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Math Problems
Grade 8
Describe the graph of a linear equation
−
27
-27
−
27
x +
54
54
54
y =
9
9
9
x^
2
2
2
-
19
19
19
(\newline\)
3
3
3
x -
6
6
6
y =
−
5
-5
−
5
(\newline\)If
(
x
1
,
y
1
)
(x_1, y_1)
(
x
1
,
y
1
)
and
(
x
2
,
y
2
)
(x_2, y_2)
(
x
2
,
y
2
)
are distinct solutions to the system of equations shown, what is the sum of the
y
y
y
-values
y
1
y_1
y
1
and
y
2
y_2
y
2
?
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Graph
y
=
2
x
−
7
y = 2x - 7
y
=
2
x
−
7
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Graph
−
14
x
+
21
y
=
84
-14 x+21 y=84
−
14
x
+
21
y
=
84
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Find the unknown number in each equation:
\newline
14
e
=
420
14e=420
14
e
=
420
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What value of
u
u
u
is a solution to this equation?
\newline
4
u
=
36
4u = 36
4
u
=
36
\newline
Choices:
\newline
(A)
u
=
8
u = 8
u
=
8
\newline
(B)
u
=
9
u = 9
u
=
9
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Pick the story that can be modeled by the equation
4
x
=
8
4x = 8
4
x
=
8
.
\newline
Choices:
\newline
(A) Deb used
4
4
4
roses and
8
8
8
daisies to make a flower bouquet for her mom's birthday. She used
x
x
x
flowers in all.
\newline
(B) In her mom's birthday bouquet, Deb used
x
x
x
roses and
4
4
4
times as many daisies. She used
8
8
8
daisies.
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Solve:
2
2
2
(
2
2
2
x)+
5
5
5
y=
63
63
63
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If
(
3
−
2
i
)
(
3
−
i
)
(
2
+
i
)
=
a
+
i
b
(3-2i)(3-i)(2+i)=a+ib
(
3
−
2
i
)
(
3
−
i
)
(
2
+
i
)
=
a
+
ib
, where
a
a
a
and
b
b
b
are real numbers and the imaginary number
i
i
i
is such that
i
2
=
−
1
i^2=-1
i
2
=
−
1
, what is the value of
(
2
a
+
3
b
)
(2a+3b)
(
2
a
+
3
b
)
?
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Prove that
cot
2
θ
+
tan
2
θ
=
2
sin
4
θ
\cot 2\theta + \tan 2\theta = 2\sin 4\theta
cot
2
θ
+
tan
2
θ
=
2
sin
4
θ
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What is the value of x?
\newline
3
:
11
:
:
27
:
x
3 : 11 :: 27 : x
3
:
11
::
27
:
x
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2
(
x
−
16
)
+
1
=
41
2(x-16)+1=41
2
(
x
−
16
)
+
1
=
41
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4
x
+
3
x
=
28
4 x+3 x=28
4
x
+
3
x
=
28
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3
y
+
11
y
=
28
3 y+11 y=28
3
y
+
11
y
=
28
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a)
5
N
=
0.01
(
N
−
76
)
5 N=0.01(N-76)
5
N
=
0.01
(
N
−
76
)
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y
=
x
−
2
y=x-2
y
=
x
−
2
and
x
2
+
y
2
=
52
x^2+y^2=52
x
2
+
y
2
=
52
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15
x
−
10
=
20
15x-10=20
15
x
−
10
=
20
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−
4
x
=
64
-4x=64
−
4
x
=
64
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(
x
−
10
)
2
=
121
(x-10)^2 = 121
(
x
−
10
)
2
=
121
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Find
x
x
x
.
\newline
6
x
+
5
=
14
6x+5=14
6
x
+
5
=
14
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Solve the following for `r`
\newline
8
(
1
0
3
r
)
=
12
8(10^{3r})=12
8
(
1
0
3
r
)
=
12
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What is the slope of the line represented by the equation
2
x
−
5
y
=
9
2x-5y=9
2
x
−
5
y
=
9
?
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4
×
y
+
7
=
39
4 \times y+7=39
4
×
y
+
7
=
39
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−
8
x
+
4
y
>
3
-8x+4y > 3
−
8
x
+
4
y
>
3
\newline
6
x
−
7
y
<
−
5
6x-7y < -5
6
x
−
7
y
<
−
5
\newline
Is (
2
2
2
,
3
3
3
) a solution of the system?
\newline
Choose
1
1
1
answer:
\newline
(A) Yes
\newline
(B) No
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If
2
x
−
5
y
=
7
\mathbf{2 x}-\mathbf{5 y}=\mathbf{7}
2x
−
5y
=
7
and
−
9
x
−
2
y
=
10
-\mathbf{9 x}-\mathbf{2 y}=\mathbf{1 0}
−
9x
−
2y
=
10
are true equations, what would be the value of
−
7
x
−
7
y
-7 x-7 y
−
7
x
−
7
y
?
\newline
Answer:
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If
−
6
x
−
9
y
=
6
-6 x-9 y=6
−
6
x
−
9
y
=
6
and
−
4
x
+
y
=
−
1
-4 x+y=-1
−
4
x
+
y
=
−
1
are true equations, what would be the value of
−
10
x
−
8
y
\mathbf{- 1 0 x}-\mathbf{8 y}
−
10x
−
8y
?
\newline
Answer:
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If
5
x
−
y
=
−
7
5 \mathbf{x}-\mathbf{y}=-\mathbf{7}
5
x
−
y
=
−
7
and
x
−
2
y
=
2
\mathbf{x}-\mathbf{2 y}=\mathbf{2}
x
−
2y
=
2
are true equations, what would be the value of
−
4
x
−
y
-4 x-y
−
4
x
−
y
?
\newline
Answer:
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If
−
3
x
+
5
y
=
−
8
-3 x+5 y=-8
−
3
x
+
5
y
=
−
8
is a true equation, what would be the value of
−
3
x
+
5
y
−
4
-3 x+5 y-4
−
3
x
+
5
y
−
4
?
\newline
Answer:
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If
−
8
x
−
9
y
=
2
-\mathbf{8 x}-\mathbf{9 y}=\mathbf{2}
−
8x
−
9y
=
2
and
−
7
x
−
6
y
=
6
-\mathbf{7 x}-6 \mathbf{y}=6
−
7x
−
6
y
=
6
are true equations, what would be the value of
−
15
x
−
15
y
-15 x-15 y
−
15
x
−
15
y
?
\newline
Answer:
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If
−
10
x
+
y
=
4
-\mathbf{1 0 x}+\mathbf{y}=\mathbf{4}
−
10x
+
y
=
4
and
−
2
x
−
3
y
=
−
5
-\mathbf{2 x}-\mathbf{3 y}=-\mathbf{5}
−
2x
−
3y
=
−
5
are true equations, what would be the value of
−
8
x
+
4
y
-8 x+4 y
−
8
x
+
4
y
?
\newline
Answer:
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If
−
8
x
+
4
y
=
−
6
-8 x+4 y=-6
−
8
x
+
4
y
=
−
6
is a true equation, what would be the value of
−
16
x
+
8
y
?
-\mathbf{1 6 x}+\mathbf{8 y} ?
−
16x
+
8y
?
\newline
Answer:
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If
10
x
+
5
y
=
−
8
10 x+5 y=-8
10
x
+
5
y
=
−
8
and
−
7
x
−
10
y
=
−
9
-\mathbf{7 x}-\mathbf{1 0 y}=-9
−
7x
−
10y
=
−
9
are true equations, what would be the value of
3
x
−
5
y
\mathbf{3 x}-\mathbf{5 y}
3x
−
5y
?
\newline
Answer:
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−
8
x
+
4
y
>
3
-8x+4y > 3
−
8
x
+
4
y
>
3
\newline
6
x
−
7
y
<
−
5
6x-7y < -5
6
x
−
7
y
<
−
5
\newline
Is (
2
2
2
,
3
3
3
) a solution of the system?
\newline
Choose
1
1
1
answer:
\newline
(A) Yes
\newline
(B) No
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The value of Yong's investment account increases at a rate that is proportional at any time to the value of the account at that time.
\newline
Her account was worth
$
2000
\$ 2000
$2000
initially, and it increases by
10
%
10 \%
10%
every
4
4
4
years.
\newline
What is the value of Yong's investment account after
7
7
7
years?
\newline
Choose
1
1
1
answer:
\newline
(A)
$
2036
\$ 2036
$2036
\newline
(B)
$
2350
\$ 2350
$2350
\newline
(C)
$
2363
\$ 2363
$2363
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