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Math Problems
Algebra 1
Identify equivalent linear expressions
Which expression is equivalent to
7
(
y
+
5
)
7(y + 5)
7
(
y
+
5
)
?
\newline
Choices:
\newline
(A)
35
y
+
7
35y + 7
35
y
+
7
\newline
(B)
35
y
35y
35
y
\newline
(C)
12
y
12y
12
y
\newline
(D)
7
y
+
35
7y + 35
7
y
+
35
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Which expression is equivalent to
2
(
x
+
9
)
2(x + 9)
2
(
x
+
9
)
?
\newline
Choices:
\newline
(A)
2
x
+
18
2x + 18
2
x
+
18
\newline
(B)
11
x
11x
11
x
\newline
(C)
18
x
+
2
18x + 2
18
x
+
2
\newline
(D)
18
x
18x
18
x
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Which expression is equivalent to
6
(
7
c
)
6(7c)
6
(
7
c
)
?
\newline
Choices:
\newline
(A)
c
+
13
c + 13
c
+
13
\newline
(B)
7
c
+
6
7c + 6
7
c
+
6
\newline
(C)
c
+
42
c + 42
c
+
42
\newline
(D)
42
c
42c
42
c
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Which expression is equivalent to
6
(
8
x
)
6(8x)
6
(
8
x
)
?
\newline
Choices:
\newline
(A)
48
x
48x
48
x
\newline
(B)
8
x
+
6
8x + 6
8
x
+
6
\newline
(C)
x
+
48
x + 48
x
+
48
\newline
(D)
x
+
14
x + 14
x
+
14
Get tutor help
Which expression is equivalent to
5
(
7
g
)
5(7g)
5
(
7
g
)
?
\newline
Choices:
\newline
(A)
7
g
+
5
7g + 5
7
g
+
5
\newline
(B)
g
+
12
g + 12
g
+
12
\newline
(C)
35
g
35g
35
g
\newline
(D)
g
+
35
g + 35
g
+
35
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Which expression is equivalent to
4
(
s
+
8
)
4(s + 8)
4
(
s
+
8
)
?
\newline
Choices:
\newline
(A)
32
s
+
4
32s + 4
32
s
+
4
\newline
(B)
4
s
+
32
4s + 32
4
s
+
32
\newline
(C)
32
s
32s
32
s
\newline
(D)
12
s
12s
12
s
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Which expression is equivalent to
9
(
a
+
3
)
9(a + 3)
9
(
a
+
3
)
?
\newline
Choices:
\newline
(A)
27
a
27a
27
a
\newline
(B)
12
a
12a
12
a
\newline
(C)
9
a
+
27
9a + 27
9
a
+
27
\newline
(D)
27
a
+
9
27a + 9
27
a
+
9
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Which expression is equivalent to
5
(
7
u
)
5(7u)
5
(
7
u
)
?
\newline
Choices:
\newline
(A)
u
+
12
u + 12
u
+
12
\newline
(B)
u
+
35
u + 35
u
+
35
\newline
(C)
7
u
+
5
7u + 5
7
u
+
5
\newline
(D)
35
u
35u
35
u
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Which expression is equivalent to
3
(
9
m
)
3(9m)
3
(
9
m
)
?
\newline
Choices:
\newline
(A)
27
m
27m
27
m
\newline
(B)
m
+
12
m + 12
m
+
12
\newline
(C)
9
m
+
3
9m + 3
9
m
+
3
\newline
(D)
m
+
27
m + 27
m
+
27
Get tutor help
Which expression is equivalent to
6
(
v
+
5
)
6(v + 5)
6
(
v
+
5
)
?
\newline
Choices:
\newline
(A)
11
v
11v
11
v
\newline
(B)
6
v
+
30
6v + 30
6
v
+
30
\newline
(C)
30
v
+
6
30v + 6
30
v
+
6
\newline
(D)
30
v
30v
30
v
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Which expression is equivalent to
9
(
p
+
5
)
9(p + 5)
9
(
p
+
5
)
?
\newline
Choices:
\newline
(A)
45
p
45p
45
p
\newline
(B)
9
p
+
45
9p + 45
9
p
+
45
\newline
(C)
14
p
14p
14
p
\newline
(D)
45
p
+
9
45p + 9
45
p
+
9
Get tutor help
Which expression is equivalent to
9
(
5
c
)
9(5c)
9
(
5
c
)
?
\newline
Choices:
\newline
(A)
5
c
+
9
5c + 9
5
c
+
9
\newline
(B)
45
c
45c
45
c
\newline
(C)
c
+
45
c + 45
c
+
45
\newline
(D)
c
+
14
c + 14
c
+
14
Get tutor help
Which expression is equivalent to
3
(
d
+
9
)
3(d + 9)
3
(
d
+
9
)
?
\newline
Choices:
\newline
(A)
27
d
27d
27
d
\newline
(B)
12
d
12d
12
d
\newline
(C)
27
d
+
3
27d + 3
27
d
+
3
\newline
(D)
3
d
+
27
3d + 27
3
d
+
27
Get tutor help
Which expression is equivalent to
9
(
3
v
)
9(3v)
9
(
3
v
)
?
\newline
Choices:
\newline
(A)
v
+
12
v + 12
v
+
12
\newline
(B)
27
v
27v
27
v
\newline
(C)
3
v
+
9
3v + 9
3
v
+
9
\newline
(D)
v
+
27
v + 27
v
+
27
Get tutor help
Which expression is equivalent to
4
(
9
k
)
4(9k)
4
(
9
k
)
?
\newline
Choices:
\newline
(A)
9
k
+
4
9k + 4
9
k
+
4
\newline
(B)
36
k
36k
36
k
\newline
(C)
k
+
13
k + 13
k
+
13
\newline
(D)
k
+
36
k + 36
k
+
36
Get tutor help
Which expression is equivalent to
7
(
4
d
)
7(4d)
7
(
4
d
)
?
\newline
Choices:
\newline
(A)
d
+
28
d + 28
d
+
28
\newline
(B)
28
d
28d
28
d
\newline
(C)
4
d
+
7
4d + 7
4
d
+
7
\newline
(D)
d
+
11
d + 11
d
+
11
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Which expression is equivalent to
6
(
w
+
5
)
6(w + 5)
6
(
w
+
5
)
?
\newline
Choices:
\newline
(A)
30
w
+
6
30w + 6
30
w
+
6
\newline
(B)
30
w
30w
30
w
\newline
(C)
6
w
+
30
6w + 30
6
w
+
30
\newline
(D)
11
w
11w
11
w
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Which expression is equivalent to
9
(
4
z
)
9(4z)
9
(
4
z
)
?
\newline
Choices:
\newline
(A)
4
z
+
9
4z + 9
4
z
+
9
\newline
(B)
36
z
36z
36
z
\newline
(C)
z
+
13
z + 13
z
+
13
\newline
(D) $z + \(36\)
Get tutor help
Which expression is equivalent to
5
(
q
+
8
)
5(q + 8)
5
(
q
+
8
)
?
\newline
Choices:
\newline
(A)
5
q
+
40
5q + 40
5
q
+
40
\newline
(B)
13
q
13q
13
q
\newline
(C)
40
q
+
5
40q + 5
40
q
+
5
\newline
(D)
40
q
40q
40
q
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Which expression is equivalent to
7
(
7
p
)
7(7p)
7
(
7
p
)
?
\newline
Choices:
\newline
(A)
7
p
+
7
7p + 7
7
p
+
7
\newline
(B)
49
p
49p
49
p
\newline
(C)
p
+
14
p + 14
p
+
14
\newline
(D)
p
+
49
p + 49
p
+
49
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Which expression is equivalent to
8
(
4
r
)
8(4r)
8
(
4
r
)
?
\newline
Choices:
\newline
(A)
r
+
12
r + 12
r
+
12
\newline
(B)
r
+
32
r + 32
r
+
32
\newline
(C)
4
r
+
8
4r + 8
4
r
+
8
\newline
(D)
32
r
32r
32
r
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Which expression is equivalent to
5
(
m
+
9
)
5(m + 9)
5
(
m
+
9
)
?
\newline
Choices:
\newline
(A)
5
m
+
45
5m + 45
5
m
+
45
\newline
(B)
14
m
14m
14
m
\newline
(C)
45
m
45m
45
m
\newline
(D)
45
m
+
5
45m + 5
45
m
+
5
Get tutor help
Which expression is equivalent to
−
19
−
11
-19-11
−
19
−
11
?
\newline
Choose
1
1
1
answer:
\newline
(A)
−
11
+
(
19
)
-11+(19)
−
11
+
(
19
)
\newline
(B)
−
19
+
(
−
11
)
-19+(-11)
−
19
+
(
−
11
)
\newline
(C)
19
+
11
19+11
19
+
11
\newline
(D)
11
−
19
11-19
11
−
19
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Which expression is equivalent to
24
−
(
−
6
)
?
24-(-6) ?
24
−
(
−
6
)?
\newline
Choose
1
1
1
answer:
\newline
(A)
−
6
−
24
-6-24
−
6
−
24
\newline
(B)
6
−
24
6-24
6
−
24
\newline
(C)
24
+
6
24+6
24
+
6
\newline
(D)
24
+
(
−
6
)
24+(-6)
24
+
(
−
6
)
Get tutor help
Which expression is equivalent to
−
51
−
(
−
60
)
?
-51-(-60) ?
−
51
−
(
−
60
)?
\newline
Choose
1
1
1
answer:
\newline
(A)
60
+
51
60+51
60
+
51
\newline
(B)
−
60
+
(
−
51
)
-60+(-51)
−
60
+
(
−
51
)
\newline
(C)
−
51
+
60
-51+60
−
51
+
60
\newline
(D)
51
−
60
51-60
51
−
60
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Which decimal is equivalent to
4
15
\frac{4}{15}
15
4
?
\newline
Choose
1
1
1
answer:
\newline
(A)
0
0
0
.
26
26
26
\newline
(B)
0
0
0
.
2626
2626
2626
\newline
(C)
0.
26
‾
0 . \overline{26}
0.
26
\newline
(D)
0.2
6
‾
0.2 \overline{6}
0.2
6
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Which decimal is equivalent to
13
11
\frac{13}{11}
11
13
?
\newline
Choose
1
1
1
answer:
\newline
(A)
1.
1
‾
1 . \overline{1}
1.
1
\newline
(B)
1.
181
‾
1 . \overline{181}
1.
181
\newline
(C)
1.
18
‾
1 . \overline{18}
1.
18
\newline
(D)
1.1
8
‾
1.1 \overline{8}
1.1
8
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Which decimal is equivalent to
4
3
\frac{4}{3}
3
4
?
\newline
Choose
1
1
1
answer:
\newline
(A)
0
0
0
.
75
75
75
\newline
(B)
1
1
1
.
25
25
25
\newline
(C)
1.
1
‾
1 . \overline{1}
1.
1
\newline
(D)
1.
3
‾
1 . \overline{3}
1.
3
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Which decimal is equivalent to
29
11
\frac{29}{11}
11
29
?
\newline
Choose
1
1
1
answer:
\newline
(A)
2.6
3
‾
2.6 \overline{3}
2.6
3
\newline
(B)
2
2
2
.
6363
6363
6363
\newline
(C)
2.
63
‾
2 . \overline{63}
2.
63
\newline
(D)
2.
6
‾
2 . \overline{6}
2.
6
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Which decimal is equivalent to
11
25
\frac{11}{25}
25
11
?
\newline
Choose
1
1
1
answer:
\newline
(A)
0
0
0
.
44
44
44
\newline
(B)
0.
4
‾
0 . \overline{4}
0.
4
\newline
(C)
2.2
7
‾
2.2 \overline{7}
2.2
7
\newline
(D)
2.
27
‾
2 . \overline{27}
2.
27
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Which decimal is equivalent to
31
9
\frac{31}{9}
9
31
?
\newline
Choose
1
1
1
answer:
\newline
(A)
0.
4
‾
0 . \overline{4}
0.
4
\newline
(B)
0
0
0
.
4444
4444
4444
\newline
(C)
3.
4
‾
3 . \overline{4}
3.
4
\newline
(D)
3
3
3
.
4444
4444
4444
Get tutor help
Which decimal is equivalent to
19
4
\frac{19}{4}
4
19
?
\newline
Choose
1
1
1
answer:
\newline
(A)
4
4
4
.
3
3
3
\newline
(B)
4.
3
‾
4 . \overline{3}
4.
3
\newline
(C)
4
4
4
.
75
75
75
\newline
(D)
4.
75
‾
4 . \overline{75}
4.
75
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Which decimal is equivalent to
5
6
\frac{5}{6}
6
5
?
\newline
Choose
1
1
1
answer:
\newline
(A)
0
0
0
.
83
83
83
\newline
(B)
0.8
3
‾
0.8 \overline{3}
0.8
3
\newline
(C)
0.
83
‾
0 . \overline{83}
0.
83
\newline
(D)
0.
8
‾
0 . \overline{8}
0.
8
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Which decimal is equivalent to
1
3
\frac{1}{3}
3
1
?
\newline
Choose
1
1
1
answer:
\newline
(A)
0.
13
‾
0 . \overline{13}
0.
13
\newline
(B)
0.
3
‾
0 . \overline{3}
0.
3
\newline
(C)
1.
3
‾
1 . \overline{3}
1.
3
\newline
(D)
3.
3
‾
3 . \overline{3}
3.
3
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Which decimal is equivalent to
10
3
\frac{10}{3}
3
10
?
\newline
Choose
1
1
1
answer:
\newline
(A)
0.
3
‾
0 . \overline{3}
0.
3
\newline
(B)
1.
3
‾
1 . \overline{3}
1.
3
\newline
(C)
3.
1
‾
3 . \overline{1}
3.
1
\newline
(D)
3.
3
‾
3 . \overline{3}
3.
3
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Which decimal is equivalent to
25
6
\frac{25}{6}
6
25
?
\newline
Choose
1
1
1
answer:
\newline
(A)
4.
1
‾
4 . \overline{1}
4.
1
\newline
(B)
4.
16
‾
4 . \overline{16}
4.
16
\newline
(C)
4.1
6
‾
4.1 \overline{6}
4.1
6
\newline
(D)
4.1
667
‾
4.1 \overline{667}
4.1
667
Get tutor help
Which equation has a constant of proportionality equal to
3
3
3
?
\newline
Choose
1
1
1
answer:
\newline
(A)
y
=
8
5
x
y=\frac{8}{5} x
y
=
5
8
x
\newline
(B)
y
=
1
3
x
y=\frac{1}{3} x
y
=
3
1
x
\newline
(C)
y
=
1
4
x
y=\frac{1}{4} x
y
=
4
1
x
\newline
(D)
y
=
18
6
x
y=\frac{18}{6} x
y
=
6
18
x
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Which value for the constant
c
c
c
makes
z
=
4
z=4
z
=
4
an extraneous solution in the following equation?
\newline
3
2
z
+
10
=
c
z
+
8
c
=
□
\begin{array}{l} \sqrt{\frac{3}{2} z+10}=c z+8 \\ c=\square \end{array}
2
3
z
+
10
=
cz
+
8
c
=
□
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Which exponential expression is equivalent to
b
7
\sqrt[7]{b}
7
b
?
\newline
Choose
1
1
1
answer:
\newline
(A)
b
7
b^{7}
b
7
\newline
(B)
b
1
7
b^{\frac{1}{7}}
b
7
1
\newline
(C)
1
b
7
\frac{1}{b^{7}}
b
7
1
\newline
(D)
1
b
1
7
\frac{1}{b^{\frac{1}{7}}}
b
7
1
1
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Which exponential expression is equivalent to
x
4
\sqrt[4]{x}
4
x
?
\newline
Choose
1
1
1
answer:
\newline
(A)
1
x
4
\frac{1}{x^{4}}
x
4
1
\newline
(B)
1
x
1
4
\frac{1}{x^{\frac{1}{4}}}
x
4
1
1
\newline
(C)
x
1
4
x^{\frac{1}{4}}
x
4
1
\newline
(D)
x
4
x^{4}
x
4
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Which expressions are equivalent to
(
d
4
)
3
(\sqrt[4]{d})^{3}
(
4
d
)
3
?
\newline
Choose all answers that apply:
\newline
A
d
3
4
\sqrt[4]{d^{3}}
4
d
3
\newline
B
(
d
1
4
)
3
\left(d^{\frac{1}{4}}\right)^{3}
(
d
4
1
)
3
\newline
c
d
4
3
\sqrt[3]{d^{4}}
3
d
4
\newline
D None of the above
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Which expressions are equivalent to
x
1.4
x^{1.4}
x
1.4
?
\newline
Choose all answers that apply:
\newline
A
x
7
5
\sqrt[5]{x^{7}}
5
x
7
\newline
B
(
x
5
)
7
(\sqrt[5]{x})^{7}
(
5
x
)
7
\newline
C.
(
x
1
5
)
7
\left(x^{\frac{1}{5}}\right)^{7}
(
x
5
1
)
7
\newline
D None of the above
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Which exponential expression is equivalent to
z
9
\sqrt[9]{z}
9
z
?
\newline
Choose
1
1
1
answer:
\newline
(A)
z
9
z^{9}
z
9
\newline
(B)
1
z
1
9
\frac{1}{z^{\frac{1}{9}}}
z
9
1
1
\newline
(C)
1
z
9
\frac{1}{z^{9}}
z
9
1
\newline
(D)
z
1
9
z^{\frac{1}{9}}
z
9
1
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Which expressions are equivalent to
x
4
5
x^{\frac{4}{5}}
x
5
4
?
\newline
Choose all answers that apply:
\newline
A
(
x
4
)
5
(\sqrt[4]{x})^{5}
(
4
x
)
5
\newline
B
x
1
4
5
\sqrt[5]{x^{\frac{1}{4}}}
5
x
4
1
\newline
C
(
x
4
)
5
\left(x^{4}\right)^{5}
(
x
4
)
5
\newline
D None of the above
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Which exponential expression is equivalent to
z
7
8
\sqrt[8]{z^{7}}
8
z
7
?
\newline
Choose
1
1
1
answer:
\newline
(A)
z
7
z
8
\frac{z^{7}}{z^{8}}
z
8
z
7
\newline
(B)
z
8
7
z^{\frac{8}{7}}
z
7
8
\newline
(C)
z
7
8
z^{\frac{7}{8}}
z
8
7
\newline
(D)
z
8
z
7
\frac{z^{8}}{z^{7}}
z
7
z
8
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Which exponential expression is equivalent to
a
3
\sqrt[3]{a}
3
a
?
\newline
Choose
1
1
1
answer:
\newline
(A)
1
a
3
\frac{1}{a^{3}}
a
3
1
\newline
(B)
a
3
a^{3}
a
3
\newline
(C)
a
1
3
a^{\frac{1}{3}}
a
3
1
\newline
(D)
1
a
1
3
\frac{1}{a^{\frac{1}{3}}}
a
3
1
1
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Which exponential expression is equivalent to
k
5
6
\sqrt[6]{k^{5}}
6
k
5
?
\newline
Choose
1
1
1
answer:
\newline
(A)
k
6
k
5
\frac{k^{6}}{k^{5}}
k
5
k
6
\newline
(B)
k
5
k
6
\frac{k^{5}}{k^{6}}
k
6
k
5
\newline
(C)
k
5
6
k^{\frac{5}{6}}
k
6
5
\newline
(D)
k
6
5
k^{\frac{6}{5}}
k
5
6
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Which exponential expression is equivalent to
c
5
\sqrt[5]{c}
5
c
?
\newline
Choose
1
1
1
answer:
\newline
(A)
c
5
c^{5}
c
5
\newline
(B)
1
c
5
\frac{1}{c^{5}}
c
5
1
\newline
(C)
1
c
1
5
\frac{1}{c^{\frac{1}{5}}}
c
5
1
1
\newline
(D)
1
c
5
\frac{1}{c^{5}}
c
5
1
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Which exponential expression is equivalent to
y
8
\sqrt[8]{y}
8
y
?
\newline
Choose
1
1
1
answer:
\newline
(A)
1
y
1
8
\frac{1}{y^{\frac{1}{8}}}
y
8
1
1
\newline
(B)
y
1
8
y^{\frac{1}{8}}
y
8
1
\newline
(C)
y
8
y^{8}
y
8
\newline
(D)
1
y
8
\frac{1}{y^{8}}
y
8
1
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Which exponential expression is equivalent to
t
6
\sqrt[6]{t}
6
t
?
\newline
Choose
1
1
1
answer:
\newline
(A)
t
6
t^{6}
t
6
\newline
(B)
1
t
1
6
\frac{1}{t^{\frac{1}{6}}}
t
6
1
1
\newline
(C)
t
1
6
t^{\frac{1}{6}}
t
6
1
\newline
(D)
1
t
6
\frac{1}{t^{6}}
t
6
1
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