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Math Problems
Algebra 2
Composition of linear and quadratic functions: find a value
Let
d
2
=
−
18
d^2 = -18
d
2
=
−
18
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7
∣
x
−
7
∣
=
42
7|x-7|=42
7∣
x
−
7∣
=
42
\newline
What is the sum of the solutions to the given equation?
\newline
(A)
−
6
-6
−
6
\newline
(B)
0
0
0
\newline
(C)
14
14
14
\newline
(D)
49
49
49
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Find the value of
c
c
c
so that the polynomial
p
(
x
)
p(x)
p
(
x
)
is divisible by
(
x
−
3
)
(x-3)
(
x
−
3
)
.
\newline
p
(
x
)
=
−
x
3
+
c
x
2
−
4
x
+
3
p(x) = -x^3 + cx^2 - 4x + 3
p
(
x
)
=
−
x
3
+
c
x
2
−
4
x
+
3
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Find the value of
c
c
c
so that the polynomial
p
(
x
)
p(x)
p
(
x
)
is divisible by
(
x
−
3
)
(x-3)
(
x
−
3
)
.
\newline
p
(
x
)
=
−
x
3
+
c
x
2
−
4
x
+
3
p(x) = -x^3 + cx^2 - 4x + 3
p
(
x
)
=
−
x
3
+
c
x
2
−
4
x
+
3
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evaluate
15
k
\frac{15}{k}
k
15
when
k
=
3
k =3
k
=
3
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Find the unknown number in each equation:
\newline
364
h
=
7
\frac{364}{h}=7
h
364
=
7
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Estimate. Which sign makes the statement true?
\newline
201
2
÷
6
?
8
\frac{201}{2} \div 6\;?\;8
2
201
÷
6
?
8
\newline
Choices:
\newline
(A)
>
>
>
\newline
(B)
<
<
<
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Estimate. Which sign makes the statement true?
\newline
867
?
8964
5
÷
2
867 \, ? \, \frac{8964}{5} \div 2
867
?
5
8964
÷
2
\newline
Choices:
\newline
(A)
>
>
>
\newline
(B)
<
<
<
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Which sign makes the statement true?
\newline
2
5
\frac{2}{5}
5
2
?
\text{?}
?
2.6
2.6
2.6
\newline
Choices:
\newline
(A)
>
>
>
\newline
(B)
<
<
<
\newline
(C)
=
=
=
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Which sign makes the statement true?
\newline
−
9.6
?
−
9
2
3
-9.6 \, ? \, -9 \frac{2}{3}
−
9.6
?
−
9
3
2
\newline
Choices:
\newline
(A)
=
=
=
\newline
(B)
≠
\neq
=
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Which sign makes the statement true?
\newline
−
4.7
?
−
4.77
-4.7 \, ? \, -4.77
−
4.7
?
−
4.77
\newline
Choices:
\newline
(A)
=
=
=
\newline
(B)
≠
\neq
=
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Which sign makes the statement true?
\newline
6
1
4
?
6.25
6 \frac{1}{4} ? 6.25
6
4
1
?
6.25
\newline
Choices:
\newline
(A)
=
=
=
\newline
(B)
≠
\neq
=
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Which sign makes the statement true?
\newline
3
3
5
?
3.4
3 \frac{3}{5} ? 3.4
3
5
3
?
3.4
\newline
Choices:
\newline
(A)
=
=
=
\newline
(B)
≠
\neq
=
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Which sign makes the statement true?
\newline
5.89
5.89
5.89
?
5.890
5.890
5.890
\newline
Choices:
\newline
(A)
=
=
=
\newline
(B)
≠
\neq
=
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Which sign makes the statement true?
\newline
−
0.5
-0.5
−
0.5
?
−
1
2
-\frac{1}{2}
−
2
1
\newline
Choices:
\newline
(A)
=
=
=
\newline
(B)
≠
\neq
=
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Which sign makes the statement true?
\newline
5
?
−
5
5 ? -5
5
?
−
5
\newline
Choices:
\newline
(A)
=
=
=
\newline
(B)
≠
\neq
=
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(
x
−
h
)
2
+
(
y
−
k
)
2
=
r
2
(x-h)^2+(y-k)^2=r^2
(
x
−
h
)
2
+
(
y
−
k
)
2
=
r
2
find
y
y
y
.
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Choose the correct symbol to compare the expressions. Do not multiply.
\newline
7
×
2
2
?
7
7 \times \frac{2}{2} \,?\, 7
7
×
2
2
?
7
\newline
Choices:
\newline
(A)
>
>
>
\newline
(B)
<
<
<
\newline
(C)
=
=
=
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Choose the correct symbol to compare the expressions. Do not multiply.
\newline
1
×
4
5
1 \times \frac{4}{5}
1
×
5
4
?
1
1
1
\newline
Choices:
\newline
(A)
>
>
>
\newline
(B)
<
<
<
\newline
(C)
=
=
=
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Evaluate
9
y
1
−
y
0
9y^1-y^0
9
y
1
−
y
0
if
y
=
−
4
y=-4
y
=
−
4
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3
×
10
+
8
÷
2
−
2
×
5
=
?
3\times10+8\div2-2\times5=\ ?
3
×
10
+
8
÷
2
−
2
×
5
=
?
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Which sign makes the statement true?
\newline
0.32
?
0.71
−
0.58
0.32 \, ? \, 0.71 - 0.58
0.32
?
0.71
−
0.58
\newline
Choices:
\newline
(A)
>
>
>
\newline
(B)
<
<
<
\newline
(C)
=
=
=
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Find
y
′
′
y^{\prime \prime}
y
′′
if
x
4
+
y
4
=
16
x^{4}+y^{4}=16
x
4
+
y
4
=
16
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X
2
+
6
−
8
=
0
X^2+6-8=0
X
2
+
6
−
8
=
0
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If
x
x
x
is an integer such that
(
−
5
)
6
x
=
5
10
+
x
(-5)^{6x} = 5^{10 + x}
(
−
5
)
6
x
=
5
10
+
x
, what is the value of
x
x
x
?
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Simplifying the Expression:
2
π
V
∗
1
+
(
e
−
J
2
)
2\pi V*1+\left(\frac{e^{-J}}{2}\right)
2
πV
∗
1
+
(
2
e
−
J
)
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Solve the following equation for
x
x
x
. Express your answer in the simplest form.
\newline
10
x
+
9
(
2
x
+
1
)
=
−
7
(
−
4
x
−
2
)
−
5
10 x+9(2 x+1)=-7(-4 x-2)-5
10
x
+
9
(
2
x
+
1
)
=
−
7
(
−
4
x
−
2
)
−
5
\newline
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3
y
=
3
2
3 y=\frac{3}{2}
3
y
=
2
3
, value of
y
y
y
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(
−
2
)
2
n
=
16
(-2)^{2n} = 16
(
−
2
)
2
n
=
16
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If
2
×
5
=
9
2 \times 5=9
2
×
5
=
9
and
4
×
0
=
16
4 \times 0=16
4
×
0
=
16
and
8
×
3
=
67
8 \times 3=67
8
×
3
=
67
, and
3
×
8
=
17
3 \times 8=17
3
×
8
=
17
, what is the value of
8
×
8
?
8 \times 8 ?
8
×
8
?
\newline
(A)
64
64
64
\newline
(B)
65
65
65
\newline
(C)
66
66
66
\newline
(D)
72
72
72
\newline
(E)
68
68
68
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If
f
(
x
)
=
(
x
−
2
)
2
−
x
3
f(x)=(x-2)^{2}-x^{3}
f
(
x
)
=
(
x
−
2
)
2
−
x
3
, what is
f
(
−
3
)
−
f
(
3
)
?
f(-3)-f(3) ?
f
(
−
3
)
−
f
(
3
)?
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If
3
x
2
−
18
x
−
15
=
0
3 x^{2}-18 x-15=0
3
x
2
−
18
x
−
15
=
0
, what is the value of
x
2
−
6
x
x^{2}-6 x
x
2
−
6
x
?
\newline
□
\square
□
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Calculate
5.76
+
2.
8
3
\sqrt{5.76}+2.8^{3}
5.76
+
2.
8
3
.
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−
22
≤
x
+
8
-22 \leq x+8
−
22
≤
x
+
8
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y
=
5
(
x
−
2
)
2
−
4
y=5(x-2)^2-4
y
=
5
(
x
−
2
)
2
−
4
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y
=
2
(
x
−
3
)
2
+
5
y=2(x-3)^2+5
y
=
2
(
x
−
3
)
2
+
5
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Solve for the exact value of
x
x
x
.
\newline
6
ln
(
8
x
−
5
)
+
10
=
52
6 \ln (8 x-5)+10=52
6
ln
(
8
x
−
5
)
+
10
=
52
\newline
Answer:
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Point
L
\mathrm{L}
L
is located at
−
7
-7
−
7
. Point
M
\mathrm{M}
M
is
2
2
2
greater than Point
L
\mathrm{L}
L
. Where is
M
\mathrm{M}
M
located?
\newline
M
=
□
\mathbf{M}= \square
M
=
□
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Point A is located at
−
8
-8
−
8
. Point
B
\mathrm{B}
B
is
4
4
4
greater than Point
A
\mathrm{A}
A
. Where is
B
\mathrm{B}
B
located?
\newline
B
=
□
B= \square
B
=
□
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Point
W
\mathrm{W}
W
is located at
−
6
-6
−
6
. Point
X
\mathrm{X}
X
is
8
8
8
greater than Point
W
\mathrm{W}
W
. Where is
X
\mathrm{X}
X
located?
\newline
X
=
□
\mathrm{X}=\square
X
=
□
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What is the value of the expression below when
z
=
3
z=3
z
=
3
?
\newline
9
z
2
−
5
z
+
10
9 z^{2}-5 z+10
9
z
2
−
5
z
+
10
\newline
Answer:
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What is the value of the expression below when
w
=
4
w=4
w
=
4
?
\newline
7
w
2
−
7
w
−
3
7 w^{2}-7 w-3
7
w
2
−
7
w
−
3
\newline
Answer:
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What is the value of the expression below when
z
=
3
z=3
z
=
3
?
\newline
6
z
2
−
5
z
+
3
6 z^{2}-5 z+3
6
z
2
−
5
z
+
3
\newline
Answer:
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85
85
85
. Prove the identity.
\newline
cot
2
x
=
1
−
tan
2
x
2
tan
x
\cot 2 x=\frac{1-\tan ^{2} x}{2 \tan x}
cot
2
x
=
2
tan
x
1
−
tan
2
x
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Evaluate the following expression:
\newline
x
3
+
4
x
2
+
4
x
+
2
−
x
=
2
\sqrt{x^{3}+4x^{2}+4x+2}-x=2
x
3
+
4
x
2
+
4
x
+
2
−
x
=
2
.
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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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Find the positive solution of the equation.
\newline
4
x
4
3
−
12
=
26232
4 x^{\frac{4}{3}}-12=26232
4
x
3
4
−
12
=
26232
\newline
Answer:
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Find an angle
θ
\theta
θ
coterminal to
−
14
7
∘
-147^{\circ}
−
14
7
∘
, where
0
∘
≤
θ
<
36
0
∘
0^{\circ} \leq \theta<360^{\circ}
0
∘
≤
θ
<
36
0
∘
.
\newline
Answer:
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b
3
×
(
b
4
)
2
=
b
x
b^3 \times (b^4)^2 = b^x
b
3
×
(
b
4
)
2
=
b
x
\newline
x
=
□
x=\square
x
=
□
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For the following quadratic equation, find the discriminant.
\newline
−
3
x
2
+
2
x
−
4
=
x
2
−
6
x
-3 x^{2}+2 x-4=x^{2}-6 x
−
3
x
2
+
2
x
−
4
=
x
2
−
6
x
\newline
Answer:
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1
2
3
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