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Homework Elementary
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notes will help you remember how to solve the quiz and test problems. You can bring one sheet of these notes to all the
quizzes and the first test. You will also receive 1 bonus point on each quiz if you turn them in.
Translate to an algebraic expression.
1) 3 less than 6 times a number
Simplify.
13) -142
2) One tenth of x
14) 112 + 6 · 7 - (12 + 5 · 6)
Change this expression using the commutative law of
multiplication.
3) 7a + b
15) 4 · (5 + 5)2 - 2 · (6 - 4)2
16) 5(-6) + 2(-4)
Change this expression using the associative law of
addition.
4) w + (xy + z)
17) x - (3x + 8)
18) 3(-6) + 12(-4)
Use the distributive law to remove parenthesis.
5) 3(9x + 3)
Evaluate.
19)
Find the prime factorization of the number.
6) 198
20) -15 ÷ m 2 - 2(m - 2), for m = 8
Simplify.
7)
208
284
Determine if the given value is a solution to the equation.
Answer Yes or No.
21) 8x -10 = 5; x = 2
Multiply.
8) -
23
18
· 2
5
22) 4n + 5.1 = 5n + 9.2; n = -4.1
23) 3(x - 1) - x = 4x + 5; x = -4
Perform the indicated operation and, if possible, simplify.
63
9)
÷9
4
10)
3x - 2x2
, for x = -3
x2 - 10
Solve the equation using the Addition Property of
Equality. Be sure to check your solution.
24) b + 9 = 14
7 1
9 2
25) t - 8 = 10
Determine whether the statement is true or false.
11) -1 ≤ -8
26) 13 = - 2 + x
27) 4 = b - 5
Divide.
12)
-90
0
Solve the equation.
28) -36 = 9k
29) -7x = -28
1
Homework Elementary (continued)
Solve the equation.
30) -3.6 = y + 5.8
Convert to decimal.
47) 55.8%
31) 4 = -7x - 10
Convert to percent.
48) 0.00861
32) -6p - 5 = -9 + 8p
Solve.
33) 4y - 5 + y = 1 + 3y - 4y
49) What number is 8.1% of 25
34) 8x - (3x - 1) = 2
50) 44% of what number is 84?
35) 5(2z - 3) = 9(z + 3)
51) What percent of 3036 is 19?
52) 60% of what number is 99?
Solve the equation.
a
36) -7 =
3
37)
x
= -3
-9
38)
9
x = 72
10
53) What percent of 7 is 0.02?
54) The parking lot at a grocery store has 80 cars in
it. 25% of the cars are blue. How many cars are
blue?
Solve the problem.
55) If Gloria received a 4 percent raise and is now
making $24,960 a year, what was her salary
before the raise? Round to the nearest dollar if
necessary.
Solve the equation. Check your solution.
b
39)
- 6 = -4
20
56) Stevie bought a stereo for $235 and put it on
sale at his store at a 65% markup rate. What
was the retail price of the stereo? Round to the
nearest cent if necessary.
2x x
40)
- =2
5
3
Solve the formula for the indicated variable.
41) P = 2L + 2W for W
57) In a local election, 27,900 people voted. This
was a decrease of 12% over the last election.
How many people voted in the last election?
Round to the nearest whole person if
necessary.
42) d = rt for t
43) V =
44) x =
1
Bh for B
3
58) At the end of the day, a storekeeper had $1284
in the cash register, counting both the sale of
goods and the sales tax of 7%. Find the amount
that is the tax. Round to the nearest dollar if
necessary.
w+y+z
for y
4
Solve the formula for the indicated letter.
45) A = P(1 + nr) for r
46) F =
Solve the problem.
59) The sum of two consecutive integers is -265.
Find the larger integer.
9
C + 32 for C
5
2
Homework Elementary (continued)
69) x > -3
Solve the problem.
60) Eight times a number is 17 more than two
times that number. Find the number.
Solve the problem.
61) The second angle of a triangle is 3 times as
large as the first. The third angle is 75° more
than the first. Find the measure of the smallest
angle.
70) x ≤ 1
Write this solution using inequality symbols.
71)
Solve the Problem.
62) The sum of three consecutive integers is 480.
Find the integers.
-7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7
Solve the problem.
63) Two angles are complementary. The second
angle measures 48° less than the first angle.
What is the measure of the first angle?
72)
-7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7
Solve the Problem.
64) Find the measures of the supplementary
angles.
Solve the inequality and graph the solution on a number
line.
73) 4x + 3 < 11
Solve, then graph the solution.
74) 9t + 5 ≥ 8t + 7
65) A rectangular Persian carpet has a perimeter of
224 inches. The length of the carpet is 26 inches
more than the width. What are the dimensions
of the carpet?
Solve, then graph the solution.
b
75) -2 <
3
Solve the problem.
66) The second angle of a triangle is 3 times as
large as the first. The third angle is 40° more
than the first. Find the measure of the smallest
angle.
Determine whether the given number is a solution of the
inequality.
67) x > -2, -7
76) -7 >
Graph on a number line.
68) x < 4
k
-4
Solve the inequality.
77) -10a - 9 ≤ -11a - 3
78) -6 - 10z + 3 ≥ -11z - 10
3
Homework Elementary (continued)
79) -5(6y - 8) < -35y + 20
80)
Find the coordinates of the labeled points.
83)
x
+ 5 ≤ 10
2
Plot the ordered pairs.
81) A(-5, 0), B (0, 3)
C
8
y
7
6
5
4
3
2
1
y
1 2 3 4 5 6 7 x
-7 -6 -5 -4 -3 -2 -1-1
-2
-3
-4
-5
-6
-7
D
8 x
-8
84)
7
6
5
4
3
2
1
-8
82) A(4, 6), B(6, -4)
8
y
-7 -6 -5 -4 -3 -2 -1-1
-2
-3
-4
H
-5
-6
-7
y
G
1 2 3 4 5 6 7 x
8 x
-8
Is the ordered pair given a solution to the equation ?
85) 4x - 5y = 33; (2, 5)
86) 5x + 5y = 35; (5, 2)
-8
87) y = -2x; (2, -4)
4
Homework Elementary (continued)
91) 2x - y = -4
Graph the equation.
88) x + y = 7
y
10
y
10
5
5
-10
-10
-5
5
10
-5
5
10
x
5
10
x
5
10
x
x
-5
-5
-10
-10
92) 3y - 27x = 24
89) y = x - 3
y
10
y
10
5
5
-10
-10
-5
5
10
-5
x
-5
-5
-10
-10
93) 6x + y = 0
90) y = 4x - 4
y
10
y
10
5
5
-10
-10
-5
5
10
-5
x
-5
-5
-10
-10
5
Homework Elementary (continued)
94) y =
1
x
4
97)
y
10
y
10
5
5
-10
-10
-5
5
10
-5
x
5
10
x
-5
-5
-10
-10
Find the x- and y-intercepts and use them to graph the
equation.
98) -2x - 4y = 8
95) y = 3x - 4
y
y
10
10
5
5
-10
-5
5
10
x
-10
-5
5
10
x
10
20
x
-5
-5
-10
-10
Find the coordinates of the x- and y-intercepts of the line.
96)
99) -x + 3y = 9
y
y
-10
10
20
5
10
-5
5
10
-20
x
-10
-5
-10
-10
-20
6
Homework Elementary (continued)
100) y = -5x+ 15
103) 3x - y = 3
y
20
10
y
10
5
-20
-10
10
20
x
-10
-5
5
x
5
x
5
x
-10
-5
-20
-10
101) x + y = 4
104) x - 2y = 2
10
y
10
y
5
5
-10
-5
5
x
-10
-5
-5
-5
-10
-10
102) 2x - y = 2
10
Graph the equation.
105) x - y = 2
y
10
y
5
5
-10
-5
5
x
-10
-5
-5
-5
-10
-10
7
Homework Elementary (continued)
106) x = -2
109) 5x = -30
8
7
6
5
4
3
2
1
y
y
10
5
-10
-8 -7 -6 -5 -4 -3 -2 -1
-1
-2
-3
-4
-5
-6
-7
-8
5
10
x
-5
-10
Solve the problem.
110) On March 17 Henry rented a van with a full
tank of gas and 16,887.0 miles on the
odometer. On March 21 he returned the van
with 17,283 miles on the odometer. The rental
agency charged Henry $128 for the rental and
needed 15 gallons to fill up the tank. What was
the van's rate of gas consumption in miles per
gallon?
107) 35 + 7y = 0
y
10
5
-10
-5
1 2 3 4 5 6 7 8 x
-5
5
10
x
111) To the nearest dollar, the average tuition at a
public four-year college was $3032 in 1998 and
$3462 in 2000. Find, to the nearest dollar per
year, the rate at which tuition was increasing.
-5
-10
112) At 10:00 AM, Gavin rented a mountain bike.
He returned the bike at 3:00 PM. He biked for
25 miles. He paid $27.50 for the rental. Find
the rental rate, in dollars per mile.
108) y = 1
8
7
6
5
4
3
2
1
-8 -7 -6 -5 -4 -3 -2 -1
-1
-2
-3
-4
-5
-6
-7
-8
y
1 2 3 4 5 6 7 8 x
8
Homework Elementary (continued)
113) The following graph shows data for a recent
train ride from New York to Toronto. At what
rate did the train travel?
Use the graph to solve the problem.
115) Find the rate of change of Simone's salary.
300
200
100
1
2
3
4
5
Time of Day (PM)
116) Find the rate of change in the temperature.
114) Data regarding the amount spent by a
government department is represented in the
following graph. At what rate does the amount
change?
8.8
8
7.2
117) Find the rate of change in the height of the tree.
1998
1999
2000
40
Year
32
24
16
8
2
4
6
Age (years)
9
8
10
Homework Elementary (continued)
118) Find the rate of change in the value of Bob's
car.
Find the slope of the line, or state that the slope is
undefined if appropriate.
121)
5
y
4800
4400
4000
5 x
-5
3600
3200
90
91
92
93
94
95
96
Year
-5
119) Find the rate of change in Carlos's weight.
122) (-3, 3) (-3, -3)
y
172
10
168
5
164
160
-10
156
-5
5
152
x
10
-5
148
-10
144
-1
1
2
3
4
5
6
7
months since start of diet
123)
120) Find the rate of change of the temperature of
the water being heated.
5
y
4
3
80
2
75
1
-5
70
-4
-3
-2
-1
1
-1
-2
65
-3
-4
60
-5
-1
1
2
3
4
5
6
7
Minutes since heating started
10
2
3
4
5 x
Homework Elementary (continued)
124) (-2, -4) (5, -4)
135) The pitch of a roof is its slope. Find the pitch of
the roof shown.
y
10
5
10 feet
-10
-5
5
10
14 feet
x
-5
-10
Find the slope of the line containing the given pair of
points. If the slope is undefined, state so.
125) (4, 5) and (9, 3)
Draw a line that has the given slope and y-intercept.
1
136) Slope ; y-intercept (0, 5)
4
126) (-1, -3) and (1, -8)
127) (-5, -8) and (-5, -2)
y
10
128) (5, 7) and (9, 7)
5
Find the slope of the line. If the slope is undefined, state
so.
129) y = 1
-10
-5
5
10
x
10
x
-5
130) x = -4
-10
Determine whether the pair of equations represents
parallel lines.
131) 9x + 3y = 12
6x + 2y = 9
137) Slope -
1
; y-intercept (0, 4)
3
132) y = 3x - 5
9x + 3y = 6
y
10
Solve the problem.
133) Over one particular stretch of road, the
Whitepoint Highway rises 414 ft over a
horizontal distance of 3300 ft. Find the grade of
the road.
5
-10
-5
5
-5
134) Kannanaski Rapids drops 68 ft vertically over
a horizontal distance of 907 ft. What is the
slope of the rapids?
-10
11
Homework Elementary (continued)
141) y = - 6x + 2
Graph the specified line.
1
138) The line with slope - that passes through the
6
y
10
point (0, 6)
5
y
10
-10
5
-5
5
10
x
5
10
x
-5
-10
-5
5
10
x
-10
-5
-10
142) y = -
1
x+6
4
y
Graph the linear equation.
139) 4x - y = 5
10
y
5
10
-10
5
-5
-5
-10
-5
5
10
x
-10
-5
Graph the specified line.
-10
143) The line with slope
140) y =
1
x+2
2
3
that passes through the
2
point (4, 2)
y
10
y
10
5
5
-10
-10
-5
5
10
-5
5
x
-5
-5
-10
-10
12
10
x
Homework Elementary (continued)
144) The line with slope -
3
that passes through the
2
155) (9, 4) and (1, 4)
156) (-7, 7) and (4, -2)
point (1, 5)
y
10
Write the equation of the line.
157)
5
y
10
-10
-5
5
10
x
5
-5
-10
-5
5
10
x
5
10
x
5
10
x
-10
-5
Find the slope and the y-intercept of the line.
11
145) y =
x-4
4
-10
158)
146) -4x + y = 16
y
10
Find the equation for the line with the indicated slope
and y-intercept.
5
147) Slope - ; y-intercept (0, 9)
3
5
-10
148) Slope
-5
3
; y-intercept (0, -1)
2
-5
-10
Find an equation of the line having the specified slope
and containing the indicated point.
4
149) m = - ; (5, -1)
5
Write an equation for the graph.
159)
y
150) m = -4; (-5, 6)
10
151) m = -3; (2, -3)
5
152) m = -3; (4, -3)
153) m = -
-10
-5
-5
3
; (11, -2)
5
-10
Find an equation of the line containing the given pair of
points.
154) (2, -3) and (6, 5)
13
Homework Elementary (continued)
160)
172)
y
5x-4
y-3 z-7
10
-10
10
s-2 6
t-3
176) 1.27 × 10-4
Convert to scientific notation.
177) 49,000
Simplify.
162) (-4a 5 )4
178) 0.00008701
163) (5r6 )2
Perform the indicated operation. Write the answer in
scientific notation.
179) (6.1 × 10-3 )(7.6 × 106)
Simplify.
164) (pq6)(pq)3
165) (6x3 )(2x5 )
180)
30m 3p2
5m 9p
a5
174)
Convert to decimal notation.
175) 4.83 × 107
Simplify the expression.
161) 5x0
167)
x6 y5 -5
wz 6
x
-10
166)
173)
16 × 10-6
4 × 103
Combine like terms.
181) y3 + 8y4 + 7y2 + y4 - 12y3
4
- 5b2
182) 5x2 y - 2 - 4xy2 + 6x2 y - 5
Evaluate the polynomial.
183) -2x3 - 6x2 - 26 for x = -3
Simplify. Do not use negative exponents in your answer.
p3
168)
p-4
184) -5x3 - 6x2 - x + 27 for x = -2
169)
t-3
t-8
Evaluate as requested.
185) Evaluate the polynomial 2x2 - y2 + 2xy for x =
-3 and y = -5.
170) (x-1 y-5)-6
186) Evaluate the polynomial x2yz + x + y for x = 1,
y= -4, and z = 2.
171) (x-5 y-5)(x9 y-9)
14
Homework Elementary (continued)
Add.
Find the product of the polynomials.
205) (x + 4)(x2 - 4x + 16)
187) (-9 + 7n 7 + 7n 4 ) + (3n 7 + 5n 4 + 6)
188) (-8 - 6x6 + 6x8 + 7x7 ) + (5x7 - 5x6 + 3 + 5x8 )
206) (8 - p)(4 - 2p + 3p2 )
Subtract.
207) (x - y)(x2 + xy + y2 )
189) (-16n + 9n 6 + 2n 5) - (11n 5 + 5n 6 - 13n)
208) (x + y)(x2 + 3xy - y2 )
190) (7x6 + 7x8 - 3 + 4x7 ) - (-1 + 6x7 + 4x8 - 2x6 )
Multiply.
Add or subtract, as indicated.
191) (x2 - 6xy + 4y2) + (6x2 - 5xy - y2 ) + (-2x2 + xy
209) (4x5 - 1)(4x5 + 1)
- y2 )
210) (p + 12q)(p - 12q)
192) (8m 2n - 4mn + 8mn 2 ) - (2m 2 n + 4mn - 9mn 2 )
Find the product.
211) (n + 4)2
Multiply.
193) -10x(11x + 3)
212) (w - 16)2
194) 12x7 (-5x4 + 10x3 )
Multiply.
213) (5a - 9)2
Multiply.
195) 7y2 (2y2 - 2y - 5)
214) (8x + 5y) 2
Multiply.
196) (3x + 5)(x - 11)
Divide.
215)
30x6 - 24x
6
216)
9x8 + 5x7 + x2
x
217)
20x3 + 8x2 + 40x
4x
197) (2x + 5)(x + 4)
198) (5x + 11)(4x + 6)
199) (2x2 + 1)(4x - 1)
Find the product of the two binomials.
200) (x - 7y)(x - 12y)
Perform the indicated operation.
218) (12x8 + 20x5 - 12x3 ) ÷ (-4x3)
201) (3x - 5)(2x + 7)
Multiply.
Divide.
202) (x + 5)(x2 - x + 8)
219) (64x7 + 40x5 - 32x2 ) ÷ (-8x2)
203) (x - 4)(7x2 + x + 7)
220)
204) (x2 - x - 4)(x - 1)
15
30m 9n - 18m 8 n 7 + 12m 7 n 9
6m 6 n
Homework Elementary (continued)
Factor.
241) 5a2 - 40a + 80
221) t2 + 13t + 36
242) 2t3 - 12t2 + 18t
222) t2 + 15t + 50
243) m 3 - 14m 2 + 49m
223) x2 - x - 6
244) x3 + 7x2 - 30x
224) - 3b - 88 + b2
245) p4 - 11p3 + 30p2
225) y2 + 5y - 66
246) x5 + 5x4 - 50x3
226) a 2 - 13a + 40
247) x5 - 9x4 + 18x3
227) a 2 - 9a + 14
248) 5x2 - 15xy - 20y2
228) 28 - 11y + y2
249) 3x2 + 3xy - 18y2
229) a 2 - 21a + 108
250) 6x2 - 18xy - 24y2
230) x2 + 2xy - 8y2
251) 4x3 + 4x2 y - 24xy2
231) x2 - 4xy + 4y2
252) 10y2 + 45y - 25
232) x2 + 2xy - 35y2
253) 18y2 + 81y - 45
Factor out the greatest common factor (GCF or common
binomial).
233) 80m 9 + 16m 7 - 56m 4
254) -30a 2 - 69a - 36
255) -16x3 + 12x2 + 10x
234) y(y + 4) - 10(y + 4)
256) 16a 2 - 28a + 10
235) 6x(3x - 5) + 5(3x - 5)
257) 9x2 + 40x + 16
Factor by grouping.
236) x2 + 3x - 5x - 15
258) 9x2 - 50x - 24
237) 18a 2 - 9a - 12a + 6
259) 4x2 + 11x - 20
Factor.
238) 2x2 - 18x + 40
260) 12x2 + 17x + 6
239) 4x2 - 14x - 8
261) 16x2 - 56x + 49
240) 3a3 + 9a 2 - 54a
16
Homework Elementary (continued)
262) 7x3 + 55x2 - 8x
283) x2 + 2x - 48 = 0
263) 9x2 + 6xt - 8t2
284) 2x2 - 18x + 40 = 0
264) 60x2 + 35xy + 5y2
285) x2 - x = 6
265) 12x2 - 17xt + 6t2
286) 5x2 - 6x = 8
266) y2 - 81
287) 16k2 - 36 = 0
267) -25 + t2
288) 16x2 = 4
268) 64x2 - 9
289) 2k2 = -15k - 25
269) 81k2 - 49m 2
290) 6x2 + 4x = 16 + 24x
270) 81y2 - 81w2
291) x(x - 7) = 30
Solve.
271) 7x2 - 175
292) x2 - x = 56
272) 98 - 2a 2
293) (x + 3)(x + 9) = -5
273) 32 - 98y2
Solve the problem.
294) The product of the page numbers on two
facing pages of a book is 702. Find the page
numbers.
274) 50x2 - 32
275) 4x3 - 25x
295) The length of a rectangular frame is 3 cm more
than the width. The area inside the frame is
154 square cm. Find the width of the frame.
276) 25x - 9x3
277) 75x2 - 108y2
296) A rectangular garden is three times as long as
it is wide. If the area of the garden is 1200 ft2 ,
278) x3 - 3x2 - 9x + 27
find the length and width of the garden.
279) x3 - 4x2 - 16x + 64
Solve by setting factors = 0.
280) x(2x + 12) = 0
281) (y - 7)(5y + 23) = 0
Solve by factoring.
282) 4x2 = 7x
17
Homework Elementary (continued)
297) A triangle is 8 cm wider than it is tall. The area
is 280 cm2 . Find the width (length of the base).
306)
m2 - 4
m 2 - 4m + 4
Simplify.
307)
t2 - 3t - 18
t2 + 10t + 21
Simplify by factoring and dividing out common factors.
x2 - 2x - 24
308)
x2 + 2x - 48
h+8
298) A 15-ft ladder is leaning against a building. If
the bottom of the ladder is 9 ft from the base of
the building, how high does the ladder reach?
299) One leg of a right triangle is 2 cm shorter than
the other leg. The length of the hypotenuse is
10 cm. Find the length of the shorter leg.
List all numbers that make the expression undefined
(division by zero).
8
301)
b+ 7
305)
310)
3-m
m-3
312)
y2 - 1 y - 6
·
6y - 6 y + 1
313)
5x + 10 3x2 - 6x + 3
·
x-1
x2 - 4
314)
k2 + 7k + 12
k2 + 8k
·
k2 + 12k + 32 k2 - 2k - 15
315)
x2 + 3x - 4 25x3 - 9x
·
3x - 3
5x3 - 3x2
b- 7
7b - 21
Simplify by factoring and dividing out common factors.
9x + 21
303)
12x + 28
304)
x-5
5-x
Multiply and simplify.
5x2 14y6
311)
·
x3
2y2
300) A lot is in the shape of a right triangle. The
shorter leg measures 60 meters. The
hypotenuse is 20 meters longer than the length
of the longer leg. How long is the longer leg?
302)
309)
Divide and, if possible, simplify.
-20 + 5x 8 - 2x
316)
÷
20
8
8x2 - 16x
4x2 - 8x
Divide and simplify.
4x2 - 25 2x - 5
317)
÷
x+4
x2 - 16
a2 - 36
2
a + 9a + 18
18
Homework Elementary (continued)
318)
319)
x2 - 36
x2 + 18x + 81
÷
8x - 48
x2 + 15x + 54
x2 - 16
x-4
÷
25x2 - 4 2 - 5x
Divide and, if possible, simplify.
z 2 + 9 z + 20
z2 + 4 z
320)
÷
z 2 + 13 z + 40 z 2 + 4 z - 32
Add or subtract and simplify.
23
3
321)
+
x-8 x-8
331)
18x
x
2
x
-9
x - 81
332)
5
3
+
x- 5
5 -x
333)
3
8
+
5 -m m- 5
334)
5
7
1 - y y- 1
335)
-6x - 8 -2x - 2
+
x
9x
322)
6a + 13 5a + 8
a+1
a+1
336)
z + 11 z - 8
8z
5z
323)
3y2
-3y
+
y- 1 y- 1
337)
6
2
+
x+5 x
324)
m 2 - 8m
12
+
m-2
m-2
338)
2
2
x+2
x-2
325)
2x + 8
x+5
2
2
x + 4x + 3 x + 4x + 3
339)
Get an LCD, add or subtract, then simplify.
z + 13 z - 7
326)
2z
9z
340)
6
(x + 5)2
20x
x2 - 100
+
-
2
x+5
x
x - 10
4x + 8 -3x + 3
327)
+
x
5x
341)
2
3
+
x- 6
6 -x
6
2
328)
+
x+4 x
342)
1
6
+
2 -m m- 2
5
5
329)
x+5
x-5
343)
3
5
1 - y y- 1
9
344)
3
9
7 - y y- 7
4
330)
+
2
x
+5
(x + 5)
19
Homework Elementary (continued)
Solve. If no solution exists, state this.
6
9
1
345) =
5 10 x
346) x +
-60
= -4
x
347)
x 3
- =0
3 x
348)
3 7
+ =1
2t t
349)
354) For the pair of similar triangles, find the value
of b.
8
10
4
5
6
x
x
= 2
3
7
355) A church steeple casts a shadow 116 ft long,
and at the same time a 9.0-ft post casts a
shadow 5.0 ft long. How high is the steeple?
Round to the nearest unit.
9
4
350)
=
x+1 x
351)
x-6
5
=
x-1
x-1
352)
1
x
=
x-1 x-1
Solve.
356) Dr. Wong can see 12 patients in 2 hours. At
this rate, how long would it take her to see 48
patients?
357) Maria and Charlie can deliver 40 papers in 2
hours. How long would it take them to deliver
42 papers?
Solve the problem.
353) For the pair of similar triangles, find the value
of a.
358) A machine can fill 6041 cartons of milk in 0.7
hour. How many cartons of milk can it fill per
hour?
10
359) If a boat uses 24 gallons of gas to go 61 miles,
how many miles can the boat travel on 120
gallons of gas?
8
5
360) On a map, the length of a nature-center trail is
5.1 cm. If the scale is 2 cm to 49 km, what is the
actual length of the trail? Round your answer
to the nearest tenth, if necessary.
3
4
Determine whether the ordered pair is a solution of the
system of equations.
361) (-2, -6); x + y = -8
x-y=4
20
Homework Elementary (continued)
362) (-1, -3); x + y = -2
x-y=4
365) 2x + y = 10
x + 2y = 14
y
Solve the system of equations by graphing. If there is no
solution or an infinite number of solutions, state this.
363) x - y = 6
x + y = 10
10
8
6
4
2
y
10
8
-10 -8 -6 -4 -2
-2
6
-4
4
-6
2
2
4
6
8
10
x
2
4
6
8
10
x
2
4
6
8
10
x
-8
-10 -8 -6 -4 -2
-2
2
4
6
8 10
-10
x
-4
366) x - y = -2
3
y= x
2
-6
-8
-10
y
10
364) y = x - 2
y = -x + 8
8
6
4
y
10
2
8
6
-10 -8 -6 -4 -2
-2
4
-4
2
-6
-10 -8 -6 -4 -2
-2
2
4
6
8 10
-8
x
-10
-4
-6
367)
-8
-10
2x + y = 8
8x + 4y = 32
y
10
8
6
4
2
-10 -8 -6 -4 -2
-2
-4
-6
-8
-10
21
Homework Elementary (continued)
368)
3x - y = 8
-9x + 3y = -27
371) 4x + y = -3
x + 2y = 8
y
y
10
10
8
8
6
6
4
4
2
2
-10 -8 -6 -4 -2
-2
2
4
6
8 10
x
-10 -8 -6 -4 -2
-2
-4
-4
-6
-6
-8
-8
-10
-10
369) x - y = 6
x + y = 14
2
4
6
8
10
x
2
4
6
8
10
x
372) x - y = -4
y = 2x
y
y
10
10
8
8
6
6
4
4
2
2
-10 -8 -6 -4 -2
-2
2
4
6
8 10
x
-10 -8 -6 -4 -2
-2
-4
-4
-6
-6
-8
-8
-10
-10
370) y = x - 4
y = -x + 16
Solve the system using the substitution method. If the
system has no solution or an infinite number of solutions,
state this.
373)
y = 2x + 3
2x + y = -1
y
10
8
6
374) x - 4y = 8
-4x - 3y = 6
4
2
-10 -8 -6 -4 -2
-2
2
4
6
8 10
x
375) x + 7y = 51
-4x + 6y = 0
-4
-6
376) 5x + 9y = 4
5x - y = 10
-8
-10
22
Homework Elementary (continued)
377) y - 2x = 8
2y - x = 8
392) 5x - 2y = -4
15x - 6y = 12
378) x + y = 2
5x + 5y = 10
Solve the problem.
393) The sum of two numbers is 37. One number is
11 more than the other. Find the numbers.
379) x + y = -3
x+y=9
394) The sum of two numbers is 40. The larger
number is three times the smaller number.
Find the numbers.
380) x - 6y = -6
-4x - 5y = -5
395) The difference between two numbers is 64.
Five times the smaller number equals the
larger number. Find the numbers.
Solve using the elimination method. If the system has no
solution or an infinite number of solutions, state this.
381) x + y = 7
x - y = 11
396) Two angles are supplementary. One angle is 5°
more than six times the other. Find the
measure of each angle.
382) -x - 6y = -10
-4x + 6y = 20
397) Two angles are complementary. Twice one
angle plus the other is 159°. Find the measure
of each angle.
383) 5x - y = 25
2x + y = 17
384)
398) Bob fenced in a rectangular garden in his yard.
The length of the rectangle is 6 feet longer than
the width, and the perimeter is 100 feet. What
is the width of the rectangle?
x + 6y = -23
3x + 6y = -21
385) x + 7y = 21
2x + 7y = 14
386)
Solve.
399) Two angles have a sum of 82°. Their difference
is 12°. Find the measure of each angle.
x + 6y = -36
5x + 5y = -5
400) Two angles have a sum of 132°. One angle is
24° less than twice the other. Find the measure
of each angle.
387) -7x - 6y = -42
5x - 2y = -14
388) 7x - 7y = 28
5x + 3y = 20
401) In a recent game, Will scored 29 points on a
combination of 12 two- and three-point
baskets. How many shots of each type were
made?
389) -5x + 9y = -9
-2x - 6y = 6
402) In a local high school basketball game, the
winning team scored 57 of their points on a
combination of 23 two- and three-pointers.
How many shots of each type did the team
make?
390) -6x + 3y = -2
18x - 9y = -6
391) -4x + 3y = 2
-16x + 12y = 8
23
Homework Elementary (continued)
403) Mrs. Boyd has a desk full of quarters and
nickels. If she has a total of 13 coins worth $
1.85, then how many of the coins are nickels?
411) Ellen wishes to mix candy worth $1.40 per
pound with candy worth $3.00 per pound to
form 24 pounds of a mixture worth $2.40 per
pound. How many pounds of the more
expensive candy should she use? Round your
answer to the nearest pound, if necessary.
404) Joan has a pocketful of dimes and quarters
worth $2.95. If there are 22 coins in all, then
how many are quarters?
412) Tim and Judy mix two kinds of feed for
pedigreed dogs. They wish to make 30 pounds
of feed worth $0.50 per pound by mixing one
kind worth $0.25 per pound with another
worth $0.93 per pound. How many pounds of
the cheaper kind should they use in the mix?
Round your answer to the nearest pound, if
necessary.
405) A woman made a deposit of $337. If her
deposit consisted of 101 bills, some of them
one-dollar bills and the rest five-dollar bills,
then how many one-dollar bills did she
deposit?
406) Ron and Kathy are ticket sellers at their class
play, Ron selling student tickets for $2.00 each
and Kathy selling adult tickets for $4.50 each. If
their total income for 364 tickets was $1175.50,
then how many tickets did Ron sell?
413) Anne and Nancy use a metal alloy that is
15.6% copper to make jewelry. How many
ounces of an alloy that is 14% copper must be
mixed with an alloy that is 16% copper to form
100 ounces of the desired alloy?
407) Don runs a charity fruit sale, selling boxes of
oranges for $11 and boxes of grapefruit for $10.
If he sold a total of 762 boxes and his total
income was $8125, then how many boxes of
oranges did he sell?
Solve.
414) Mardi received an inheritance of $70,000. She
invested part at 9% and the rest at 7%. Her
total annual income from the investments was
$5700. Find the amount she invested at 9%.
408) There were 44,000 people at a ballgame in Los
Angeles. The day's receipts from $12 reserved
seats and $6 general-admission seats were
$354,000. How many of each type of seat were
sold?
415) Walt made an extra $7000 last year from a
part-time job. He invested part of the money at
10% and the rest at 9%. He made a total of $660
in interest. How much was invested at 9%?
409) There were 540 people at a play. The
admission price was $2 for adults and $1 for
children. The admission receipts were $850.
How many adults and how many children
attended?
Find the square roots of the number.
416) 361
417) 2500
Solve the problem.
410) Tim and Judy mix two kinds of feed for
pedigreed dogs. They wish to make 27 pounds
of feed worth $0.46 per pound by mixing one
kind worth $0.31 per pound with another
worth $0.77 per pound. How many pounds of
the cheaper kind should they use in the mix?
Round your answer to the nearest pound, if
necessary.
418) 25
419) 900
Simplify.
420)
421) 422)
24
400
64
324
Homework Elementary (continued)
423) 424)
425) 426)
427) -
442) x2 = 196
529
443) x2 + 5 = 54
25
444) 8z2 + 4 = 516
81
81
445) 3x2 = 21
441
Solve the quadratic equation.
446) x2 - x = 56
Simplify. Assume x can represent any real number.
428) x2
447) x2 + 2x - 120 = 0
429)
64x2
448) 2x2 - 14x + 24 = 0
430)
(13y) 2
449) 16y2 + 24y + 9 = 0
431)
(16x + 4)2
450) 81k2 - 64 = 0
432)
(11 - x)2
451) 8m 2 - 3m = 0
452) x2 + 3x - 18 = 0
Simplify. Assume that the variable represents a
nonnegative number.
433) x2
453) 2x2 - 18x + 40 = 0
434)
16x2
454) 10y2 + 31y + 15 = 0
435)
(12y) 2
455) 84n 2 + 36n = 0
436)
(x + 7)2
456) 6m 2 + 10m + 2 = 0
457) 6n 2 = -10n - 3
Simplify. Assume that all variables represent nonnegative
numbers.
437) 48
458) 6x2 + 12x = - 3
438)
24
459) 4n 2 = -10n - 1
439)
50
460) 3x2 + 6x = - 1
440)
28
Solve. Use the principle of square roots.
441) y2 = 21
25
Answer Key
Testname: HWE-B
1) 6x - 3
x
2)
10
207
5
9)
7
4
10)
5
18
d
r
42) t =
a7 + b
(w + xy) + z
27x + 9
2 · 3 · 3 · 11
52
7)
71
3)
4)
5)
6)
8)
P - 2L
2
41) W =
43) B =
3V
h
44) y = 4x - w - z
A- P
45) r =
Pn
46) C =
5
(F - 32)
9
47) 0.558
48) 0.861%
49) 2.03
50) 190.91
51) 0.6%
52) 165
53) 0.3%
54) 20 cars
55) $24,000
56) $387.75
57) 31,705 people
58) $84
59) -132
11) False
12) Undefined
13) -196
14) 121
15) 392
16) -22
17) -2x - 8
18) 30
19) 27
783
20) 64
60) 8x = 2x + 17;
21) No
22) Yes
23) Yes
24) {5 }
25) {18}
26) {15}
27) {9}
28) -4
29) 4
30) -9.4
31) -2
2
32)
7
17
6
61) 21°
62) 159, 160, 161
63) 69°
64) 101.25° and 78.75°
65) 43 in., 69 in.
66) 28°
67) No
33) 1
1
34)
5
68)
-8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8
69)
70)
-8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8
-8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8
71) {x∣x > -3}
72) {x∣x ≤ -2}
73) x < 2
35) 42
36) -21
37) 27
38) 80
39) {40}
40) {30}
-10-9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9 10
26
Answer Key
Testname: HWE-B
74) {t t ≥ 2}
88)
y
-1
0
1
2
3
4
10
5
75) {b b > -6}
5
-9
-8
-7
-6
-5
-4
-3
76) {k k > 28}
-10
-5
5
10
x
5
10
x
5
10
x
-5
25
77) {a
78) {z
79) {y
80) {x
81)
26
27
28
29
30
31
a ≤ 6}
z ≥ -7}
y < -4}
x ≤ 10}
-10
89)
y
10
8
y
5
B
-10
-5
A
-5
8 x
-8
-10
90)
y
-8
10
82)
8
y
5
A
-10
-5
-5
8 x
-8
-10
B
-8
83) C(-5, 1); D(4, -4)
84) G(6, 3); H(-7, -5)
85) No
86) Yes
87) Yes
27
Answer Key
Testname: HWE-B
91)
y
10
y
10
5
5
-10
-10
-5
5
10
-5
5
10
x
5
10
x
5
10
x
x
-5
-5
-10
94)
-10
y
92)
10
y
10
5
5
-10
-10
-5
5
10
-5
-5
x
-5
-10
95)
96) (0, -3), (-6, 0)
97) (0, -4), (-3, 0)
98) (0, -2), (-4, 0)
-10
93)
y
-10
y
10
10
5
5
-5
5
10
x
-10
-5
-5
-5
-10
-10
28
Answer Key
Testname: HWE-B
99) (0, 3), (-9, 0)
102)
y
10
y
20
5
10
-20
-10
10
20
x
-10
-5
-10
5
x
5
x
5
x
-5
-20
-10
100) (0, 15), (3, 0)
103)
y
10
y
20
5
10
-20
-10
10
20
x
-10
-5
-10
-5
-20
-10
101)
104)
10
y
10
5
-10
-5
y
5
5
x
-10
-5
-5
-5
-10
-10
29
Answer Key
Testname: HWE-B
105)
108)
10
y
8
7
6
5
4
3
2
1
5
-10
-5
x
5
-8 -7 -6 -5 -4 -3 -2 -1
-1
-2
-3
-4
-5
-6
-7
-8
-5
-10
106)
8
7
6
5
4
3
2
1
-8 -7 -6 -5 -4 -3 -2 -1
-1
-2
-3
-4
-5
-6
-7
-8
y
y
10
5
1 2 3 4 5 6 7 8 x
-10
-5
5
10
-5
-10
110)
111)
112)
113)
114)
115)
116)
117)
118)
119)
120)
26.4 miles/gallon
$215 per year
$1.10/mi
60 miles per hour
Increase of $0.8 billion per year
$3000 per year
3 degrees per hour
4 feet per year
-$400 per year
-6 pounds per month
2.5 degrees per minute
1
121) 2
y
10
5
-5
1 2 3 4 5 6 7 8 x
109)
107)
-10
y
5
10
x
-5
-10
122) Undefined
1
123)
3
124) 0
30
125) -
2
5
126) -
5
2
x
Answer Key
Testname: HWE-B
127)
128)
129)
130)
131)
132)
133)
134)
Undefined
0
0
Undefined
Yes
No
12.5%
-0.075
5
135)
7
139)
y
10
5
-10
-5
5
10
x
5
10
x
5
10
x
-5
136)
-10
y
10
y
10
5
5
-10
-5
5
10
x
-5
-10
-5
-5
-10
137)
-10
140)
141)
y
10
y
10
5
5
-10
-5
5
10
x
-5
-10
-5
-5
-10
138)
-10
y
10
5
-10
-5
5
10
x
-5
-10
31
Answer Key
Testname: HWE-B
151) y = -3x + 3
152) y = -3x + 9
3
23
153) y = - x +
5
5
142)
y
10
154) y = 2x - 7
155) y = 4
9
14
156) y = x+
11
11
5
-10
-5
5
10
x
157) y = x - 4
4
158) y = - x + 4
5
-5
-10
159) x = -1
160) y = -2
161) 5
162) (-4)4 a 20
143)
y
10
163) 25r12
164) p4 q9
5
-10
-5
5
10
165) 12x8
6p
166)
m6
x
-5
167)
-10
168) p7
169) t5
144)
170) x6y30
x4
171)
y14
y
10
172)
5y3 z7
x4
173)
w5 z 30
x30y25
174)
t18
s12
5
-10
-5
5
10
x
-5
-10
145)
175) 48,300,000
176) 0.000127
177) 4.9 × 104
11
; (0, -4)
4
146) 4; (0, 16)
5
147) y = - x + 9
3
178) 8.701 × 10-5
179) 4.636 × 104
180) 4 × 10-9
181) 9y4 - 11y3 + 7y2
3
148) y = x - 1
2
149) y = -
a 20
625b8
182) 11x2 y - 4xy2 - 7
183) -26
184) 45
4
x+3
5
150) y = -4x - 14
32
Answer Key
Testname: HWE-B
229) (a - 12)(a - 9)
230) (x + 4y)(x - 2y)
231) (x - 2y) 2
185) 23
186) -11
187) 10n 7 + 12n 4 - 3
188) 11x8 + 12x7 - 11x6 - 5
232) (x + 7y)(x - 5y)
233) 8m 4(10m 5 + 2m 3 - 7)
189) 4n 6 - 9n 5 - 3n
190) 3x8 - 2x7 + 9x6 - 2
(y + 4)(y - 10)
(3x - 5)(6x + 5)
(x - 5)(x + 3)
3(2a - 1)(3a - 2)
2(x - 5)(x - 4)
2(2x + 1)(x - 4)
3a(a + 6)(a - 3)
241) 5(a - 4)2
242) 2t(t - 3)2
234)
235)
236)
237)
238)
239)
240)
191) 5x2 - 10xy + 2y2
192) 6m 2n - 8mn + 17mn 2
193) -110x2 - 30x
194) -60x11 + 120x10
195) 14y4 - 14y3 - 35y2
196) 3x2 - 28x - 55
197) 2x2 + 13x + 20
198) 20x2 + 74x + 66
243) m(m - 7)2
244) x(x + 10)(x - 3)
245) p2 (p - 6)(p - 5)
199) 8x3 - 2x2 + 4x - 1
200) x2 - 19xy + 84y2
246) x3(x + 10)(x - 5)
247) x3(x - 6)(x - 3)
201) 6x2 + 11x - 35
202) x3 + 4x2 + 3x + 40
248) 5(x + y)(x - 4y)
203) 7x3 - 27x2 + 3x - 28
204) x3 - 2x2 - 3x + 4
249) 3(x - 2y)(x + 3y)
250) 6(x + y)(x - 4y)
205) x3 + 64
4x(x - 2y)(x + 3y)
5(2y - 1)(y + 5)
9(2y - 1)(y + 5)
-3(2a + 3)(5a + 4)
-2x(4x - 5)(2x + 1)
2(2a - 1)(4a - 5)
(9x + 4)(x + 4)
(9x + 4)(x - 6)
(x + 4)(4x - 5)
(4x + 3)(3x + 2)
261) (4x - 7)2
262) x(7x - 1)(x + 8)
263) (3x - 2t)(3x + 4t)
264) 5(3x + y)(4x + y)
265) (3x - 2t)(4x - 3t)
266) (y + 9)(y - 9)
267) (t + 5)(t - 5)
251)
252)
253)
254)
255)
256)
257)
258)
259)
260)
206) 32 - 20p + 26p2 - 3p3
207) x3 - y3
208) x3 + 4x2 y + 2xy2 - y3
209) 16x10 - 1
210) p2 - 144q2
211) n 2 + 8n + 16
212) w2 - 32w + 256
213) 25a 2 - 90a + 81
214) 64x2 + 80xy + 25y2
215) 5x6 - 4x
216) 9x7 + 5x6 + x
217) 5x2 + 2x + 10
218) -3x5 - 5x2 + 3
219) -8x5 - 5x3 + 4
220)
221)
222)
223)
224)
225)
226)
227)
228)
5m 3 - 3m 2 n 6 + 2mn 8
(t + 9)(t + 4)
(t + 5)(t + 10)
(x + 2)(x - 3)
(b + 8)(b - 11)
(y + 11)(y - 6)
(a - 5)(a - 8)
(a - 7)(a - 2)
(y - 7)(y - 4)
268) (8x + 3)(8x - 3)
269)
270)
271)
272)
273)
274)
(9k + 7m)(9k - 7m)
81(y + w)(y - w)
7(x + 5)(x - 5)
2(7 + a)(7- a)
2(4 + 7y)(4- 7y)
2(5x + 4)(5x - 4)
275) x(2x + 5)(2x - 5)
33
Answer Key
Testname: HWE-B
276) x(5 + 3x)(5 - 3x)
277) 3(5x - 6y)(5x + 6y)
278) (x - 3)2(x + 3)
311)
35y4
x
279) (x - 4)2(x + 4)
280) 0, -6
23
281) ,7
5
312)
y- 6
6
313)
15(x - 1)
x-2
7
282) , 0
4
314)
k
k- 5
283) -8, 6
284) 4, 5
285) -2, 3
4
286) - , 2
5
315)
(x + 4)(5x + 3)
3x
287)
3
3
,2
2
318)
288)
1
1
,2
2
319) -
316) -1
2x + 5
317)
x-4
(x + 6)(x + 6)
8(x + 9)
x+4
5x + 2
289) -
5
, -5
2
320)
z -4
z
290) -
2
,4
3
321)
26
x-8
322)
a+5
a+1
-3, 10
-7, 8
-8, -4
26, 27
11 cm
length: 60 ft; width: 20 ft
28 cm
12 ft
6 cm
80 meters
-7
3
3
303)
4
291)
292)
293)
294)
295)
296)
297)
298)
299)
300)
301)
302)
323) 3y
324) m - 6
1
325)
x+1
326)
7z + 131
18z
327)
17x + 43
5x
328)
8x + 8
x(x + 4)
329)
304) 2
a-6
305)
a+3
-50
x2 - 25
330)
4x + 29
(x + 5)2
306)
m+2
m-2
331)
-x
x+9
307)
t- 6
t+ 7
332)
2
x- 5
308)
x+4
x+8
333)
-5
5 -m
309) -1
310) -1
34
Answer Key
Testname: HWE-B
334)
12
1 -y
335)
-56x - 74
9x
336)
-3z + 119
40z
337)
8x + 10
x(x + 5)
338)
-8
2
x -4
339)
365)
366)
367)
368)
369)
370)
371)
372)
373)
374)
375)
(2, 6)
(4, 6)
Infinite number of solutions
No solution
(10, 4)
(10, 6)
(-2, 5)
(4, 8)
(-1, 1)
(0, -2)
(9, 6)
47
3
376)
,25
5
2x + 16
(x + 5)2
340)
-x
x + 10
341)
-1
x- 6
342)
-5
2 -m
343)
8
1 -y
344)
12
7 -y
345)
10
3
377) 378)
379)
380)
381)
382)
383)
384)
385)
386)
387)
388)
389)
390)
391)
392)
393)
394)
395)
396)
397)
398)
399)
400)
401)
402)
403)
404)
405)
406)
407)
408)
409)
410)
411)
346) -10, 6
347) -3, 3
17
348)
2
349)
21
2
350)
4
5
351)
352)
353)
354)
355)
356)
357)
358)
359)
360)
361)
362)
363)
364)
11
No solution
6
12
209 ft
8 hours
2.1 hours
8630 cartons
305 miles
125 km
Yes
No
(8, 2)
(5, 3)
35
8 8
,
3 3
Infinite number of solutions
No solution
(0, 1)
(9, -2)
(-2, 2)
(6, 5)
(1, -4)
(-7, 4)
(6, -7)
(0, 7)
(4, 0)
(0, -1)
No solution
Infinite number of solutions
No solution
24, 13
10, 30
16, 80
25°, 155°
69°, 21°
22 feet
47°, 35°
52°, 80°
Two-pointers: 7; three-pointers: 5
Two-pointers: 12; three-pointers: 11
7 nickels
5 quarters
42 one-dollar bills
185 tickets
505 boxes
$12 seats: 15,000; $6 seats: 29,000
Adults: 310; children: 230
18 pounds
15 pounds
Answer Key
Testname: HWE-B
412)
413)
414)
415)
416)
417)
418)
419)
420)
421)
422)
423)
424)
425)
426)
427)
428)
429)
430)
431)
432)
433)
434)
435)
436)
437)
438)
439)
440)
441)
442)
443)
444)
445)
446)
447)
448)
19 pounds
20 ounces
$40,000
$4000
-19, 19
-50, 50
-5, 5
-30, 30
20
-8
18
- 23
5
-9
9
- 21
x
8 x
13 y
16x + 4
11 - x
x
4x
12y
x+7
4 3
2 6
5 2
2 7
± 21
±14
±7
±8
± 7
-7, 8
-12, 10
3, 4
3
3
449) - , 4
4
450)
8
8
,9
9
451)
3
,0
8
455) -
452) -6, 3
453) 4, 5
5
3
454) - , 2
5
36
3
,0
7
456)
-5 ± 13
6
457)
-5 ± 7
6
458)
-2 ± 2
2
459)
-5 ± 21
4
460)
-3 ± 6
3