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Math Problems
Algebra 2
Composition of linear and quadratic functions: find a value
Factor completely:
\newline
21
x
+
18
x
2
−
3
x
3
21 x+18 x^{2}-3 x^{3}
21
x
+
18
x
2
−
3
x
3
\newline
Answer:
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Factor completely:
\newline
x
3
+
3
x
2
−
10
x
x^{3}+3 x^{2}-10 x
x
3
+
3
x
2
−
10
x
\newline
Answer:
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Factor completely.
\newline
1
−
x
6
y
4
1-x^{6} y^{4}
1
−
x
6
y
4
\newline
Answer:
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Solve for
n
n
n
and simplify your answer.
\newline
−
10
=
−
5
6
n
-10=-\frac{5}{6} n
−
10
=
−
6
5
n
\newline
Answer:
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Which equation has the solution
x
=
3
x=3
x
=
3
?
\newline
6
x
+
8
=
26
6 x+8=26
6
x
+
8
=
26
\newline
8
x
−
8
=
88
8 x-8=88
8
x
−
8
=
88
\newline
4
x
+
8
=
−
20
4 x+8=-20
4
x
+
8
=
−
20
\newline
5
x
−
6
=
3
5 x-6=3
5
x
−
6
=
3
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Solve for all values of
b
b
b
in simplest form.
\newline
10
=
∣
7
−
2
b
∣
10=|7-2 b|
10
=
∣7
−
2
b
∣
\newline
Answer:
b
=
b=
b
=
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For the following equation, evaluate
d
y
d
x
\frac{d y}{d x}
d
x
d
y
when
x
=
3
x=3
x
=
3
.
\newline
y
=
−
x
2
−
3
y=-x^{2}-3
y
=
−
x
2
−
3
\newline
Answer:
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For the following equation, evaluate
f
′
(
1
)
f^{\prime}(1)
f
′
(
1
)
.
\newline
f
(
x
)
=
−
3
x
5
+
3
f(x)=-3 x^{5}+3
f
(
x
)
=
−
3
x
5
+
3
\newline
Answer:
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For the following equation, evaluate
f
′
(
5
)
f^{\prime}(5)
f
′
(
5
)
.
\newline
f
(
x
)
=
4
x
2
+
3
x
f(x)=4 x^{2}+3 x
f
(
x
)
=
4
x
2
+
3
x
\newline
Answer:
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For the following equation, evaluate
f
′
(
1
)
f^{\prime}(1)
f
′
(
1
)
.
\newline
f
(
x
)
=
−
2
x
3
+
5
f(x)=-2 x^{3}+5
f
(
x
)
=
−
2
x
3
+
5
\newline
Answer:
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For the following equation, evaluate
f
′
(
2
)
f^{\prime}(2)
f
′
(
2
)
.
\newline
f
(
x
)
=
−
2
x
3
+
2
f(x)=-2 x^{3}+2
f
(
x
)
=
−
2
x
3
+
2
\newline
Answer:
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For the following equation, find
f
′
(
x
)
f^{\prime}(x)
f
′
(
x
)
.
\newline
f
(
x
)
=
−
2
x
2
+
6
x
+
3
f(x)=-2 x^{2}+6 x+3
f
(
x
)
=
−
2
x
2
+
6
x
+
3
\newline
Answer:
f
′
(
x
)
=
f^{\prime}(x)=
f
′
(
x
)
=
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Which expression is equivalent to
\newline
16.8
−
18.6
16.8-18.6
16.8
−
18.6
?
\newline
Choose
1
1
1
answer:
\newline
(A)
18.6
−
16.8
18.6-16.8
18.6
−
16.8
\newline
(B)
−
18.6
+
(
−
16.8
)
-18.6+(-16.8)
−
18.6
+
(
−
16.8
)
\newline
(C)
16.8
−
(
−
18.6
)
16.8-(-18.6)
16.8
−
(
−
18.6
)
\newline
(D)
16.8
+
(
−
18.6
)
16.8+(-18.6)
16.8
+
(
−
18.6
)
Get tutor help
Which expression is equivalent to
16.8
−
18.6
16.8-18.6
16.8
−
18.6
?
\newline
Choose
1
1
1
answer:
\newline
(A)
18.6
−
16.8
18.6-16.8
18.6
−
16.8
\newline
(B)
−
18.6
+
(
−
16.8
)
-18.6+(-16.8)
−
18.6
+
(
−
16.8
)
\newline
(C)
16.8
−
(
−
18.6
)
16.8-(-18.6)
16.8
−
(
−
18.6
)
\newline
(D)
16.8
+
(
−
18.6
)
16.8+(-18.6)
16.8
+
(
−
18.6
)
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Find
X
X
X
and the given problem is
x
2
=
7
2
+
2
4
2
x^2 = 7^2 + 24^2
x
2
=
7
2
+
2
4
2
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D
=
[
2
3
4
]
and
A
=
[
−
2
−
2
]
\mathrm{D}=\left[\begin{array}{l} 2 \\ 3 \\ 4 \end{array}\right] \text { and } \mathrm{A}=\left[\begin{array}{ll} -2 & -2 \end{array}\right]
D
=
⎣
⎡
2
3
4
⎦
⎤
and
A
=
[
−
2
−
2
]
\newline
Let
H
=
D
A
\mathrm{H}=\mathrm{DA}
H
=
DA
. Find
H
\mathrm{H}
H
.
\newline
H
=
\mathbf{H}=
H
=
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Evaluate
−
1
−
(
−
z
)
-1-(-z)
−
1
−
(
−
z
)
where
z
=
−
2
z=-2
z
=
−
2
.
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lim
x
→
3
x
3
−
9
x
x
2
−
3
x
=
\lim _{x \rightarrow 3} \frac{x^{3}-9 x}{x^{2}-3 x}=
lim
x
→
3
x
2
−
3
x
x
3
−
9
x
=
Get tutor help
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}+c x^{2}-4 x+3
p
(
x
)
=
−
x
3
+
c
x
2
−
4
x
+
3
\newline
c
=
c=
c
=
Get tutor help
Find the value of
c
c
c
so that
(
x
−
2
)
(x-2)
(
x
−
2
)
is a factor of the polynomial
p
(
x
)
p(x)
p
(
x
)
.
\newline
p
(
x
)
=
x
3
−
4
x
2
+
3
x
+
c
p(x)=x^{3}-4 x^{2}+3 x+c
p
(
x
)
=
x
3
−
4
x
2
+
3
x
+
c
\newline
c
=
c=
c
=
Get tutor help
Find the value of
c
c
c
so that
(
x
+
3
)
(x+3)
(
x
+
3
)
is a factor of the polynomial
p
(
x
)
p(x)
p
(
x
)
.
\newline
p
(
x
)
=
x
3
−
4
x
2
+
c
x
+
33
p(x)=x^{3}-4 x^{2}+c x+33
p
(
x
)
=
x
3
−
4
x
2
+
c
x
+
33
\newline
c
=
c=
c
=
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P
(
x
)
=
2
x
4
−
x
3
+
2
x
2
−
6
P(x)=2 x^{4}-x^{3}+2 x^{2}-6
P
(
x
)
=
2
x
4
−
x
3
+
2
x
2
−
6
\newline
What is the remainder when
P
(
x
)
P(x)
P
(
x
)
is divided by
(
x
−
2
)
(x-2)
(
x
−
2
)
?
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P
(
x
)
=
x
4
−
2
x
3
−
3
x
2
+
4
P(x)=x^{4}-2 x^{3}-3 x^{2}+4
P
(
x
)
=
x
4
−
2
x
3
−
3
x
2
+
4
\newline
What is the remainder when
P
(
x
)
P(x)
P
(
x
)
is divided by
(
x
−
3
)
(x-3)
(
x
−
3
)
?
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P
(
x
)
=
3
x
4
−
2
x
3
+
2
x
2
−
1
P(x)=3 x^{4}-2 x^{3}+2 x^{2}-1
P
(
x
)
=
3
x
4
−
2
x
3
+
2
x
2
−
1
\newline
What is the remainder when
P
(
x
)
P(x)
P
(
x
)
is divided by
(
x
+
1
)
(x+1)
(
x
+
1
)
?
Get tutor help
Find the value of
c
c
c
so that the polynomial
p
(
x
)
p(x)
p
(
x
)
is divisible by
(
x
−
4
)
(x-4)
(
x
−
4
)
.
\newline
p
(
x
)
=
c
x
3
−
15
x
−
68
p(x)=c x^{3}-15 x-68
p
(
x
)
=
c
x
3
−
15
x
−
68
\newline
c
=
c=
c
=
Get tutor help
Find the value of
c
c
c
so that the polynomial
p
(
x
)
p(x)
p
(
x
)
is divisible by
(
x
+
2
)
(x+2)
(
x
+
2
)
.
\newline
p
(
x
)
=
4
x
3
+
c
x
2
+
x
+
2
p(x)=4 x^{3}+c x^{2}+x+2
p
(
x
)
=
4
x
3
+
c
x
2
+
x
+
2
\newline
c
=
c=
c
=
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What is the value of
A
A
A
when we rewrite
4
x
+
3
−
4
x
4^{x+3}-4^{x}
4
x
+
3
−
4
x
as
A
⋅
4
x
A \cdot 4^{x}
A
⋅
4
x
?
\newline
A
=
A=
A
=
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Solve the exponential equation for
x
x
x
.
\newline
12
5
−
x
−
7
⋅
5
6
x
−
12
=
12
5
2
x
+
3
125^{-x-7} \cdot 5^{6 x-12}=125^{2 x+3}
12
5
−
x
−
7
⋅
5
6
x
−
12
=
12
5
2
x
+
3
\newline
x
=
x=
x
=
Get tutor help
Solve the exponential equation for
x
x
x
.
\newline
4
9
−
x
−
7
⋅
7
4
x
+
8
=
4
9
5
x
−
3
49^{-x-7} \cdot 7^{4 x+8}=49^{5 x-3}
4
9
−
x
−
7
⋅
7
4
x
+
8
=
4
9
5
x
−
3
\newline
x
=
x=
x
=
Get tutor help
lim
x
→
2
(
x
3
−
5
x
2
+
1
)
=
\lim _{x \rightarrow 2}\left(x^{3}-5 x^{2}+1\right)=
lim
x
→
2
(
x
3
−
5
x
2
+
1
)
=
Get tutor help
Find the sum.
\newline
∑
k
=
1
50
(
5
k
−
161
)
=
\sum_{k=1}^{50}(5 k-161)=
k
=
1
∑
50
(
5
k
−
161
)
=
Get tutor help
Find the sum.
\newline
∑
k
=
1
50
(
131
−
4
k
)
=
\sum_{k=1}^{50}(131-4 k)=
k
=
1
∑
50
(
131
−
4
k
)
=
Get tutor help
∑
j
=
0
1
(
2
j
−
4
)
=
\sum_{j=0}^{1}(2 j-4)=
∑
j
=
0
1
(
2
j
−
4
)
=
Get tutor help
∑
n
=
1
3
(
n
2
−
1
)
=
\sum_{n=1}^{3}\left(n^{2}-1\right)=
∑
n
=
1
3
(
n
2
−
1
)
=
Get tutor help
∑
x
=
0
2
(
x
+
5
)
=
\sum_{x=0}^{2}(x+5)=
∑
x
=
0
2
(
x
+
5
)
=
Get tutor help
∑
j
=
1
2
(
j
2
+
1
)
=
\sum_{j=1}^{2}\left(j^{2}+1\right)=
∑
j
=
1
2
(
j
2
+
1
)
=
Get tutor help
∑
j
=
1
2
(
5
j
)
=
\sum_{j=1}^{2}(5 j)=
∑
j
=
1
2
(
5
j
)
=
Get tutor help
∑
k
=
0
2
(
2
k
+
2
)
=
\sum_{k=0}^{2}(2 k+2)=
∑
k
=
0
2
(
2
k
+
2
)
=
Get tutor help
4
(
1
−
t
)
=
5
t
2
4(1-t)=5 t^{2}
4
(
1
−
t
)
=
5
t
2
\newline
Let
t
=
x
t=x
t
=
x
and
t
=
y
t=y
t
=
y
be the solutions to the given equation. What is the value of
−
x
y
-x y
−
x
y
?
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ℓ
(
x
)
=
x
4
+
36
x
2
−
10
,
000
\ell(x)=x^{4}+36 x^{2}-10,000
ℓ
(
x
)
=
x
4
+
36
x
2
−
10
,
000
\newline
The polynomial function
ℓ
\ell
ℓ
is defined. What is the remainder of
ℓ
(
x
)
\ell(x)
ℓ
(
x
)
when divided by
x
+
10
x+10
x
+
10
?
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The polynomial function
f
f
f
is defined as
\newline
f
(
c
)
=
(
c
−
k
)
(
c
2
−
4
c
+
4
)
f(c)=(c-k)\left(c^{2}-4 c+4\right)
f
(
c
)
=
(
c
−
k
)
(
c
2
−
4
c
+
4
)
\newline
where
k
k
k
is a constant. The value
2
2
2
is a zero of
f
f
f
. What is the remainder of
f
(
c
)
f(c)
f
(
c
)
when divided by
(
c
−
2
)
(c-2)
(
c
−
2
)
?
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What is the midline equation of the function
\newline
h
(
x
)
=
−
3
cos
(
π
x
+
2
)
−
6
?
h(x)=-3 \cos (\pi x+2)-6 ?
h
(
x
)
=
−
3
cos
(
π
x
+
2
)
−
6
?
\newline
y
=
y=
y
=
Get tutor help
If
u
2
−
u
t
=
6
u^{2}-u t=6
u
2
−
u
t
=
6
and
t
2
−
u
t
=
−
2
t^{2}-u t=-2
t
2
−
u
t
=
−
2
, what is the value of
2
(
u
−
t
)
2
2(u-t)^{2}
2
(
u
−
t
)
2
?
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x
2
+
3
x
−
a
x
−
2
=
x
+
5
\frac{x^{2}+3 x-a}{x-2}=x+5
x
−
2
x
2
+
3
x
−
a
=
x
+
5
\newline
Given the equation for all
x
≠
2
x \neq 2
x
=
2
, what is the value of
a
a
a
?
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If
2
7
x
9
y
=
81
\frac{27^{x}}{9^{y}}=81
9
y
2
7
x
=
81
, what is the value of
3
x
−
2
y
3 x-2 y
3
x
−
2
y
?
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y
=
2
−
3
x
y=2-3 x
y
=
2
−
3
x
\newline
y
=
5
x
2
y=5 x^{2}
y
=
5
x
2
\newline
If
(
x
,
y
)
(x, y)
(
x
,
y
)
is a solution to the system of equations shown and
x
>
0
x>0
x
>
0
, what is the value of
x
x
x
?
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If
x
7
=
9
\frac{x}{7}=9
7
x
=
9
, what is the value of
x
x
x
?
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If
6
=
x
5
6=\frac{x}{5}
6
=
5
x
, what is the value of
x
x
x
?
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If
x
3
=
7
\frac{x}{3}=7
3
x
=
7
, what is the value of
x
x
x
?
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If
x
6
=
3
\frac{x}{6}=3
6
x
=
3
, what is the value of
x
x
x
?
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