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Math Problems
Grade 8
Solve equations with variables on both sides
Solve for
p
p
p
.
\newline
6
p
=
7
p
+
10
6p = 7p + 10
6
p
=
7
p
+
10
\newline
p
=
p =
p
=
____
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Solve for
z
z
z
.
\newline
9
z
=
6
z
+
6
9z = 6z + 6
9
z
=
6
z
+
6
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Today, the population of Canyon Falls is
22
22
22
,
500
500
500
and the population of Swift Creek is
15
15
15
,
200
200
200
. The population of Canyon Falls is decreasing at the rate of
740
740
740
people each year while the population of Swift Creek is increasing at the rate of
1
1
1
,
500
500
500
people each year. Assuming these rates continue into the future, in how many years from today will the population of Swift Creek equal twice the population of Canyon Falls?
\newline
Choose
1
1
1
answer:
\newline
(A)
9
9
9
years
\newline
(B)
10
\mathbf{1 0}
10
years
\newline
(C)
11
\mathbf{1 1}
11
years
\newline
(D)
12
12
12
years
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Water and other materials necessary for biological activity in trees are absorbed by the roots and transported throughout the stem and branches in thin, hollow tubes in the xylem. Water may travel as fast as
150
150
150
feet per hour. Which of the following inequalities best describes the number of minutes,
m
m
m
, after being absorbed by the root, that it takes for water to reach a height of
250
250
250
feet above the ground?
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The concession stand at a football game sells hot dogs and drinks. It costs
34
34
34
.
25
25
25
for
2
2
2
hot dogs and
1
1
1
drink. It costs
$
7.00
\$ 7.00
$7.00
for
3
3
3
hot dogs and
2
2
2
Irinks. Which of the following systems of equations can be solved to letermine the cost,
h
h
h
, of each hot dog and the cost,
d
d
d
, of each drink?
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A piece of glass with an initial temperature of
9
9
∘
C
99^{\circ} \mathrm{C}
9
9
∘
C
is cooled at a rate of
3.
5
∘
C
3.5^{\circ} \mathrm{C}
3.
5
∘
C
per minute. At the same time, a piece of copper with an initial temperature of
0
∘
C
0^{\circ} \mathrm{C}
0
∘
C
is heated at
2.
5
∘
C
2.5^{\circ} \mathrm{C}
2.
5
∘
C
per minute. Which of the following systems of equations can be used to solve for the temperature,
T
T
T
, in degrees Celsius, and the time,
m
m
m
, in minutes, when the glass and copper reach the same temperatures?
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At the beginning of the week, Paloma opened a new box of
275
275
275
coffee creamers. Sixty-four coffee creamers were used during the week. Which equation could be used to find
x
x
x
, the number of coffee creamers left at the end of the week?
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Silas took
18
18
18
bags of glass to the recycling center. He still has
6
6
6
bags of plastic to take to the recycling center. Which equation could be used to find
x
x
x
, the total number of bags of glass and plastic Silas will take to the recycling center?
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Given that
f
(
x
)
=
x
+
4
,
g
(
x
)
=
2
x
f(x)=x+4, \quad g(x)=2 x
f
(
x
)
=
x
+
4
,
g
(
x
)
=
2
x
and
h
(
x
)
=
−
3
f
(
x
+
2
)
+
2
g
(
x
)
h(x)=-3 f(x+2)+2 g(x)
h
(
x
)
=
−
3
f
(
x
+
2
)
+
2
g
(
x
)
, then what is the value of
h
(
2
)
h(2)
h
(
2
)
?
\newline
Answer:
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Given that
f
(
x
)
=
3
x
,
g
(
x
)
=
x
+
2
f(x)=3 x, \quad g(x)=x+2
f
(
x
)
=
3
x
,
g
(
x
)
=
x
+
2
and
h
(
x
)
=
−
3
f
(
x
−
2
)
+
2
g
(
x
+
2
)
h(x)=-3 f(x-2)+2 g(x+2)
h
(
x
)
=
−
3
f
(
x
−
2
)
+
2
g
(
x
+
2
)
, then what is the value of
h
(
3
)
h(3)
h
(
3
)
?
\newline
Answer:
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Given that
f
(
x
)
=
−
4
x
,
g
(
x
)
=
x
−
4
f(x)=-4 x, \quad g(x)=x-4
f
(
x
)
=
−
4
x
,
g
(
x
)
=
x
−
4
and
h
(
x
)
=
−
f
(
x
−
1
)
+
3
g
(
x
)
h(x)=-f(x-1)+3 g(x)
h
(
x
)
=
−
f
(
x
−
1
)
+
3
g
(
x
)
, then what is the value of
h
(
2
)
h(2)
h
(
2
)
?
\newline
Answer:
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Determine the value of
y
y
y
, if
x
x
x
is
100
100
100
.
\newline
y
=
x
−
10
y=\sqrt{x}-10
y
=
x
−
10
\newline
Answer:
y
=
y=
y
=
Get tutor help
Determine the value of
y
y
y
, if
x
x
x
is
64
64
64
.
\newline
y
=
x
+
3
y=\sqrt{x}+3
y
=
x
+
3
\newline
Answer:
y
=
y=
y
=
Get tutor help
Determine the value of
y
y
y
, if
x
x
x
is
121
121
121
.
\newline
y
=
x
−
6
y=\sqrt{x}-6
y
=
x
−
6
\newline
Answer:
y
=
y=
y
=
Get tutor help
Determine the value of
y
y
y
, if
x
x
x
is
1
1
1
.
\newline
y
=
x
−
9
y=\sqrt{x}-9
y
=
x
−
9
\newline
Answer:
y
=
y=
y
=
Get tutor help
Determine the value of
y
y
y
, if
x
x
x
is
81
81
81
.
\newline
y
=
x
−
1
y=\sqrt{x}-1
y
=
x
−
1
\newline
Answer:
y
=
y=
y
=
Get tutor help
Determine the value of
y
y
y
, if
x
x
x
is
9
9
9
.
\newline
y
=
x
+
10
y=\sqrt{x}+10
y
=
x
+
10
\newline
Answer:
y
=
y=
y
=
Get tutor help
Determine the value of
y
y
y
, if
x
x
x
is
16
16
16
.
\newline
y
=
x
−
4
y=\sqrt{x}-4
y
=
x
−
4
\newline
Answer:
y
=
y=
y
=
Get tutor help
Determine the value of
y
y
y
, if
x
x
x
is
4
4
4
.
\newline
y
=
x
−
5
y=\sqrt{x}-5
y
=
x
−
5
\newline
Answer:
y
=
y=
y
=
Get tutor help
Determine the value of
y
y
y
, if
x
x
x
is
64
64
64
.
\newline
y
=
x
−
11
y=\sqrt{x}-11
y
=
x
−
11
\newline
Answer:
y
=
y=
y
=
Get tutor help
Determine the value of
y
y
y
, if
x
x
x
is
1
1
1
.
\newline
y
=
x
−
4
y=\sqrt{x}-4
y
=
x
−
4
\newline
Answer:
y
=
y=
y
=
Get tutor help
Determine the value of
y
y
y
, if
x
x
x
is
9
9
9
.
\newline
y
=
x
+
1
y=\sqrt{x}+1
y
=
x
+
1
\newline
Answer:
y
=
y=
y
=
Get tutor help
Determine the value of
y
y
y
, if
x
x
x
is
100
100
100
.
\newline
y
=
x
−
12
y=\sqrt{x}-12
y
=
x
−
12
\newline
Answer:
y
=
y=
y
=
Get tutor help
Determine the value of
y
y
y
, if
x
x
x
is
4
4
4
.
\newline
y
=
x
+
10
y=\sqrt{x}+10
y
=
x
+
10
\newline
Answer:
y
=
y=
y
=
Get tutor help
Determine the value of
y
y
y
, if
x
x
x
is
121
121
121
.
\newline
y
=
x
−
3
y=\sqrt{x}-3
y
=
x
−
3
\newline
Answer:
y
=
y=
y
=
Get tutor help
Determine the value of
y
y
y
, if
x
x
x
is
121
121
121
.
\newline
y
=
x
−
2
y=\sqrt{x}-2
y
=
x
−
2
\newline
Answer:
y
=
y=
y
=
Get tutor help
Determine the value of
y
y
y
, if
x
x
x
is
1
1
1
.
\newline
y
=
x
−
6
y=\sqrt{x}-6
y
=
x
−
6
\newline
Answer:
y
=
y=
y
=
Get tutor help
Determine the value of
y
y
y
, if
x
x
x
is
100
100
100
.
\newline
y
=
x
−
11
y=\sqrt{x}-11
y
=
x
−
11
\newline
Answer:
y
=
y=
y
=
Get tutor help
Determine the value of
y
y
y
, if
x
x
x
is
81
81
81
.
\newline
y
=
x
−
5
y=\sqrt{x}-5
y
=
x
−
5
\newline
Answer:
y
=
y=
y
=
Get tutor help
Determine the value of
y
y
y
, if
x
x
x
is
81
81
81
.
\newline
y
=
x
−
2
y=\sqrt{x}-2
y
=
x
−
2
\newline
Answer:
y
=
y=
y
=
Get tutor help
Determine the value of
y
y
y
, if
x
x
x
is
4
4
4
.
\newline
y
=
x
+
12
y=\sqrt{x}+12
y
=
x
+
12
\newline
Answer:
y
=
y=
y
=
Get tutor help
Determine the value of
y
y
y
, if
x
x
x
is
49
49
49
.
\newline
y
=
x
−
4
y=\sqrt{x}-4
y
=
x
−
4
\newline
Answer:
y
=
y=
y
=
Get tutor help
Determine the value of
y
y
y
, if
x
x
x
is
144
144
144
.
\newline
y
=
x
−
6
y=\sqrt{x}-6
y
=
x
−
6
\newline
Answer:
y
=
y=
y
=
Get tutor help
Determine the value of
y
y
y
, if
x
x
x
is
121
121
121
.
\newline
y
=
x
−
10
y=\sqrt{x}-10
y
=
x
−
10
\newline
Answer:
y
=
y=
y
=
Get tutor help
A stone fell from the top of a cliff into the ocean.
\newline
In the air, it had an average speed of
16
m
/
s
16 \mathrm{~m} / \mathrm{s}
16
m
/
s
. In the water, it had an average speed of
3
m
/
s
3 \mathrm{~m} / \mathrm{s}
3
m
/
s
before hitting the seabed. The total distance from the top of the cliff to the seabed is
127
127
127
meters, and the stone's entire fall took
12
12
12
seconds.
\newline
How long did the stone fall in the air and how long did it fall in the water?
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Factor the expression completely.
\newline
8
x
+
12
8 x+12
8
x
+
12
\newline
Answer:
Get tutor help
In
△
I
J
K
,
m
∠
I
=
(
x
+
6
)
∘
,
m
∠
J
=
(
2
x
+
16
)
∘
\triangle \mathrm{IJK}, \mathrm{m} \angle I=(x+6)^{\circ}, \mathrm{m} \angle J=(2 x+16)^{\circ}
△
IJK
,
m
∠
I
=
(
x
+
6
)
∘
,
m
∠
J
=
(
2
x
+
16
)
∘
, and
m
∠
K
=
(
6
x
+
14
)
∘
\mathrm{m} \angle K=(6 x+14)^{\circ}
m
∠
K
=
(
6
x
+
14
)
∘
. What is the value of
x
x
x
?
\newline
Answer:
Get tutor help
In
△
B
C
D
,
B
D
‾
\triangle \mathrm{BCD}, \overline{B D}
△
BCD
,
B
D
is extended through point
D
\mathrm{D}
D
to point
E
,
m
∠
C
D
E
=
(
6
x
+
7
)
∘
\mathrm{E}, \mathrm{m} \angle C D E=(6 x+7)^{\circ}
E
,
m
∠
C
D
E
=
(
6
x
+
7
)
∘
,
m
∠
B
C
D
=
(
3
x
+
9
)
∘
\mathrm{m} \angle B C D=(3 x+9)^{\circ}
m
∠
BC
D
=
(
3
x
+
9
)
∘
, and
m
∠
D
B
C
=
(
x
+
20
)
∘
\mathrm{m} \angle D B C=(x+20)^{\circ}
m
∠
D
BC
=
(
x
+
20
)
∘
. What is the value of
x
?
x ?
x
?
\newline
Answer:
Get tutor help
Solve for
n
\mathrm{n}
n
.
\newline
15
=
−
3
n
15=-3 n
15
=
−
3
n
\newline
Answer:
n
=
n=
n
=
Get tutor help
Solve for
b
\mathrm{b}
b
.
\newline
−
7
=
−
7
b
-7=-7 b
−
7
=
−
7
b
\newline
Answer:
b
=
b=
b
=
Get tutor help
Solve for
b
\mathrm{b}
b
.
\newline
−
9
=
−
9
b
-9=-9 b
−
9
=
−
9
b
\newline
Answer:
b
=
b=
b
=
Get tutor help
Solve for
x
\mathrm{x}
x
.
\newline
−
2
=
2
x
-2=2 x
−
2
=
2
x
\newline
Answer:
x
=
x=
x
=
Get tutor help
Solve for
u
\mathrm{u}
u
. You must write your answer in fully simplified form.
\newline
−
10
=
−
8
u
-10=-8 u
−
10
=
−
8
u
\newline
Answer:
u
=
u=
u
=
Get tutor help
Solve for
x
\mathrm{x}
x
. You must write your answer in fully simplified form.
\newline
8
=
−
8
x
8=-8 x
8
=
−
8
x
\newline
Answer:
x
=
x=
x
=
Get tutor help
Solve for w. You must write your answer in fully simplified form.
\newline
18
=
−
7
w
18=-7 w
18
=
−
7
w
\newline
Answer:
w
=
w=
w
=
Get tutor help
Solve for
t
t
t
. You must write your answer in fully simplified form.
\newline
−
19
=
−
6
t
-19=-6 t
−
19
=
−
6
t
\newline
Answer:
t
=
t=
t
=
Get tutor help
Solve for
x
\mathrm{x}
x
. You must write your answer in fully simplified form.
\newline
−
10
=
−
7
x
-10=-7 x
−
10
=
−
7
x
\newline
Answer:
x
=
x=
x
=
Get tutor help
Find the value of
x
x
x
in the equation below.
\newline
35
=
5
x
35=5 x
35
=
5
x
\newline
Answer:
x
=
x=
x
=
Get tutor help
Find the value of
x
x
x
in the equation below.
\newline
48
=
6
x
48=6 x
48
=
6
x
\newline
Answer:
x
=
x=
x
=
Get tutor help
Solve for a.
\newline
−
6
=
3
+
a
-6=3+a
−
6
=
3
+
a
\newline
Answer:
a
=
a=
a
=
Get tutor help
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