)

19.

Answer.
  1. \(\displaystyle 0\)
  2. \(\displaystyle -8\)
  3. undefined

21.

Answer.
  1. \(\displaystyle -16\)
  2. \(\displaystyle 48\)
  3. \(\displaystyle -8\)
  4. \(\displaystyle -16\)
  5. \(\displaystyle -3\)

23.

Answer.
  1. \(\displaystyle 5,~-5\)
  2. \(\displaystyle 5,~5\)
  3. \(\displaystyle 0,~5\)
  4. \(\displaystyle 0,~5\)

25.

Answer.
\(x=5\)

27.

Answer.
\(a=-32\)

29.

Answer.
\(t=-13\)

31.

Answer.
  1. \(\displaystyle x=3\)
  2. \(\displaystyle x=-6\)

33.

Answer.
$500

35.

Answer.
\(-6 \degree\)

37.

Answer.
14,776 feet

39.

Answer.
\(-48\) meters

41.

Answer.
\(n+12=5\)

43.

Answer.
\(-12+n=-5\)

2.2 Expressions and Equations
Homework 2.2

1.

Answer.
29.8 meters

3.

Answer.
$5400

5.

Answer.
\(-18\)

7.

Answer.
\(-15\)

9.

Answer.
  1. \(\displaystyle -24\)
  2. \(\displaystyle 24\)
  3. \(\displaystyle -24\)
  4. \(\displaystyle 48\)
  5. \(\displaystyle -48\)
  6. \(\displaystyle 48\)

11.

Answer.
  1. \(\displaystyle 2\)
  2. \(\displaystyle -2\)

13.

Answer.
  1. \(\displaystyle -6\)
  2. \(\displaystyle -2\)

15.

Answer.
  1. \(\displaystyle -60\)
  2. \(\displaystyle 7\)
  3. \(\displaystyle 27\)
  4. \(\displaystyle 6\)
  5. \(\displaystyle -23\)
  6. \(\displaystyle 35\)

16.

Answer.

17.

Answer.
\(13\)

19.

Answer.
\(-18\)

21.

Answer.
\(-\dfrac{1}{9}\)

23.

Answer.
    1. \(\displaystyle -\dfrac{15}{4}\)
    2. \(\displaystyle -\dfrac{15}{4}\)
    3. \(\displaystyle -3.75\)
  2. No

25.

Answer.
\(2x+10\)

27.

Answer.
  1. $4400;~ $2600
  2. Multiply the number of weeks by $200, then subtract from $5000.
  3. Number of weeks \(2\) \(4\) \(5\)
    Savings left \(4600\) \(4200\) \(4000\)
  4. \(\displaystyle S=5000-200w\)

29.

Answer.
  1. \(w=~\) width (inches);\(~~2w-3\)
  2. 23 inches

31.

Answer.
  1. \(t=~\) number of children’s tickets; \(8(150-t)\)
  2. $536

33.

Answer.
\(65+30t\)

35.

Answer.
\(\dfrac{80-M}{4}\)

37.

Answer.
\(200-15w\)

39.

Answer.
\(\dfrac{c-50}{10}\)

41.

Answer.
  1. \(\displaystyle \dfrac{x}{4+x}\)
  2. Many answers possible

2.3 Graphs of Linear Equations
Homework 2.3

1.

Answer.
  1. No
  2. Yes
  3. No
  4. Yes

3.

Answer.
  1. \(\displaystyle (-6,2)\)
  2. \(\displaystyle (-5,-7)\)
  3. \(\displaystyle (8,-4)\)
  4. \(\displaystyle (1,7)\)
  5. \(\displaystyle (0,-9)\)
  6. \(\displaystyle (-2,0)\)

5.

Answer.
  1. \(\displaystyle (0,-600)\)
  2. \(\displaystyle (10,-200)\)
  3. \(\displaystyle (15,0)\)
  4. \(\displaystyle (20,200)\)

7.

Answer.
  1. \(\displaystyle M=200+\frac{1}{5}U \)
  2. \(U\) \(20\) \(40\) \(80\) \(100\) \(200\)
    \(M\) \(204\) \(208\) \(216\) \(220\) \(240\)
  3. graph

9.

Answer.
  1. $5400
  2. $30
  3. $360
  4. 18
  5. \(\displaystyle B=540-30m\)

11.

Answer.
  1. \(\displaystyle d=120-\frac{1}{2}w \)
  2. \(w\) \(24\) \(36\) \(84\) \(120\)
    \(d\) \(108\) \(102\) \(78\) \(60\)
    line on grid
  3. \(96=120-{1}{2}w \text{;}\) 48 weeks

13.

Answer.
line on grid

15.

Answer.
line on grid

17.

Answer.
  1. \(\displaystyle x=-16\)
  2. \(\displaystyle x=-40\)

19.

Answer.
\(t\approx 1.5\)

2.4 Linear Equations and Inequalities
Homework 2.4

1.

Answer.
\(x\) \(2x\) \(2x+4\)
\(3\) \(6\) \(10\)
\(6\) \(12\) \(16\)
\(5\) \(10\) \(14\)
\(8\) \(16\) \(20\)

3.

Answer.
\(x=3\)

5.

Answer.
\(x=4\)

7.

Answer.
\(p=13\)

9.

Answer.
\(k=41\)

11.

Answer.
\(b=6\)

13.

Answer.
\(t=1\)

15.

Answer.
\(b=18\)

17.

Answer.
\(x=-4\)

19.

Answer.
\(x=3.4\)

21.

Answer.
  1. \(\displaystyle y\gt -5\)
  2. number line
  3. \(y=-4.9\) is a solution, \(y=-5\) is not.

23.

Answer.
  1. \(\displaystyle x\gt 2\)
  2. number line
  3. \(x=-7\) is a solution, \(x=-6\) is not.

25.

Answer.
  1. \(\displaystyle x \lt -6\)
  2. number line
  3. \(x=-7\) is a solution, \(x=-6\) is not.

27.

Answer.
  1. \(\displaystyle -7 \lt b \le -2\)
  2. number line
  3. \(b=-2\) is a solution, \(b=-7\) is not.

29.

Answer.

31.

Answer.

33.

Answer.
  1. \(\displaystyle P\approx 20\)
  2. \(m\approx 80\) minutes
  3. \(\displaystyle P=13+0.15m\)
  4. \(25=13+0.15m\text{;}\) \(80=m\)

35.

Answer.
  1. \(d=\)Greta’s assigned distance (mi)
  2. \(\displaystyle 5(d+0.5)=22.5\)
  3. She is assigned 4 miles.

37.

Answer.
  1. \(c=\)average temperature change per day
  2. \(\displaystyle 26=-6+4c\)
  3. The average change was 8 degrees per day.

39.

Answer.
175 yards

41.

Answer.
\(4x+8=36 \text{;}\) \(~x=7\)

2.5 Like Terms
Homework 2.5

1.

Answer.
\(-4x\)

3.

Answer.
\(t\)

5.

Answer.
\(12y-4\)

7.

Answer.
\(9x-2\)

9.

Answer.
\(2a\)

11.

Answer.
4

13.

Answer.
0

15.

Answer.
\(\dfrac{8}{3} \)

17.

Answer.
\(w \ge 21\)

19.

Answer.
  1. \(\displaystyle -21\)
  2. \(\displaystyle -6y-6\)
  3. \(\displaystyle -21\)

21.

Answer.
\(\begin{aligned} x=0:\amp\amp 2+7x\amp=2+7(0)=2;\\ \amp\amp 9x\amp=9(0)=0 \end{aligned}\)

23.

Answer.
\(6x+8y\)

25.

Answer.
  1. \(\displaystyle d+8\)
  2. \(\displaystyle 2d+8\)
  3. There are 16 dogs.

27.

Answer.
  1. \(\displaystyle 9.8t\)
  2. \(98\) feet
  3. 15 seconds

29.

Answer.
  1. \(\displaystyle 596x-1355\)
  2. 30

31.

Answer.
\(3p+33=p+131\text{;}\) \(p=49\) in

33.

Answer.
\(3g-70=2g+220\text{;}\) \(g=290\) mg

2.6 Chapter 2 Summary and Review
Review Problems

Exercises

1.
Answer.
f
3.
Answer.
c
5.
Answer.
b
7.
Answer.
\(\dfrac{5}{3} \)
9.
Answer.
8
11.
Answer.
\(V=2000-200t\)
line
13.
Answer.
\(5.75+4.50b=19.25\text{;}\) 3 bushels
15.
Answer.
  1. 3
  2. \(\displaystyle -6\)
  3. 6
  4. \(\displaystyle -3\)
17.
Answer.
\(\gt\)
19.
Answer.
\(\gt\)
21.
Answer.
20
23.
Answer.
9
25.
Answer.
31
27.
Answer.
\(\dfrac{-13}{16} \)
29.
Answer.
\(-3\)
31.
Answer.
\(-1\)
33.
Answer.
\(6\degree\text{F}\)
35.
Answer.
$460,000
37.
Answer.
\(-12\) yd
39.
Answer.
6.9, 6, 5
41.
Answer.
3, 2, 1
43.
Answer.
  1. \(h\) \(-4\) \(-2\) \(0\) \(1\) \(3\) \(5\) \(8\)
    \(T\) \(30\) \(24\) \(18\) \(15\) \(9\) \(3\) \(-6\)
  2. \(\displaystyle T=18-3h\)
  3. line
  4. \(\displaystyle 24\degree\text{F}\)
  5. 11 p.m.
  6. \(\displaystyle -18\degree\text{F}\)
45.
Answer.
line
47.
Answer.
\(2m+7n\)
49.
Answer.
\(z=-1\)
51.
Answer.
\(w=-3\)
53.
Answer.
\(h=-6\)
55.
Answer.
  1. \(\displaystyle -5\)
  2. \(\displaystyle 2\)
57.
Answer.
  1. \(\displaystyle 3x\)
  2. \(\displaystyle 8x\)
  3. 6 cm by 18 cm
59.
Answer.
number line
61.
Answer.
number line
63.
Answer.
numberline

3 Graphs of Linear Equations
3.1 Intercepts
Homework 3.1

1.

Answer.
  1. \((4,0)\text{,}\) \(~(0,2)\)
  2. line

3.

Answer.
  1. \((7,0)\text{,}\) \(~(0,-2)\)
  2. line

5.

Answer.
  1. \((20,0)\text{,}\) \(~(0,30)\)
  2. line

7.

Answer.
d

9.

Answer.
c

11.

Answer.
a

13.

Answer.
  1. \(\displaystyle x=-3\)
  2. \(\displaystyle x=-\dfrac{k}{2}\)

15.

Answer.
  1. \(\displaystyle x=14\)
  2. \(\displaystyle x=k+5\)

17.

Answer.
  1. \(\displaystyle x=3\)
  2. \(\displaystyle x=\dfrac{k-15}{-4}\)

19.

Answer.
  1. 360 miles
  2. 24 hours
  3. 180 miles
  4. 60 mil3s

21.

Answer.
  1. \((-9,0)\text{,}\) \(~(0,225) \)
  2. line
  3. \((0,225) \text{:}\) She has $225 this week.

23.

Answer.
  1. \(\displaystyle (12.5,0) \)
  2. \(\displaystyle (0,-5) \)

3.2 Ratio and Proportion
Skills Warm-Up
Exercises

1.

Answer.
\(0.375\)

2.

Answer.
\(1.4\)

3.

Answer.
\(1.\overline{3}\)

4.

Answer.
\(0.41\overline{6}\)

5.

Answer.
\(\dfrac{1}{25}\)

6.

Answer.
\(\dfrac{2}{3}\)

7.

Answer.
\(\dfrac{15}{8}\)

8.

Answer.
\(\dfrac{11}{5}\)

Homework 3.2

1.

Answer.
\(\dfrac{5}{7} \)

3.

Answer.
\(\dfrac{11}{6} \)

5.

Answer.
a and d are proportions.

7.

Answer.
\(w=\dfrac{15}{2} \)

9.

Answer.
\(z=\dfrac{7}{2} \)

11.

Answer.
no

13.

Answer.
no

15.

Answer.
yes

17.

Answer.
40 lbs

19.

Answer.
80 kilometers

21.

Answer.
about 13.78 in.

23.

Answer.
  1. \(\displaystyle w=7.5h\)
  2. line
  3. 67 hours

25.

Answer.
  1. \(\displaystyle C=0.04S\)
  2. $8000

27.

Answer.
  1. \(\displaystyle T=0.06T\)
  2. line
  3. The tax is also cut in half.

29.

Answer.
  1. \(\displaystyle C=2\pi r\)
  2. \(r\) \(2\) \(5\) \(7\) \(10\)
    \(C\) \(12.6\) \(31.4\) \(44.0\) \(62.8\)
  3. line
  4. Yes

31.

Answer.
  1. 3 to 2
  2. \(416\frac{2}{3} \) servings; \(7\frac{1}{2} \) cans
  3. 2.4 oz; 15.5 lb
  4. 24.75 cans; 90 lb

3.3 Slope
Homework 3.3

1.

Answer.
  1. \(\displaystyle \dfrac{3}{2} \)
  2. \(\displaystyle -2\)

3.

Answer.
\(15 \)

5.

Answer.
\(\dfrac{-1}{2} \)

7.

Answer.
  1. \((0,4) \text{,}\) \(~(6,0) \)
  2. triangle
  3. \(\displaystyle \dfrac{-2}{3} \)

9.

Answer.
  1. \((0,5) \text{,}\) \(~(5,0) \)
  2. triangle
  3. \(\displaystyle -1 \)

11.

Answer.
\(\dfrac{2}{3} \)

13.

Answer.
The line with slope \(\dfrac{5}{3} \) is steeper.

15.

Answer.
\(\Delta y = 17.5\)

17.

Answer.
  1. \(\displaystyle d=25g\)
  2. \(\dfrac{25\text{ miles}}{1\text{ gallon}} \text{;}\) the car gets 25 miles per gallon

19.

Answer.
  1. $50
  2. \((0,200) \text{,}\) \((2,300) \text{,}\) \(~\dfrac{\Delta A}{\Delta w}=50 \)
  3. dollars/week. She is saving $50 per week.

21.

Answer.
950.4 ft

23.

Answer.
  1. 0
  2. All the \(y\)-coordinates on the line are the same, so the change in \(y\) is 0

25.

Answer.
  1. (I) appears steeper.
  2. (I) has \(m=3\text{;}\) (II) has \(m=20\text{,}\) so (II) has the larger slope.

3.4 Slope-Intercept Form
Homework 3.4

1.

Answer.
  1. \(\displaystyle y=3x+4\)
  2. slope 3 and \(y\)-intercept \((0,4) \text{.}\)

3.

Answer.
  1. \(\displaystyle y=\dfrac{2}{3} x-2\)
  2. slope \(\dfrac{2}{3}\) and \(y\)-intercept \((0,-2) \text{.}\)

5.

Answer.
  1. \(m=3\text{;}\) \(y\)-intercept \((0,-4) \)
  2. \(\displaystyle y=3x-4 \)

7.

Answer.
  1. \(m=-\dfrac{8}{5} \text{;}\) \(y\)-intercept \((0,1) \)
  2. \(\displaystyle y=\dfrac{-8}{5}x+1 \)

9.

Answer.
  1. three parallel lines
  2. All three lines have the same slope of 1.
  3. I: \((0,-6) \text{;}\) II: \((0,1) \text{;}\) III: \((0,3) \)

11.

Answer.
  1. three lines with common y-intercept
  2. I: \(\dfrac{1}{4} \text{;}\) II: \(\dfrac{1}{2} \text{;}\) III: \(1 \)
  3. All three lines have the same \(y\)-intercept \((0,2) \)

13.

Answer.
  1. \((0,3) \text{,}\) \(~(4,0) \)
    line
  2. \(\displaystyle m=\dfrac{-3}{4} \)
  3. \(\displaystyle y=\dfrac{-3}{4}x+3\)

15.

Answer.
  1. \(\displaystyle y=\dfrac{3}{5}x \)
  2. \((0,0) \text{,}\) \(~\dfrac{3}{5} \)
  3. line

17.

Answer.
line

19.

Answer.
line

21.

Answer.
  1. \(\displaystyle (0,-240) \)
  2. 3
  3. \(\displaystyle P=-240+3x\)
  4. He spent $240 to open the shop and makes $3 of profit per smoothie.

23.

Answer.
  1. line
  2. The slope gives the weekly rate that the beans are growing: 3 inches per week. The \(h\)-intercept, \((0,18) \text{,}\) means that today, the beans are 18 inches tall.

3.5 Properties of Lines
Homework 3.5

1.

Answer.
Parallel

3.

Answer.
Neither

5.

Answer.
  1. horizontal line
  2. \(\displaystyle m=0\)

7.

Answer.
  1. horizontal line
  2. \(m\) is undefined

9.

Answer.
\(x=2\)

11.

Answer.
\(y=0\)

13.

Answer.
\(m=0\text{,}\) \(~b=-6\)

15.

Answer.
\(m=\dfrac{-1}{6} \text{,}\) \(~b=0\)

17.

Answer.
\(\dfrac{5}{3} \)

19.

Answer.
\(\dfrac{1}{9} \)

21.

Answer.
  1. \((5,0) \text{,}\) \(~(0,7) \)
  2. \(\displaystyle \dfrac{-7}{5} \)

23.

Answer.
  1. \(\left(\dfrac{1}{3},0\right) \text{,}\) \(~\left(0,\dfrac{7}{2}\right) \)
  2. \(\displaystyle \dfrac{-21}{2} \)

25.

Answer.
  1. \(\displaystyle \left(6,-8\right) \)
  2. \(\displaystyle (-4,-3) \)

27.

Answer.
  1. $0.08/1 page
  2. The cost of making copies is 8 cents per page.

29.

Answer.
  1. \(\displaystyle -3\degree/\text{ 1 hour}\)
  2. The temperature dropped at an average rate of \(3\degree\) per hour.

31.

Answer.
  1. \(\displaystyle -75 \text{miles/ 1 hour}\)
  2. Roy’s distance from home decreases by 75 miles each hour.
  3. 800; Roy boarded the train 800 miles away from home.
  4. \(10\frac{2}{3} \text{;}\) Roy will arrive home in about ten hours and 40 minutes.

3.6 Chapter 3 Summary and Review
Review Problems

Exercises

1.
Answer.
\((2,0) \text{,}\) \((0,-3)\)
triangle
3.
Answer.
  1. \(\displaystyle S=7800-600m\)
  2. \(2400=7800-600m\text{;}\) \(~m=9\) months
  3. The \(S\)-intercept at \(S=7800\) shows that she started with $7800. The \(m\)-intercept at \(m=13\) shows that she will use all the money in 13 months.
5.
Answer.
\(\dfrac{2}{3} \)
7.
Answer.
\(119\)
9.
Answer.
\(50\)
11.
Answer.
52 hr
13.
Answer.
  1. 10 mi by 15 mi
  2. 50 mi; 30 cm
  3. \(\displaystyle \dfrac{5}{3} \)
  4. 150 sq mi; 54 sq cm
  5. \(\displaystyle \dfrac{25}{9} \)
15.
Answer.
  1. No
  2. Yes
17.
Answer.
\(\dfrac{-3}{2} \)
19.
Answer.
8515 ft
21.
Answer.
  1. \((0,-6) \text{,}\) \(~(3,0) \)
  2. line
  3. \(\displaystyle m=2\)
23.
Answer.
  1. \((2,0) \text{,}\) \(~(0,-3) \)
  2. line
  3. \(\displaystyle m=\dfrac{3}{2} \)
25.
Answer.
  1. \(m=\dfrac{-3}{5} \text{,}\) \(~b=3\)
  2. \(\displaystyle y=\dfrac{-3}{5}x+3 \)
27.
Answer.
  1. \(\dfrac{-5}{2} \text{,}\) \(~b=-5\)
  2. line
29.
Answer.
  1. \(\dfrac{3}{4} \text{,}\) \(~b=2\)
  2. line
31.
Answer.
\(h=36+6t\)
33.
Answer.
\(m=-15\text{:}\) Beryl is descending at a rate of 15 ft/sec.
\(b=500\text{:}\) At 2 pm, Beryl’s altitude was 500 ft.
35.
Answer.
line
37.
Answer.
\(\dfrac{-3}{2} \)
39.
Answer.
\(-0.4\)
41.
Answer.
undefined
43.
Answer.
  1. 4.2
  2. Gas costs $4.20 per gallon.
45.
Answer.
\(y=\dfrac{1}{5} x-1\)
47.
Answer.
\(x=-4\)
49.
Answer.
  1. parallel
  2. perpendicular
51.
Answer.
line
53.
Answer.
line
55.
Answer.
line
57.
Answer.
line

4 Applications of Linear Equations
4.1 The Distributive Law
Homework 4.1

1.

Answer.
\(10y-15\)

3.

Answer.
\(-5b+3\)

5.

Answer.
  1. \(\displaystyle 32c\)
  2. \(\displaystyle 32+8c\)

7.

Answer.
d

9.

Answer.
\(-4x-6\)

11.

Answer.
\(-12z-15\)

13.

Answer.
\(y=-2\)

15.

Answer.
\(c=0\)

17.

Answer.
\(t \lt 2\)

19.

Answer.
\(a=4\)

21.

Answer.
  1. \(\displaystyle x=0\)
  2. \(5(x+3)=15\) and \(5x+3=3\)

23.

Answer.
  1. \(\displaystyle 2w-8\)
  2. \(\displaystyle 6w-16\)
  3. \(\displaystyle 2w^2-8w\)

25.

Answer.
  1. \(\displaystyle 3s\)
  2. \(\displaystyle 3s+45\)
  3. \(\displaystyle 45\)
  4. \(\displaystyle 6s+45\)

27.

Answer.
  1. \(\displaystyle 8-x\)
  2. \(\displaystyle 0.6x\)
  3. \(\displaystyle 2-0.25x\)
  4. \(\displaystyle 0.35x+2\)

29.

Answer.
\(5(2x+3):~10x+15\)

31.

Answer.
  1. \(\displaystyle 6w+12\)
  2. 5 by 16 yards

33.

Answer.
  1. \(\displaystyle 260-a\)
  2. \(\displaystyle 780-a\)
  3. \(\displaystyle 120\)

35.

Answer.
\(10x+6(47-x)=330;~\) 12 reserved seats

4.2 Systems of Linear Equations
Homework 4.2

1.

Answer.
No

3.

Answer.
Intercept method

5.

Answer.
Slope-intercept method

7.

Answer.
\((-4,-5)\)

9.

Answer.
\((-2,3)\)

11.

Answer.
Inconsistent

15.

Answer.
  1. Cost of one rose: \(x\text{,}\) cost of one carnation: \(y\)
  2. \(\displaystyle \begin{aligned}[t] 4x+8y=14\\ 6x+9y=18 \end{aligned}\)
  3. \(\displaystyle (1.50, 1.00)\)
  4. \(\displaystyle 4(1.5)+8(1)=14;~6(1.5)+9(1)=18\)

4.3 Algebraic Solution of Systems
Homework 4.3

1.

Answer.
\((2,4)\)

3.

Answer.
\((5,2)\)

5.

Answer.
\(\left(\dfrac{2}{3}, \dfrac{-4}{3}\right)\)

7.

Answer.
\((3,2)\)

9.

Answer.
\((1,2)\)

11.

Answer.
\((1,-1)\)

13.

Answer.
Inconsistent

15.

Answer.
Dependent

17.

Answer.
Elimination

19.

Answer.
  1. Number of chairs: \(x\text{,}\) number of tables: \(y\)
  2. \(\displaystyle \begin{aligned}[t] 175x+250y\amp=11,400\\ x\amp=4y \end{aligned}\)
  3. He can buy 12 tables and 48 chairs.

21.

Answer.
  1. Cost of 1 lb of bacon: \(x\text{,}\) cost of 1 lb of coffee: \(y\)
  2. \(\displaystyle \begin{aligned} 3x+2y\amp=17.80\\ 2x+5y\amp=32.40 \end{aligned}\)
  3. One pound of bacon costs $2.20, and one pound of coffee costs $5.60.

4.4 Problem Solving with Systems
Interest

Warm-Up 4.1.

Answer.
$154

Warm-Up 4.2.

Answer.
  1. Amount invested in stocks
    Amount invested in bonds
    Interest from stocks
    Interest from bonds
    Total interest
    $500 $4500 $35 $540 $575
    $1000 $4000 $70 $480 $550
    $3200 $2800 $224 $216 $440
    $4000 $1000 $280 $120 $400
  2. $5000; \(0.07x;~0.12y\)
  3. \(\displaystyle 0.07x+0.12y = 345\)

Mixtures

Warm-Up 4.3.

Answer.
  1. 25%, 50%
  2. 100, 40, 40%
  3. No

Warm-Up 4.4.

Answer.
No; 45%

Skills Warm-Up
Exercises

1.

Answer.
  1. $281.40
  2. \(\displaystyle 0.075x+0.048y\)

2.

Answer.
  1. 8.5 miles
  2. \(\displaystyle \dfrac{2}{3}x+\dfrac{1}{2}y\)

3.

Answer.
  1. 3.75 hours
  2. \(\displaystyle \dfrac{180}{x}+\dfrac{30}{y}\)

4.

Answer.
  1. 3 lbs
  2. \(\displaystyle 0.06x+0.60y\)

Homework 4.4

1.

Answer.
  1. \(\displaystyle x+y=150,000\)
  2. \(\displaystyle 0.65x;~ 0.118y\)
  3. \(\displaystyle 0.65x+0.118y= \$12,930\)
  4. bonds: $90,000; mutual fund: $60,000

3.

Answer.
student loan: $5000; car loan: $10,000

5.

Answer.
  1. 15 ml, 1.8 ml
  2. 16.8 ml, 42 ml
  3. 40%
  4. \(\hphantom{0000}\)
    Number of Milliliters (\(W\))
    Percent Acid (\(r\))
    Amount of Acid (\(P\))
    50% Solution \(30\) \(0.50\) \(15\)
    15% Solution \(12\) \(0.15\) \(1.8\)
    Mixture \(42\) \(0.40\) \(16.8\)

7.

Answer.
160

9.

Answer.
  1. diagram showing Dallas, Bonnie, and Clyde
  2. \(\hphantom{0000}\) Rate Time Distance
    Bonnie \(40\) \(t\) \(d\)
    Clyde \(70\) \(t-3\) \(d\)
  3. \(\displaystyle 40t=d;~70(t-3)=d\)
  4. 7 hours, 280 miles

11.

Answer.
40 miles

4.5 Point-Slope Formula
Homework 4.5

1.

Answer.
  1. line
  2. \(\displaystyle y=2x+2\)
  3. \(\displaystyle (1,0)\)

3.

Answer.
  1. line
  2. \(\displaystyle y=\dfrac{-2}{3}x-2\)
  3. \(\displaystyle (-3,0)\)

5.

Answer.
  1. line
  2. \(\displaystyle y=\dfrac{-5}{2}x+5\)
  3. \(\displaystyle (2,0)\)

7.

Answer.
\(m=\dfrac{3}{5},~(0,-7)\)

9.

Answer.
\(m=\dfrac{4}{3},~(0,0)\)

11.

Answer.
\(y=\dfrac{5}{3}x\)

13.

Answer.
\(y=\dfrac{-5}{7}x+\dfrac{11}{7}\)

15.

Answer.
\(y=\dfrac{-5}{3}x-\dfrac{1}{3}\)

17.

Answer.
  1. \(\displaystyle y=\dfrac{3}{2}x+\dfrac{5}{2}\)
  2. \(\displaystyle \dfrac{3}{2}\)
  3. line
  4. \(\displaystyle y=\dfrac{3}{2}x-4\)

19.

Answer.
  1. \(\displaystyle 2\)
  2. \(\displaystyle 2\)
  3. \(\displaystyle y=2x+5\)

21.

Answer.
\(y=-0.0025x+85\)
  1. \(m=-0.0025~\) degrees/ft. The temperature decreases by 0.0025 degrees for each 1 foot increase in altitude.
  2. \(\displaystyle 60 \degree\)
  3. \(\displaystyle 85 \degree\)

23.

Answer.
\(C=65h+125\)
  1. 65 dollars/hr. The hourly rate for lessons is 64 dollars per hour.
  2. $775
  3. $125

4.6 Chapter 4 Summary and Review
Review Problems

Exercises

1.
Answer.
  1. \(\displaystyle 30m\)
  2. \(-30+5m~\) requires the distributive law.
3.
Answer.
\(2m+7n\)
5.
Answer.
\(-15w+26\)
7.
Answer.
\(p=25\)
9.
Answer.
\(a \lt 1\)
11.
Answer.
  1. \(\displaystyle 3x\)
  2. \(\displaystyle 8x\)
  3. 6 cm by 18 cm
13.
Answer.
  1. \(\displaystyle 30-x\)
  2. \(\displaystyle 1200x\)
  3. \(\displaystyle 800(30-x)\)
  4. \(\displaystyle 400x+24,000\)
  5. 12 with speakers and 18 without speakers
15.
Answer.
No
17.
Answer.
\((3,2)\)
19.
Answer.
\((-3,-5)\)
21.
Answer.
\((1,-3)\)
23.
Answer.
\(\left(\dfrac{1}{2}, \dfrac{7}{2}\right)\)
25.
Answer.
\((12,0)\)
27.
Answer.
Consistent
29.
Answer.
Dependent
31.
Answer.
12 lb of cereal and 18 lb of dried fruit
33.
Answer.
$500 in the first account and $700 in the second
35.
Answer.
2 lb of the 60% alloy and 6 lb of the 20% alloy
37.
Answer.
Alida: 62 mph, Steve: 31 mph
39.
Answer.
26
41.
Answer.
$3181.82 at 8%, $1818.18 at 13.5%
43.
Answer.
  1. line
  2. \(\displaystyle y=\dfrac{-5}{3}x-\dfrac{7}{3}\)
44.
Answer.
45.
Answer.
\(y=\dfrac{-9}{5}x+\dfrac{2}{5}\)
47.
Answer.
  1. \(\displaystyle F=500+0.10C\)
  2. \(m=0.10~\) The decorator charges 10% of the cost of the job (plus a $500 flat fee)>
49.
Answer.
  1. \(t\) \(0\) \(15\)
    \(P\) \(4800\) \(6780\)
  2. \(\displaystyle P=4800+132t\)
  3. \(m=132~\) people per year gives the rate of population growth
50.
Answer.
51.
Answer.
  1. \(\displaystyle y=\dfrac{5}{2}x+b\)
  2. \(\displaystyle y=\dfrac{-2}{5}x+b\)
53.
Answer.
\(y=\dfrac{-2}{3}x+\dfrac{14}{3}\)

5 Exponents and Roots
5.1 Exponents
Homework 5.1

1.

Answer.
  1. \(\displaystyle 64\)
  2. \(\displaystyle 125\)
  3. \(\displaystyle 625\)

3.

Answer.
  1. \(\displaystyle 29.79\)
  2. \(\displaystyle 45.70\)
  3. \(\displaystyle 0.41\)

5.

Answer.
  1. \(\displaystyle -4\)
  2. \(\displaystyle 8\)
  3. \(\displaystyle -12\)
  4. \(\displaystyle -36\)

7.

Answer.
  1. \(\displaystyle 192\)
  2. \(\displaystyle 61\)
  3. \(\displaystyle 361\)
  4. \(\displaystyle -84\)

9.

Answer.
  1. \(\displaystyle 25a^2\)
  2. \(\displaystyle 10a\)

11.

Answer.
  1. \(\displaystyle -6m\)
  2. \(\displaystyle 9m^2\)

13.

Answer.
\(x \cdot x = x^2\)

15.

Answer.
\(x \cdot x^2 = x^3\)

17.

Answer.
cannot be simplified

19.

Answer.
\(12k^2\)

21.

Answer.
\(7k^2\)

23.

Answer.
\(2y^3+2y^2+y+1\)

25.

Answer.
The exponents should not be added; \(14w^3\)

27.

Answer.
\(7-(-5) = 12;~~t^2+12\)

29.

Answer.
\(49\)

31.

Answer.
\(o.25h^3\)

33.

Answer.
  1. \(\displaystyle 0.3h\)
  2. \(\displaystyle 50-h\)
  3. \(\displaystyle 0.25(50-h)\)
  4. \(\displaystyle 0.3h+0.25(50-h)\)

35.

Answer.
  1. \(\displaystyle x=0,~x=2\)
  2. Any values except \(x=0,~x=2\)
  3. No

37.

Answer.
  1. \(\displaystyle 7.4\)
  2. \(\displaystyle 74\)
  3. \(\displaystyle 740\)

39.

Answer.
  1. \(\displaystyle 39\)
  2. \(\displaystyle 234\)
  3. \(\displaystyle 3456\)

41.

Answer.
\(60b\)

5.2 Square Roots and Cube Roots
Homework 5.2

1.

Answer.
  1. \(\displaystyle -12\)
  2. \(\displaystyle -2\)

3.

Answer.
  1. \(\displaystyle \dfrac{19}{2}\)
  2. \(\displaystyle \dfrac{-2}{3}\)

5.

Answer.
\(-3.055\)

7.

Answer.
\(-15.544\)

9.

Answer.
\(-1.512\)

11.

Answer.
c

13.

Answer.
  1. 85
  2. 168
  3. 4082

15.

Answer.
  1. \(\displaystyle 16\)
  2. \(\displaystyle 29\)
  3. \(\displaystyle x\)

17.

Answer.
  1. \(\displaystyle \sqrt{6}\)
  2. \(\displaystyle -\sqrt{15}\)
  3. \(\displaystyle 2\sqrt{m}\)

19.

Answer.
\(\dfrac{5}{4},~ 2,~ 2.3,~ \sqrt{8}\)

21.

Answer.
\(\sqrt{5} \approx 2.236,~1,~0\)

23.

Answer.
\(30,~4-4\sqrt{2} \approx -1.657,~\dfrac{-7}{8}\)

25.

Answer.
9.61 seconds

27.

Answer.
\(\sqrt{4},~\sqrt{9},~\sqrt{64};~\sqrt{2},~\sqrt{6},~\sqrt{11}\)

29.

Answer.
No

31.

Answer.
No

5.3 Using Formulas
Homework 5.3

1.

Answer.
\(16w^2-36t^2\)

3.

Answer.
\(\dfrac{32 \pi h^3}{3}\)

5.

Answer.
\(22a^2\)

7.

Answer.
\(8\)

9.

Answer.
\(\sqrt{68}\)

11.

Answer.
\(k=5\sqrt{2},~ 3k=15\sqrt{2}\)

13.

Answer.
Yes

15.

Answer.
Not a right triangle

17.

Answer.
The hypotenuse is \(x\text{,}\) not 11.

19.

Answer.
\(w=\dfrac{v}{lh}\)

21.

Answer.
\(h=\dfrac{2A}{b+c}\)

23.

Answer.
\(h=\dfrac{A-2\pi r^2}{\pi r}\)

25.

Answer.
  1. \(\displaystyle 10^2+24^2=x^2\)
  2. 26 ft

27.

Answer.
  1. \(\displaystyle 90^2+90^2=x^2\)
  2. 127.3 ft

29.

Answer.
  1. \(\displaystyle 28^2+x^2=84^2\)
  2. 79.2 m

31.

Answer.
Area; \(49\pi \approx 153.94\) sq in

33.

Answer.
Volume; \(\approx 105,904.14\) cubic feet

35.

Answer.
  1. hemisphere dome
  2. \(\dfrac{128,000 \pi}{3}\) cubic feet
  3. \(3200 \pi\) square feet

5.4 Products of Binomials
Homework 5.4

1.

Answer.
  1. \(\displaystyle 12n\)
  2. \(\displaystyle 12n^2\)
  3. \(\displaystyle 64n^3\)

3.

Answer.
  1. \(\displaystyle -16p^2\)
  2. \(\displaystyle -16p^2\)
  3. \(\displaystyle -4p^2\)

5.

Answer.
  1. \(\displaystyle -12n^2\)
  2. \(\displaystyle -n\)
  3. \(\displaystyle 3n^2-4n\)

7.

Answer.
\(2a(5a+3)=10a^2+6a\)

9.

Answer.
\(-12b^2+4b\)

11.

Answer.
\(15v^2-6v^3\)

13.

Answer.
\(2y^4+6y^2-4y\)

15.

Answer.
\(-ax+15a\)

17.

Answer.
\(-3ax\)

19.

Answer.
  1. \(\displaystyle x^2+4x+3x+12\)
  2. \(\displaystyle (x+3)(x+4)\)

21.

Answer.
  1. \(~~~~~a~~~~~\)
    \(~~~~-3~~~~~\)
    \(a\)
    \(a^2\)
    \(-3a\)
    \(-5\)
    \(-5a\)
    \(15\)
  2. \(\displaystyle (a-5)(a-3)=a^2-8a+15\)

23.

Answer.
  1. \(~~~~~4x~~~~~\)
    \(~~~~3~~~~~\)
    \(5x\)
    \(20x^2\)
    \(15x\)
    \(-2\)
    \(-8x\)
    \(-6\)
  2. \(\displaystyle (5x-2)(4x+3)=20x^2+7x-6\)

25.

Answer.
\(6s^2+11st+3t^2\)

27.

Answer.
\(6x^2-20x+6\)

29.

Answer.
\(-4x^2+5x+6\)

31.

Answer.
\(1512\)

33.

Answer.
  1. \(\displaystyle -3x\)
  2. \(~~~~~x~~~~~\)
    \(~~~~-9~~~~~\)
    \(x\)
    \(x^2\)
    \(\alert{-9x}\)
    \(6\)
    \(\alert{6x}\)
    \(-54\)

35.

Answer.
\(x^2-9\)

37.

Answer.
\(9x^2-1\)

39.

Answer.
\(z^2-12z+36\)

41.

Answer.
No

43.

Answer.
  1. \(\displaystyle x^2+7x+7x+49\)
  2. \(\displaystyle (x+7)^2\)

45.

Answer.
No. If \(x=1,\) then \((x+4)^2 = 5^2 = 25,\) but \(x^2+4^2 = 1+16=17.\)

47.

Answer.
\(4x^2+4x+1\)

49.

Answer.
\(9x^2-24xy+16y^2\)

5.5 Chapter 5 Summary and Review
Review Problems

Exercises

1.
Answer.
  1. \(\displaystyle 147\)
  2. \(\displaystyle -441\)
  3. \(\displaystyle -40\)
  4. \(\displaystyle 16\)
3.
Answer.
  1. \(\displaystyle 1\)
  2. \(\displaystyle \dfrac{7}{5}\)
  3. \(\displaystyle \dfrac{12}{25}\)
  4. \(\displaystyle \dfrac{7}{5}\)
5.
Answer.
  1. \(\displaystyle 4\)
  2. \(\displaystyle 4\)
  3. \(\displaystyle 27\)
  4. \(\displaystyle 27\)
7.
Answer.
  1. irrational
  2. undefined
  3. rational
  4. irrational
9.
Answer.
  1. irrational, \(17.32\)
  2. irrational, \(7.47\)
11.
Answer.
\(-14\)
13.
Answer.
\(-2\)
15.
Answer.
\(-20.247\)
17.
Answer.
  1. \(\displaystyle -4\)
  2. \(\displaystyle 4\)
19.
Answer.
  1. \(\displaystyle -4\)
  2. \(\displaystyle 4\)
21.
Answer.
  1. \(\displaystyle -13\)
  2. \(\displaystyle 48\)
23.
Answer.
  1. \(\displaystyle 12\)
  2. \(\displaystyle 18\)
25.
Answer.
  1. \(\displaystyle 6\)
  2. \(\displaystyle 12\)
27.
Answer.
\(64\)
29.
Answer.
  1. \(\displaystyle 17\)
  2. \(\displaystyle 40\)
  3. \(\displaystyle 60\)
31.
Answer.
  1. \(\displaystyle 1\)
  2. \(\displaystyle 3+\sqrt{3}\)
  3. \(\displaystyle \dfrac{\sqrt{3}}{2}\)
33.
Answer.
\(V=126;~S=30\sqrt{7}+84\)
35.
Answer.
\(16b^3\)
37.
Answer.
\(V=150p^3;~S=190p^2\)
39.
Answer.
\(v=\dfrac{s}{t}-\dfrac{at}{2}\)
41.
Answer.
\(a=\dfrac{2S}{n}-f\)
43.
Answer.
13.9 yd
45.
Answer.
  1. 2.5 ft
  2. 78.54 sq ft
47.
Answer.
11.40 m
49.
Answer.
10 m
51.
Answer.
\(-20x+15x^2\)
53.
Answer.
\(6x^2y-12xy-3xy^2\)
55.
Answer.
  1. \(\displaystyle -2t^2\)
  2. cannot be simplified
  3. \(\displaystyle -48t^3\)
57.
Answer.
\(9a^2-3a\)
59.
Answer.
\(-2a^2-9a+8\)
61.
Answer.
\(1\)
63.
Answer.
  1. \(\displaystyle 5x^2-2x+5x-2\)
  2. \(\displaystyle (x+1)(5x-2)\)
65.
Answer.
\(x^3+2x-8\)
67.
Answer.
\(25a^2-1\)
69.
Answer.
\(4q^2+20q+25\)
71.
Answer.
\(u^2-7u+10\)
73.
Answer.
\(a^2+12a+36\)
75.
Answer.
\(6a^2-11ac-10c^2\)
77.
Answer.
\(18\)

6 Quadratic Equations
6.1 Extracting Roots
Homework 6.1

1.

Answer.
a, c

3.

Answer.
\(x\) \(-3\) \(-2\) \(-1\) \(0\) \(1\) \(2\) \(3\)
\(y\) \(5\) \(0\) \(-3\) \(-4\) \(-3\) \(0\) \(5\)
parabola

5.

Answer.
\(x\) \(-4\) \(-2\) \(-1\) \(0\) \(1\) \(2\) \(4\)
\(y\) \(4\) \(1\) \(0.25\) \(0\) \(0.25\) \(1\) \(4\)
parabola

7.

Answer.
  1. parabola
  2. \(\displaystyle -3,~3\)

9.

Answer.
\(\pm 11\)

11.

Answer.
\(\pm \dfrac{5}{3}\)

13.

Answer.
\(\pm \sqrt{6}\)

15.

Answer.
\(\pm 7.25\)

17.

Answer.
\(\pm 15\)

19.

Answer.
\(\pm 5.72\)

21.

Answer.
\(\pm\sqrt{\dfrac{A}{4\pi}} \)

23.

Answer.
\(\pm\sqrt{\dfrac{d-6}{k}} \)

25.

Answer.
  1. \(r\) \(C\)
    \(0\) \(0\)
    \(1\) \(0.25\)
    \(2\) \(1\)
    \(4\) \(4\)
    \(6\) \(9\)
    \(9\) \(20.25\)
    \(10\) \(25\)
    \(14\) \(49\)
  2. $2.25
  3. 8 in.
  4. The cost of a 6" radius pizza is $9.
parabola

27.

Answer.
  1. \(\sqrt{27} \) ft
  2. \(3\sqrt{27} \) sq ft

29.

Answer.
\(\sqrt{x^2-4} \)

6.2 Some Quadratic Models
Homework 6.2

1.

Answer.
\(-1, ~4\)

3.

Answer.
\(\dfrac{-3}{2}, ~\dfrac{1}{4} \)

5.

Answer.
b. \(9, ~-9~~~\)c. \(9^2-81=0\text{;}\) \((-9)^2-81=0\)

7.

Answer.
\(3ab\)

9.

Answer.
\(-3\)

11.

Answer.
\(4-3h\)

13.

Answer.
\(2a(3a-4)\)

15.

Answer.
\(h(4-9h)\)

17.

Answer.
\(r(2h-\pi r)\)

19.

Answer.
\(0, ~\dfrac{3}{2} \)

21.

Answer.
\(0, ~-48\)

23.

Answer.
\(0, ~{-1}\)

25.

Answer.
a.
\(x\) \(-1\) \(0\) \(1\) \(2\) \(3\) \(4\) \(5\) \(6\) \(7\)
\(y\) \(-7\) \(0\) \(5\) \(8\) \(9\) \(8\) \(5\) \(0\) \(-7\)
parabola
b. \(x=1\text{,}\) or \(x=5 ~~~\) d. \(x=0\text{,}\) or \(x=6\)
f. \(-x^2+6x\) d. \(0, ~~~ 0\)

27.

Answer.
  1. \(n(-2n+80)\text{;}\) \(80-2n\) dollars
  2. triangle
  3. $800; 20 bracelets
  4. 0 dollars

29.

Answer.
  1. \(\displaystyle R=180p-3p^2\)
  2. \(p\) \(R\)
    \(0\) \(0\)
    \(10\) \(1500\)
    \(20\) \(2400\)
    \(30\) \(2700\)
    \(40\) \(2400\)
    \(50\) \(1500\)
    \(60\) \(0\)
    grid
  3. $0 and $80
  4. $30; $2700

31.

Answer.
\((-4,0) \text{,}\) \(~(0,0) \)

33.

Answer.
two lines and parabola

35.

Answer.
\(\begin{aligned}[t] 4x^2 \amp= 12x\amp\amp\blert{\text{Subtract } 12x\text{.}}\\ 4x^2-12x \amp=0\amp\amp\blert{\text{Factor the left side.}}\\ 4x(x-3)\amp =0\amp\amp\blert{\text{Set each factor to 0.}}\\ x=0\amp ~\text{ or } ~x=3 \end{aligned}\)

6.3 Solving Quadratic Equations by Factoring
Homework 6.3

1.

Answer.
  1. \(~~~~~x~~~~~\)
    \(\alert{6}\)
    \(x\)
    \(x^2\)
    \(6x\)
    \(\alert{5}\)
    \(5x\)
    \(30\)
  2. \(\displaystyle (x+5)(x+6)=x^2+11x+30\)

3.

Answer.
  1. \(~~~~~x~~~~~\)
    \(\alert{2}\)
    \(\alert{x}\)
    \(x^2\)
    \(2x\)
    \(\alert{8}\)
    \(\alert{8x}\)
    \(16\)
  2. \(\displaystyle (x+8)(x+2)=x^2+10x+26\)

5.

Answer.
\(1\cdot 60\text{,}\) \(1\cdot 60\text{,}\) \(2\cdot 30\text{,}\) \(3\cdot 20\text{,}\) \(4\cdot 15\text{,}\) \(5\cdot 12\text{,}\) \(6\cdot 10\)

7.

Answer.
  1. \(\displaystyle (n+2)(n+8)\)
  2. \(-2\text{,}\) \(-8\)

9.

Answer.
  1. \(\displaystyle (a-2)(a-6)\)
  2. \(2\text{,}\) \(6\)

11.

Answer.
  1. \(\displaystyle (x+2)(x-5)\)
  2. \(-2\text{,}\) \(5\)

13.

Answer.
\((x-2)(x-15)\)

15.

Answer.
\((y+1)(y-45)\)

17.

Answer.
\((q+1)(q-6)\)

19.

Answer.
doesn’t factor

21.

Answer.
\((c+10)(c-6)\)

23.

Answer.
\(4(x-9)(x+4)\)

25.

Answer.
\(x=2\text{,}\) \(x=-5\)

27.

Answer.
\(x=-1\text{,}\) \(x=6\)

29.

Answer.
\(q=0\text{,}\) \(q=2\)

31.

Answer.
\(x=-2\text{,}\) \(x=3\)

33.

Answer.
  1. \(w+3\)
    \(w\)
  2. \(\displaystyle A=w(w+3)\)
  3. \(w\) \(-6\) \(-5\) \(-3\) \(-2\) \(-1\) \(0\) \(1\) \(2\)
    \(A\) \(18\) \(10\) \(0\) \(-2\) \(-2\) \(0\) \(4\) \(10\)
    parabola
  4. \(\displaystyle w(w+3)=28\)
  5. 4 yds

35.

Answer.
  1. \(2w+3\)
    \(w\)
  2. \(\displaystyle w(2w-2)=60\)
  3. \(w=-5\text{,}\) \(w=6\text{;}\) The circuit board should be 6 cm by 10 cm

37.

Answer.
The solution should be a number, not an algebraic expression.

6.4 Graphing Quadratic Equations
Skills Warm-Up
Exercises

1.

Answer.
\(x=3\)

2.

Answer.
\(x=-4\)

3.

Answer.
\(x=20\)

4.

Answer.
\(x=6\)

Homework 6.4

1.

Answer.
\(\left(\dfrac{-5}{2},0 \right) \text{,}\) \(~(3,0) \)

3.

Answer.
\(\left(\dfrac{8}{3},0 \right) \text{,}\) \(~(0,0) \)

5.

Answer.
parabolas

7.

Answer.
  1. parabola
  2. \(\displaystyle (-2,0)\)

9.

Answer.
  1. \((-2,0)\text{,}\) \((0,0)\)
  2. \(\displaystyle (-1,-1)\)
  3. parabola

11.

Answer.
  1. \((-3,0)\text{,}\) \((3,0)\)
  2. \(\displaystyle (0,9)\)
  3. parabola

13.

Answer.
  1. \((-1,0)\text{,}\) \((2,0)\text{;}\) \((-1,0)\text{,}\) \((2,0)\)
  2. \(\left(\frac{1}{2},\frac{-9}{4} \right)\text{;}\) \(\left(\frac{1}{2},\frac{9}{4} \right)\)
  3. parabola

15.

Answer.
  1. \(t\) \(0\) \(0.5\) \(1\) \(1.5\) \(2\) \(2.5\) \(3\)
    \(h\) \(48\) \(60\) \(64\) \(60\) \(48\) \(28\) \(0\)
  2. parabola
  3. 55 ft

17.

Answer.
1 sec

6.5 The Quadratic Formula
Homework 6.5

1.

Answer.
  1. \(\displaystyle \dfrac{8\pm\sqrt{48}}{2} \)
  2. \(0.54 \text{,}\) \(7.46\)

3.

Answer.
  1. \(\displaystyle \dfrac{1\pm\sqrt{5}}{2} \)
  2. \(-0.62\text{,}\) \(1.62\)

5.

Answer.
  1. \(\displaystyle \dfrac{\pm\sqrt{60}}{6} \)
  2. \(\displaystyle \pm\sqrt{\frac{5}{3} } \)

7.

Answer.
  1. \(\dfrac{3}{2} \text{,}\) \(2\)
  2. \(\dfrac{3}{2} \text{,}\) \(2\)

9.

Answer.
\(\dfrac{7}{8} \text{,}\) \(1\)

11.

Answer.
\(3 \text{,}\) \(15\)

13.

Answer.
width: 15 in, length: 40 in, height: 20 in

15.

Answer.
\(x=8\text{;}\) \(2x-1=15\)

17.

Answer.
  1. \((-0.73,0)\text{,}\) \((2.73,0)\)
  2. \(\displaystyle (1,-3)\)
  3. parabola

19.

Answer.
  1. \((-0.24,0)\text{,}\) \((4.24,0)\)
  2. \(\displaystyle (2,-5)\)
  3. parabola

6.6 Chapter 6 Summary and Review
Review Problems

Exercises

1.
Answer.
\(\pm\dfrac{2}{3} \)
3.
Answer.
\(\pm 2\)
5.
Answer.
\(\pm\dfrac{2}{3} \)
7.
Answer.
  1. 3 sec
  2. 36 ft
9.
Answer.
\(6x(4x-3)\)
11.
Answer.
\((a-15)(a-3)\)
13.
Answer.
\((2t-5)(t+2)\)
15.
Answer.
\((3w-1)(w+5)\)
17.
Answer.
\((z+11)(z-11)\)
19.
Answer.
\(3(2x+1)(x+3)\)
21.
Answer.
\(-5\text{,}\) \(-5\)
23.
Answer.
\(0\text{,}\) \(4\)
25.
Answer.
\(1\text{,}\) \(3\)
27.
Answer.
\(\dfrac{-6\pm\sqrt{12}}{4} \)
29.
Answer.
\(-0.47\text{,}\) \(1.07\)
31.
Answer.
\(s=\pm\sqrt{\dfrac{3V}{h}} \)
33.
Answer.
\(h=\pm\sqrt{\dfrac{C}{br}} \)
35.
Answer.
3.81 sec
37.
Answer.
  1. \(\displaystyle R=160p-2p^2\)
  2. \(\displaystyle M=136p-2p^2-80\)
  3. 30 cents or 38 cents
39.
Answer.
b. \(2w^2\)
c.
parabola
d. 4.9 in
41.
Answer.
  1. \((0,0)\text{;}\) \((0,0)\)
  2. \(\displaystyle (0,0)\)
  3. parabola
43.
Answer.
  1. \((0,0), (9,0)\text{;}\) \((0,0)\)
  2. \(\displaystyle \left(\dfrac{9}{2}, \dfrac{-81}{4}\right) \)
  3. parabola
45.
Answer.
  1. \((-6,0), (0,0)\text{;}\) \((0,0)\)
  2. \(\displaystyle (-3,-9)\)
  3. parabola
47.
Answer.
\(m=3.9\text{,}\) \(m+5=8.9\)

7 Polynomials
7.1 Polynomials
Homework 7.1

1.

Answer.
c

3.

Answer.
  1. polynomial
  2. not a polynomial: variable in denominator
  3. not a polynomial: variable in denominator
  4. polynomial

5.

Answer.
  1. 2
  2. 7
  3. 4

7.

Answer.
\(-2x^2+6xy+2y^3\)

9.

Answer.
15.8972

11.

Answer.
\(5-3\sqrt{3} \)

13.

Answer.
\(6x+6xy-9y\)

15.

Answer.
\(6+3x^2\) cannot be simplified

17.

Answer.
\(2y^3+2y^2+y+1\)

19.

Answer.
\(6x^2+2x-3\)

21.

Answer.
  1. 2000 ft
  2. Brenda has landed.

23.

Answer.
  1. 56
  2. 22,100
  3. 1140

25.

Answer.
  1. 567
  2. 5133
  3. 1001
  4. 80,080

27.

Answer.
  1. 29, before
  2. 6.632

29.

Answer.
  1. \(\displaystyle 28t^2-56t+28\)
  2. 28 ft; 7 ft
  3. 1 sec

31.

Answer.
a, b.
\(m\) \(T_m\) \(\dfrac{1}{3}m^3+\dfrac{1}{2}m^2+\dfrac{1}{6}m\)
\(1\) \(1\) \(1\)
\(2\) \(5\) \(5\)
\(3\) \(14\) \(14\)
\(4\) \(30\) \(30\)
\(5\) \(55\) \(55\)
\(6\) \(91\) \(91\)
\(7\) \(140\) \(140\)
\(8\) \(204\) \(204\)
\(9\) \(285\) \(285\)
\(10\) \(385\) \(385\)
c. They are the same.

7.2 Products of Polynomials
Homework 7.2

1.

Answer.
  1. \(\displaystyle x^9\)
  2. \(\displaystyle 5^{14}\)
  3. \(\displaystyle b^9\)

3.

Answer.
  1. \(\displaystyle -6x^8\)
  2. \(\displaystyle 2x^6\)
  3. \(\displaystyle -x^4y^3\)
  4. \(\displaystyle -9x^5 y^5\)

5.

Answer.
  1. \(\displaystyle 21z^8\)
  2. \(\displaystyle -10z^4\)

7.

Answer.
  1. \(\displaystyle 48w^5\)
  2. \(\displaystyle 144w^{10}\)

9.

Answer.
  1. \(\displaystyle 2a(5a+3)\)
  2. \(\displaystyle 10a^2+6a\)

11.

Answer.
  1. \(\displaystyle 2x^2\)
  2. \(\displaystyle x^4\)
  3. \(\displaystyle 0\)
  4. \(\displaystyle -x^4\)

13.

Answer.
  1. cannot be simplified
  2. \(\displaystyle x^3\)
  3. cannot be simplified
  4. \(\displaystyle -x^3\)

15.

Answer.
\(-x^3 y -x^2y^2 - xy^3\)

17.

Answer.
\(-3ax\)

19.

Answer.
\(x^2+xy-2y^2\)

21.

Answer.
\(2x^2-7ax+3a^2\)

23.

Answer.
\(-3x^2-9x+12\)

25.

Answer.
\(20x^2-5\)

27.

Answer.
\(6s^4t^2+s^3t^3-s^2t^4\)

29.

Answer.
\(27x^3-18x^2+6x-1\)

31.

Answer.
  1. \(\displaystyle x^3+7x^2+11x+6\)
  2. \(x=2\text{,}\) \(-4\text{,}\) \(-5\)

33.

Answer.
  1. \(\displaystyle 16-n\)
  2. \(\displaystyle 16n-n^2\)

35.

Answer.
  1. \(\displaystyle n+2\)
  2. \(\displaystyle n+4\)
  3. \(\displaystyle n^3+6n^2+8n\)

37.

Answer.
\(8w^2-18w-18\)

7.3 More About Factoring
Homework 7.3

1.

Answer.
  1. \(\displaystyle a^3\)
  2. \(\displaystyle 3^6\)
  3. \(\displaystyle \dfrac{1}{z^3}\)

3.

Answer.
\(\dfrac{1}{4xy^4} \)

5.

Answer.
\(\dfrac{5}{y^2} \)

7.

Answer.
\(-2k(2k^3-2k+1)\)

9.

Answer.
\(4ab(4a^2 b^2 - 3a +2b)\)

11.

Answer.
\(7xy(2x^2-5xy+3y^2)\)

13.

Answer.
\((2x+3)(3x^2-1)\)

15.

Answer.
\((5t+2)(t+1)\)

17.

Answer.
\(2(x+2)(x+3)\)

19.

Answer.
\(2z(2z+3)(z+1)\)

21.

Answer.
\((x-2y)(x-3y)\)

23.

Answer.
\((x+11a)(x-7a)\)

25.

Answer.
\(9ab(a+2b)(a-b)\)

27.

Answer.
\((4by+1)(by+1)\)

29.

Answer.
\(-1\text{,}\) \(\dfrac{4}{3} \)

31.

Answer.
\(\dfrac{1}{2}\text{,}\) \(\dfrac{1}{2} \)

33.

Answer.
\(-2\text{,}\) \(\dfrac{2}{3} \)

35.

Answer.
\(3\frac{1}{3} \) hrs

7.4 Special Products and Factors
Homework 7.4

1.

Answer.
  1. \(\displaystyle 64t^8\)
  2. \(\displaystyle 144a^4\)
  3. \(\displaystyle 100h^4k^2\)

3.

Answer.
  1. \(\displaystyle x^2+8x+8x+64\)
  2. \(\displaystyle (x+8)^2\)

5.

Answer.
\(n^2+2n+1\)

7.

Answer.
\(4b^2+20bc+25c^2\)

9.

Answer.
\(4x^2-12+9\)

11.

Answer.
\(9a^2+6ab+b^2\)

13.

Answer.
\(4h^2+20hk^4+25k^8\)

15.

Answer.
\(x^2-25z^2\)

17.

Answer.
\(9p^2-16\)

19.

Answer.
\(h^4-29t^2\)

21.

Answer.
\(16x^4+96x^3y+144x^2y^2\)

23.

Answer.
\((y+3)^2\)

25.

Answer.
\((a^3-2b)^2\)

27.

Answer.
\((1-g)(1+g)\)

29.

Answer.
\((x-3)(x+3)\)

31.

Answer.
\((8y-7x)(8y+7x)\)

33.

Answer.
\((6y^4+7)(6y^4-7)\)

35.

Answer.
\(3(a+5)(a-5)\)

37.

Answer.
\(9x^3(x^2+3)(x^2-3)\)

39.

Answer.
\((9x^4+y^2)(3x^2+y)(3x^2-y)\)

41.

Answer.
No. Let \(x=1\text{,}\) then \((x-1)^2=(-2)^2=4\text{,}\) but \(x^2-3^2=1-9=-8\)

43.

Answer.
No.

45.

Answer.
  1. \(\displaystyle a^3-3a^2b+3ab^2-b^3\)
  2. \(\displaystyle 8x^3-36x^2+54x-27\)
  3. \((a-b)^3=27\text{,}\) \(a^3-b^3=117\)

7.5 Chapter 7 Summary and Review
Review Problems

Exercises

1.
Answer.
  1. \(\dfrac{-1}{720}x^6+\dfrac{1}{24}x^4-\dfrac{1}{2}x^2+1 \text{,}\) degree 6
  2. \(10n^4+10^8n^2+10^6n \text{,}\) degree 4
3.
Answer.
\(26\)
5.
Answer.
\(\dfrac{1}{3} \)
7.
Answer.
0
9.
Answer.
\(6x^4-12x^3+3x^2-4x\)
11.
Answer.
  1. 4845
  2. 0, 0, 0
  3. 1; There is exactly one way to choose 4 items from a list of 4—choose all 4 items.
13.
Answer.
\(9p^2q -5pq^2\)
15.
Answer.
\(5b^3+2b^2+6b+4\)
17.
Answer.
  1. \(\displaystyle 4x^2\)
  2. \(\displaystyle 3x^4\)
19.
Answer.
  1. cannot be simplified
  2. \(\displaystyle 7a^{10}\)
21.
Answer.
  1. \(\displaystyle \dfrac{b^6}{3}\)
  2. \(\displaystyle \dfrac{3}{b^6}\)
23.
Answer.
\(-30m^5n^3\)
25.
Answer.
27.
Answer.
\(-2y^3+2y^2+24y\)
29.
Answer.
\(d^3-6d^2+12d-8\)
31.
Answer.
\(144x^5y-216x^4y^2+81x^3y^3\)
33.
Answer.
\(2a^2+a-9\)
35.
Answer.
\(\dfrac{1}{2c} \)
37.
Answer.
\(56q^2-49q^4-7q^6\)
39.
Answer.
\(81v^2-25w^2\)
41.
Answer.
\(-3p^4+9p^3+30p^2\)
43.
Answer.
\(8x^3-27\)
45.
Answer.
47.
Answer.
49.
Answer.
\(-32.6\)
51.
Answer.
  1. \(\displaystyle 140p-2p^2\)
  2. $528
53.
Answer.
Equation. \(x=\dfrac{-3}{2} \text{,}\) \(1\)
55.
Answer.
Polynomial. \((2x+3)(x-1)\)
57.
Answer.
Equation. \(x=\dfrac{-1}{2} \text{,}\) \(0\)
59.
Answer.
Equation. \(x=\dfrac{-3}{2} \)
61.
Answer.
Polynomial. \(2x(x+1)(x-1)\)
63.
Answer.
Equation. \(p=-1\text{,}\) \(0\text{,}\) \(1\)
65.
Answer.
\(4x^3(3x^2-2x+5)\)
67.
Answer.
\(6w^4(5w^5-7+9w^4)\)
69.
Answer.
\(-5d^2(2d^2-4d+1)\)
71.
Answer.
\(-vw^2(w^3+w^2-1)\)
73.
Answer.
\((3r+2)(-r^3+4)\)
75.
Answer.
\(3z(z+2)(z-2)\)
77.
Answer.
\((a^2+5)^2\)
79.
Answer.
\(2a^2b^2(b^4+16a^4)\)
81.
Answer.
\(-2a^2b(a+5b)(a-3b)\)
83.
Answer.
\(2q^2(q+8)(q-5)\)
85.
Answer.
\((x-2y)(x-y)\)
87.
Answer.
\(3b(a+3b)(a+b)\)
89.
Answer.
\((3xy+2)(3xy-1)\)
91.
Answer.
\((h-12)^2\)
93.
Answer.
Cannot be factored
95.
Answer.
\((w^4+6)^2\)
97.
Answer.
\(3(s^2+4)(s+2)(s-2)\)

8 Algebraic Fractions
8.1 Algebraic Fractions
Homework 8.1

1.

Answer.
  1. \(\dfrac{-3}{5} \text{,}\) \(\dfrac{3}{7} \)
  2. \(\displaystyle 3 \)

3.

Answer.
  1. \(-1 \text{,}\) \(1 \)
  2. \(\displaystyle \dfrac{-1}{2} \)

5.

Answer.
\(\dfrac{12b}{7} \)

7.

Answer.
\(\dfrac{1}{24v} \)

9.

Answer.
\(\dfrac{a}{9} \)

11.

Answer.
\(\dfrac{2u^3}{3w} \)

13.

Answer.
  1. \(\displaystyle \dfrac{m}{2n} \)
  2. Cannot be reduced

15.

Answer.
  1. \(\displaystyle -1 \)
  2. Cannot be reduced

17.

Answer.
  1. Cannot be reduced
  2. 2

19.

Answer.
a

21.

Answer.
b

23.

Answer.
a

25.

Answer.
\(\dfrac{x+4}{2} \)

27.

Answer.
\(\dfrac{n+2}{n-2} \)

29.

Answer.
\(\dfrac{3}{4} \)

31.

Answer.
Cannot be reduced

33.

Answer.
\(-1\)

35.

Answer.
\(\dfrac{-1}{2} \)

37.

Answer.
\(\dfrac{3x+2y}{2y-3x} \)

39.

Answer.
  1. \(n\text{:}\) number of immunized first-graders
  2. \(\displaystyle \dfrac{n}{84} \)

41.

Answer.
  1. \(g\text{:}\) gallons of gas Gladys’ car holds
  2. \(\displaystyle \dfrac{480}{3g} \)

43.

Answer.
  1. \(\dfrac{18}{x-4} \) dollars per gallon
  2. 1.8; If the tank holds 14 gallons, gas costs $1.80 per gallon.

45.

Answer.
  1. \(\dfrac{200}{2x-1} \) square centimeters
  2. 8; If \(x=13\text{,}\) the area of the cross-section is 8 \(\text{cm}^2\text{.}\)

47.

Answer.
  1. 30 min
  2. 50 min
  3. 50 min
  4. 6 mph
  5. The time increases. If the current is 10 mph, the team will not be able to row upstream

49.

Answer.
a, d

51.

Answer.
3 is not a factor of the numerator

8.2 Operations on Fractions
Homework 8.2

1.

Answer.
\(\dfrac{-3c}{4} \)

3.

Answer.
\(\dfrac{8}{5} \)

5.

Answer.
\(\dfrac{3}{2x} \)

7.

Answer.
\(\dfrac{6}{n^2+2n} \)

9.

Answer.
\(\dfrac{1}{a+1} \)

11.

Answer.
\(\dfrac{3}{4} \)

13.

Answer.
  1. \(\displaystyle \dfrac{2x}{3} \)
  2. \(\displaystyle \dfrac{3(a-b)}{4} \)
  3. \(\displaystyle \dfrac{n+2}{n-2} \)

15.

Answer.
\(\dfrac{8v^2}{9}-\dfrac{8}{v}-1 \)

17.

Answer.
\(\dfrac{25c^2}{4d^2} \)

19.

Answer.
\(-3 \)

21.

Answer.
\(\dfrac{-27}{4c^2} \)

23.

Answer.
\(\dfrac{b^2}{6a} \)

25.

Answer.
\(\dfrac{3a}{2} \)

27.

Answer.
\(\dfrac{-5}{2a} \)

29.

Answer.
\(\dfrac{4}{a} \)

31.

Answer.
\(\dfrac{2x+y}{3x} \)

33.

Answer.
\(z-3 \)

35.

Answer.
\(3x^2-2-\dfrac{2}{3x^2} \)

37.

Answer.
\(x-2+\dfrac{3}{y} \)

39.

Answer.
  1. \(\displaystyle \dfrac{p+r-1}{q+2}\)
  2. \(\displaystyle \dfrac{p-r+1}{q+2}\)
  3. \(\displaystyle \dfrac{p(r-1)}{(q+2)^2}\)
  4. \(\displaystyle \dfrac{p}{r-1}\)

41.

Answer.
\(\dfrac{AB^2}{3} \)

43.

Answer.
\(\dfrac{H}{5G^3} \)

45.

Answer.
\(\dfrac{2L}{c}+ \dfrac{2LV^2}{c^3}\)

47.

Answer.
  1. \(\displaystyle \dfrac{4-2m}{m(m+1)}\)
  2. \(\displaystyle \dfrac{-1}{6}\)

49.

Answer.
  1. \(\displaystyle \dfrac{x}{2} \)
  2. \(\displaystyle 2x\)
  3. \(\displaystyle \dfrac{1}{2x} \)
  4. \(\displaystyle \dfrac{1}{a+b} \)
  5. \(\displaystyle \dfrac{3}{4(a+b)} \)
  6. \(\displaystyle \dfrac{4}{3(a+b)} \)

8.3 Lowest Common Denominator
Homework 8.3

1.

Answer.
\(\dfrac{3y-4x}{xy} \)

3.

Answer.
\(\dfrac{a-3}{a} \)

5.

Answer.
\(\dfrac{5-x^2}{xy} \)

7.

Answer.
\(\dfrac{uv-4v+18}{3v} \)

9.

Answer.
\(\dfrac{4n^2+15n-9}{(n+3)(n-3)} \)

11.

Answer.
\(\dfrac{v^2+v-1}{v(v-1)} \)

13.

Answer.
\(\dfrac{-8+5q}{20n} \)

15.

Answer.
\(\dfrac{3z^2-2x}{12x^2z} \)

17.

Answer.
\(\dfrac{10z-17}{24z} \)

19.

Answer.
\(\dfrac{d}{x(d-x)} \)

21.

Answer.
\(\dfrac{a^2-2mt}{2at} \)

23.

Answer.
\(\dfrac{2Lc}{(c-V)(c+V)} \)

25.

Answer.
\(\dfrac{8}{x-1} \)

27.

Answer.
\(\dfrac{-m+6}{m(m-3)(m+3)} \)

29.

Answer.
\(\dfrac{2x^2+2x-3}{x(x+3)^2} \)

31.

Answer.
  1. \(\displaystyle \dfrac{8}{a}\)
  2. \(\displaystyle \dfrac{2b^2-4a}{ab}\)
  3. \(\displaystyle \dfrac{2b^2}{4a}\)
  4. \(\displaystyle \dfrac{2b^2+4a}{ab}\)

33.

Answer.
  1. \(\displaystyle \dfrac{3a-8}{a^2-4}\)
  2. \(\displaystyle \dfrac{6}{(a+2)^2(a-2)}\)
  3. \(\displaystyle \dfrac{3a-4}{a^2-4}\)
  4. \(\displaystyle \dfrac{3a-6}{2}\)

35.

Answer.
  1. \(\dfrac{100}{x-10} \) hrs
  2. \(\dfrac{100}{x+10} \) hrs
  3. \(\dfrac{200x}{x^2-100} \) hrs
  4. \(\dfrac{5}{7} \) hrs, \(\dfrac{5}{8} \) hrs, \(\dfrac{75}{56} \) hrs,

8.4 Equations with Fractions
Homework 8.4

1.

Answer.
1

3.

Answer.
4

5.

Answer.
1

7.

Answer.
\(-6\text{,}\) \(5\)

9.

Answer.
\(\dfrac{1}{2} \text{,}\) \(2\)

11.

Answer.
\(\dfrac{PV}{h} \)

13.

Answer.
\(\dfrac{y-k+hm}{m} \)

15.

Answer.
\(\dfrac{BR}{B-R} \)

17.

Answer.
\(\dfrac{r-dc}{cr} \)

21.

Answer.
50%

23.

Answer.
  1. \(AE=1\text{,}\) \(ED=x-1\text{,}\) \(CD=1\)
  2. \(\displaystyle \dfrac{x}{1}=\dfrac{1}{x-1} \)
  3. \(\displaystyle \dfrac{1+\sqrt{5}}{2} \)

25.

Answer.
  1. \(\displaystyle \dfrac{180}{x+20}=\dfrac{120}{x} \)
  2. freight train: 40 mph; express train: 60 mph

27.

Answer.
  1. \(\displaystyle \dfrac{x}{10}+\dfrac{x+4}{18}=1 \)
  2. 5 hr

29.

Answer.
Because \(x=1\text{,}\) dividing by \(x-1\) in the fourth step is dividing by \(9\text{.}\)

31.

Answer.
In the third equation, dividiing by \(m\) is dividing by \(0\) because \(m=0\) is one of the solutions. \(m=6, ~0\)

8.5 Chapter 8 Summary and Review
Review Problems

Exercises

1.
Answer.
  1. \(\displaystyle \dfrac{-1}{2} \)
  2. \(-5\text{,}\) \(~2\)
3.
Answer.
Cannot be reduced
5.
Answer.
\(\dfrac{5+y}{y} \)
7.
Answer.
\(\dfrac{1}{v+2} \)
9.
Answer.
\(\dfrac{-1}{2x+3} \)
11.
Answer.
  1. \(\displaystyle \dfrac{19}{24} \)
  2. \(\displaystyle \dfrac{5}{32} \)
13.
Answer.
  1. \(\displaystyle \dfrac{10x^2+2x+1}{6x(x+1)} \)
  2. \(\displaystyle \dfrac{1}{4} \)
15.
Answer.
  1. \(\displaystyle \dfrac{2x+1}{x} \)
  2. \(\displaystyle \dfrac{2}{x} \)
17.
Answer.
\(\dfrac{2c}{9d} \)
19.
Answer.
\(m-1 \)
21.
Answer.
\(\dfrac{8q^2-16q+21}{q(q-3)} \)
23.
Answer.
  1. \(\displaystyle \dfrac{5}{x-2} \)
  2. \(\displaystyle \dfrac{5}{x+2} \)
  3. \(\displaystyle \dfrac{10x}{x^2-4} \)
25.
Answer.
\(-2, ~8\)
27.
Answer.
\(\dfrac{-1}{2}, ~4 \)
29.
Answer.
\(\dfrac{yz}{y-z} \)
31.
Answer.
  1. \(\displaystyle \dfrac{5}{r}=\dfrac{8}{r+2}+1 \)
  2. 1.53 mph

9 More About Exponents and Roots
9.1 Laws of Exponents
Homework 9.1

1.

Answer.
  1. \(\displaystyle t^{15}\)
  2. \(\displaystyle b^{8}\)
  3. \(\displaystyle w^{144}\)

3.

Answer.
  1. \(\displaystyle \dfrac{w^6}{64} \)
  2. \(\displaystyle \dfrac{625}{v^4} \)
  3. \(\displaystyle \dfrac{-m^3}{p^3} \)

5.

Answer.
The first law simplifies a product of powers with the same base by adding the exponents. The third law simplifies a power raised to a power by multiplying the exponents.

7.

Answer.
\(32p^{15}\)

9.

Answer.
\(\dfrac{16h^8}{m^{12}} \)

11.

Answer.
\(4x^{10}y^{14} \)

13.

Answer.
\(-a^4 \)

15.

Answer.
\(-4p^5 q^{10} \)

17.

Answer.
\(2a^9+2a^8 \)

19.

Answer.
  1. \(\displaystyle 4x^2+2x^4\)
  2. \(\displaystyle 8x^6\)

21.

Answer.
  1. \(\displaystyle 324x^{16} \)
  2. \(\displaystyle 77x^8\)

23.

Answer.
  1. \(\displaystyle 6x^3-3x^6\)
  2. \(\displaystyle 3x^6\)

25.

Answer.
6

27.

Answer.
\(x^2+x^4\)

29.

Answer.
\(\lt\)

31.

Answer.
\(\lt\)

33.

Answer.
\(\gt\)

9.2 Negative Exponents and Scientific Notation
Homework 9.2

1.

Answer.
  1. \(\displaystyle \dfrac{1}{25} \)
  2. \(\displaystyle \dfrac{1}{x^6} \)
  3. \(\displaystyle 1 \)
  4. \(\displaystyle \dfrac{64}{27} \)

3.

Answer.
  1. \(\displaystyle 2^{-3} \)
  2. \(\displaystyle 3\cdot 5^{-2} \)
  3. \(\displaystyle 3^{-3} \)

5.

Answer.
  1. \(\displaystyle x^0=1\)
  2. \(\displaystyle w^{-3}=\dfrac{1}{w^3} \)
  3. \(\displaystyle 2x^{-4}=\dfrac{2}{x^4} \)

7.

Answer.
  1. \(\displaystyle c^{-3} \)
  2. \(\displaystyle 2b^4 \)
  3. \(\displaystyle 6^8 \)

9.

Answer.
  1. \(\displaystyle 8^{-10} \)
  2. \(\displaystyle w^{18} \)
  3. \(\displaystyle d^{-24} \)

11.

Answer.
\(\dfrac{a^{12}}{c^6} \)

13.

Answer.
\(\dfrac{5}{6k^{10}} \)

15.

Answer.
  1. \(\displaystyle 10^5 \)
  2. \(\displaystyle 10^{-2} \)
  3. \(\displaystyle 10^2 \)

17.

Answer.
  1. \(\displaystyle 43,000\)
  2. \(\displaystyle 0.000008\)
  3. \(\displaystyle 0.00002\)

19.

Answer.
  1. \(\displaystyle 4.834\times 10^3 \)
  2. \(\displaystyle 7.2\times 10^{-2} \)
  3. \(\displaystyle 7\times 10^{-6} \)

21.

Answer.
140

23.

Answer.
2400

25.

Answer.
Positive

27.

Answer.
Positive

29.

Answer.
  1. \(2.9141\times 10^4 \) ft
  2. \(7.6\times 10^{-5} \) cm

31.

Answer.
\(5.88\times 10^{12} \) mi

33.

Answer.
Note: figures updated
  1. \(\displaystyle 1.52\times 10^{18} \)
  2. \(4.56\times 10^{14} \) g

9.3 Properties of Radicals
Homework 9.3

1.

Answer.
True

3.

Answer.
False

5.

Answer.
\(n^{18} \)

7.

Answer.
\(-11ab^3 \)

9.

Answer.
\(\dfrac{-8}{b^3} \)

11.

Answer.
\(-2\sqrt{5} \)

13.

Answer.
\(x\sqrt{x} \)

15.

Answer.
\(p^{12}\sqrt{p} \)

17.

Answer.
\(\pm 6m^4\sqrt{2m} \)

19.

Answer.
\(4c^3 \sqrt{3d} \)

21.

Answer.
\(\dfrac{3w\sqrt{w}}{2\sqrt{7z}} \)

23.

Answer.
\(-10a^2b\sqrt{2a} \)

25.

Answer.
\(3\sqrt{3} \)

27.

Answer.
\(-7\sqrt{6} \)

29.

Answer.
\(-3\sqrt{3}-3\sqrt{2} \)

31.

Answer.
\(-3x\sqrt{5x}-6x\sqrt{5} \)

33.

Answer.
\(\sqrt{3}+\sqrt{3}=2\sqrt{3} \)

35.

Answer.
c

37.

Answer.
a

39.

Answer.
\(\sqrt{12} \)

9.4 Operations on Radicals
Homework 9.4

1.

Answer.
\(4 \)

3.

Answer.
\(36a^2 \)

5.

Answer.
\(4\sqrt{5}+10\sqrt{3} \)

7.

Answer.
\(1-2\sqrt{2} \)

9.

Answer.
\(7+4\sqrt{3} \)

11.

Answer.
3

13.

Answer.
\(\dfrac{4}{3} \)

15.

Answer.
\(\dfrac{-4+\sqrt{2}}{2} \)

17.

Answer.
\(\dfrac{5+6\sqrt{2}}{4} \)

19.

Answer.
\(\dfrac{3\sqrt{3}+6}{2} \)

21.

Answer.
Cannot be simplified

23.

Answer.
\(1-2\sqrt{3} \)

25.

Answer.
\(\dfrac{5\sqrt{2}}{2} \)

27.

Answer.
\(\sqrt{7b} \)

29.

Answer.
  1. \(\displaystyle \dfrac{w\sqrt{3}}{2} \)
  2. \(\displaystyle \dfrac{w^2\sqrt{3}}{4} \)

31.

Answer.
\(\left(\sqrt{3}\right)^2-2\sqrt{3}+3=0 \)

33.

Answer.
\(\left(\dfrac{-3+\sqrt{5}}{2} \right)^2 +3\left(\dfrac{-3+\sqrt{5}}{2} \right)+1=0 \)

9.5 Equations with Radicals
Skills Warm-Up
Exercises

1.

Answer.
  1. \(\displaystyle 9x^2\)
  2. \(\displaystyle 9+6x+x^2\)

2.

Answer.
  1. \(\displaystyle 3x\)
  2. \(\displaystyle 9x\)

3.

Answer.
  1. \(\displaystyle x+3\)
  2. \(\displaystyle x+2\sqrt{3x}+3\)

4.

Answer.
  1. \(\displaystyle x^2-2\sqrt{3}x+3\)
  2. \(\displaystyle 9-6\sqrt{x}+x\)

5.

Answer.
  1. \(\displaystyle 4-12\sqrt{x}+9x\)
  2. \(\displaystyle 8x-24\)

6.

Answer.
  1. \(\displaystyle x+1+4\sqrt{x-3}\)
  2. \(\displaystyle 4x-3+12\sqrt{x-3}\)

Homework 9.5

1.

Answer.
21

3.

Answer.
No solution

5.

Answer.
5

7.

Answer.
\(\sqrt{5} \text{,}\) \(-\sqrt{5} \)

9.

Answer.
5

11.

Answer.
\(\dfrac{-3}{4} \)

13.

Answer.
\(-125\)

15.

Answer.
\(\sqrt[3]{7} \)

17.

Answer.
\(4 \pm\sqrt{5} \)

19.

Answer.
\(\pm\sqrt{b^2-a^2} \)

21.

Answer.
  1. square root graph

23.

Answer.
  1. 144.5 km
  2. It is at least \(161\frac{1}{3} \) m

25.

Answer.
  1. 3 in
  2. 2091 \(\text{in}^3\)

9.6 Chapter 9 Summary and Review
Review Problems

Exercises

1.
Answer.
  1. \(\displaystyle a^{10}\)
  2. \(\displaystyle a^{24}\)
3.
Answer.
  1. \(\displaystyle 8a^{6}\)
  2. \(\displaystyle 2a^{8}\)
5.
Answer.
\(32x^7\)
7.
Answer.
\(-32t^8\)
9.
Answer.
  1. \(\displaystyle \dfrac{3}{x^2} \)
  2. \(\displaystyle \dfrac{1}{9x^2} \)
11.
Answer.
  1. \(\displaystyle \dfrac{z^2}{25} \)
  2. \(\displaystyle 5z^2 \)
13.
Answer.
\(\dfrac{6}{p^7} \)
15.
Answer.
\(\dfrac{8}{k} \)
17.
Answer.
5
19.
Answer.
\(5.86\times 10^{5} \)
21.
Answer.
\(7\times 10^{-4} \)
23.
Answer.
\(4.83\times 10^{5} \)
25.
Answer.
\(18,240,000,000,000,000 \)
27.
Answer.
\(0.000\,025\)
29.
Answer.
\(9.99\times 10^{-4} \) kg
31.
Answer.
  1. \(\displaystyle 2x^3 \)
  2. Cannot be simplified
  3. \(\displaystyle (4+x)^3 \)
33.
Answer.
\(-3m^2\sqrt{3m} \)
35.
Answer.
\(\dfrac{a\sqrt{ac}}{4} \)
37.
Answer.
\(\dfrac{4b^2\sqrt{3b}}{3} \)
39.
Answer.
\(\sqrt{6}+6\sqrt{2} \)
41.
Answer.
\(w^3\sqrt{6} \)
43.
Answer.
\(2-2\sqrt{3} \)
45.
Answer.
\(\dfrac{4-3\sqrt{3}}{6} \)
47.
Answer.
\(\dfrac{2\pm2\sqrt{6}}{3} \)
49.
Answer.
\(\dfrac{\pm\sqrt{c^2-2a^2}}{2} \)
51.
Answer.
\(\sqrt{6}-3\sqrt{2} \)
53.
Answer.
\(4-d \)
55.
Answer.
\(16+6\sqrt{7}\)
57.
Answer.
\(\dfrac{2\sqrt{x}}{x} \)
59.
Answer.
\(\dfrac{\sqrt{10}}{2} \)
61.
Answer.
\(\dfrac{5\sqrt{7}}{7} \)
63.
Answer.
\(2\left(\dfrac{1+\sqrt{7}}{2} \right)^2-2\left(\dfrac{1+\sqrt{7}}{2} \right)-3=0 \)
65.
Answer.
\(2\sqrt{10a} \)
67.
Answer.
7
69.
Answer.
12
71.
Answer.
41
73.
Answer.
90 ft
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