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Math Problems
Grade 8
Solve equations using cube roots
Find the value of
x
x
x
in the triangle shown below.
\newline
x
=
x=
x
=
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Look at this equation:
\newline
h
3
=
8
h^3 = 8
h
3
=
8
\newline
Solve for
h
h
h
.
\newline
h
=
h =
h
=
____
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Look at this equation:
\newline
b
3
=
125
b^3 = 125
b
3
=
125
\newline
Solve for
b
b
b
.
\newline
b
=
b =
b
=
____
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Look at this equation:
\newline
h
3
=
1
,
000
h^3 = 1,000
h
3
=
1
,
000
\newline
What is
h
h
h
, the cube root of
1
,
000
1,000
1
,
000
?
\newline
h = ____
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Look at this equation:
\newline
b
3
=
1
b^3 = 1
b
3
=
1
\newline
What is
b
b
b
, the cube root of
1
1
1
?
\newline
b = ____
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Look at this equation:
\newline
v
3
=
64
v^3 = 64
v
3
=
64
\newline
What is
v
v
v
, the cube root of
64
64
64
?
\newline
v
=
v =
v
=
__
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Look at this equation:
\newline
m
3
=
27
m^3 = 27
m
3
=
27
\newline
What is
m
m
m
, the cube root of
27
27
27
?
\newline
m
=
m =
m
=
__
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Look at this equation:
\newline
z
3
=
125
z^3 = 125
z
3
=
125
\newline
What is
z
z
z
, the cube root of
125
125
125
?
\newline
z
=
z =
z
=
____
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Look at this equation:
\newline
m
3
=
8
m^3 = 8
m
3
=
8
\newline
What is
m
m
m
, the cube root of
8
8
8
?
\newline
m
=
m =
m
=
__
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Look at this equation:
\newline
b
3
=
125
b^{3}=125
b
3
=
125
\newline
Solve for
b
b
b
.
\newline
b
=
b=
b
=
□
\square
□
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Question
5
5
5
\newline
(a) Find
x
x
x
in terms of
y
y
y
.
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f
(
x
)
=
x
2
f(x) = x^2
f
(
x
)
=
x
2
. What is
f
′
(
x
)
f'(x)
f
′
(
x
)
equal to ?
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x
2
x^2
x
2
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Determine the value of
y
y
y
, if
x
x
x
is
64
64
64
.
\newline
y
=
x
+
2
y=\sqrt{x}+2
y
=
x
+
2
\newline
Answer:
y
=
y=
y
=
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What is the sign of
46.2
+
112.3
?
46.2+112.3 ?
46.2
+
112.3
?
\newline
Choose
1
1
1
answer:
\newline
(A) Positive
\newline
(B) Negative
\newline
(C) Neither positive nor negative-the sum is zero.
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What is the constant of proportionality in the equation
y
=
5
9
x
y=\frac{5}{9} x
y
=
9
5
x
?
\newline
constant of proportionality
=
=
=
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What is the constant of proportionality in the equation
y
=
5
4
x
y=\frac{5}{4} x
y
=
4
5
x
?
\newline
constant of proportionality
=
=
=
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What is the constant of proportionality in the equation
\newline
y
=
2
3
x
?
y=\frac{2}{3} x \text { ? }
y
=
3
2
x
?
\newline
constant of proportionality
=
=
=
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What is the constant of proportionality in the equation
y
=
1
2
x
y=\frac{1}{2} x
y
=
2
1
x
?
\newline
constant of proportionality
=
=
=
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z
=
73
i
−
32
z=73 i-32
z
=
73
i
−
32
\newline
What is the real part of
z
z
z
?
\newline
What is the imaginary part of
z
z
z
?
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z
=
44
i
+
23.3
z=44 i+23.3
z
=
44
i
+
23.3
\newline
What is the real part of
z
z
z
?
\newline
What is the imaginary part of
z
z
z
?
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z
=
−
91
+
14.6
i
z=-91+14.6 i
z
=
−
91
+
14.6
i
\newline
What is the real part of
z
z
z
?
\newline
What is the imaginary part of
z
z
z
?
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z
=
−
400
i
−
44.5
z=-400 i-44.5
z
=
−
400
i
−
44.5
\newline
What is the real part of
z
z
z
?
\newline
What is the imaginary part of
z
z
z
?
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z
=
12.1
+
29
i
z=12.1+29 i
z
=
12.1
+
29
i
\newline
What is the real part of
z
z
z
?
\newline
What is the imaginary part of
z
z
z
?
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z
=
−
60
i
+
80
z=-60 i+80
z
=
−
60
i
+
80
\newline
What is the real part of
z
z
z
?
\newline
What is the imaginary part of
z
z
z
?
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z
=
−
112
−
55
i
z=-112-55 i
z
=
−
112
−
55
i
\newline
What is the real part of
z
z
z
?
\newline
What is the imaginary part of
z
z
z
?
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If
18
=
n
−
18
18=n-18
18
=
n
−
18
, what is the value of
n
n
n
?
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If
p
−
18
=
3
p-18=3
p
−
18
=
3
, what is the value of
p
p
p
?
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If
10
=
x
10
10=\frac{x}{10}
10
=
10
x
, what is the value of
x
x
x
?
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If
12
=
n
−
9
12=n-9
12
=
n
−
9
, what is the value of
n
n
n
?
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If
2
a
=
2
5
7
2^{a}=\sqrt[7]{2^{5}}
2
a
=
7
2
5
, what is the value of
a
a
a
?
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If
1
1
a
=
1
1
5
6
11^{a}=\sqrt[6]{11^{5}}
1
1
a
=
6
1
1
5
, what is the value of
a
a
a
?
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If
7
a
=
7
3
8
7^{a}=\sqrt[8]{7^{3}}
7
a
=
8
7
3
, what is the value of
a
a
a
?
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If
1
1
a
=
1
1
3
4
11^{a}=\sqrt[4]{11^{3}}
1
1
a
=
4
1
1
3
, what is the value of
a
a
a
?
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If
4
a
=
4
6
4^{a}=\sqrt[6]{4}
4
a
=
6
4
, what is the value of
a
?
a ?
a
?
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If
2
a
=
2
4
2^{a}=\sqrt[4]{2}
2
a
=
4
2
, what is the value of
a
a
a
?
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2
x
2
+
26
x
+
84
2 x^{2}+26 x+84
2
x
2
+
26
x
+
84
\newline
If
2
(
x
+
a
)
(
x
+
b
)
2(x+a)(x+b)
2
(
x
+
a
)
(
x
+
b
)
is equivalent to the given expression, what is the value of
a
b
a b
ab
?
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If
f
(
x
)
=
5
x
−
3
f(x)=5 x-3
f
(
x
)
=
5
x
−
3
, what is the value of
f
(
4
)
f(4)
f
(
4
)
?
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75
=
24
x
75=24 x
75
=
24
x
\newline
Given the equation, what is the value of
x
25
\frac{x}{25}
25
x
?
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The product
\newline
89
×
76
89 \times 76
89
×
76
equals
6
,
764
6,764
6
,
764
.
\newline
Use the previous fact to evaluate as a decimal.
\newline
89
×
7.6
=
89 \times 7.6=
89
×
7.6
=
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Write the sentence as an equation.
\newline
172
172
172
is equal to the quotient of
x
x
x
and
4
4
4
\newline
Type a slash (
/
/
/
) if you want to use a division sign.
\newline
_____
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Look at this equation:
\newline
c
3
=
27
c^3 = 27
c
3
=
27
\newline
\newline
What is
c
c
c
, the cube root of
27
27
27
?
\newline
c
=
c =
c
=
____
\newline
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