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Math Problems
Algebra 2
Composition of linear and quadratic functions: find a value
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
)
?
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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
−
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
=
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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
+
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
=
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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
=
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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
)
=
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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
)
=
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∑
j
=
0
1
(
2
j
−
4
)
=
\sum_{j=0}^{1}(2 j-4)=
∑
j
=
0
1
(
2
j
−
4
)
=
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∑
n
=
1
3
(
n
2
−
1
)
=
\sum_{n=1}^{3}\left(n^{2}-1\right)=
∑
n
=
1
3
(
n
2
−
1
)
=
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∑
x
=
0
2
(
x
+
5
)
=
\sum_{x=0}^{2}(x+5)=
∑
x
=
0
2
(
x
+
5
)
=
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∑
j
=
1
2
(
j
2
+
1
)
=
\sum_{j=1}^{2}\left(j^{2}+1\right)=
∑
j
=
1
2
(
j
2
+
1
)
=
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∑
j
=
1
2
(
5
j
)
=
\sum_{j=1}^{2}(5 j)=
∑
j
=
1
2
(
5
j
)
=
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∑
k
=
0
2
(
2
k
+
2
)
=
\sum_{k=0}^{2}(2 k+2)=
∑
k
=
0
2
(
2
k
+
2
)
=
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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
=
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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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If
x
5
=
3
\frac{x}{5}=3
5
x
=
3
, what is the value of
x
x
x
?
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If
x
2
=
6
\frac{x}{2}=6
2
x
=
6
, what is the value of
x
?
x ?
x
?
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If
14
y
2
−
21
x
=
a
(
2
y
2
−
3
x
)
14 y^{2}-21 x=a\left(2 y^{2}-3 x\right)
14
y
2
−
21
x
=
a
(
2
y
2
−
3
x
)
, where
a
a
a
is a constant, what is the value of
a
a
a
?
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What is the value of
x
3
⋅
y
1
x^{3} \cdot y^{1}
x
3
⋅
y
1
when
y
=
10
y=10
y
=
10
and
x
=
2
x=2
x
=
2
?
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What is the value of
x
2
y
1
\frac{x^{2}}{y^{1}}
y
1
x
2
when
y
=
5
y=5
y
=
5
and
x
=
10
x=10
x
=
10
?
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What is the value of
x
3
⋅
y
4
x^{3} \cdot y^{4}
x
3
⋅
y
4
when
x
=
3
x=3
x
=
3
and
y
=
0
y=0
y
=
0
?
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Solve for
h
h
h
.
\newline
h
2
−
9
h
=
0
h^2 - 9h = 0
h
2
−
9
h
=
0
\newline
Write each solution as an integer, proper fraction, or improper fraction in simplest form. If there are multiple solutions, separate them with commas.
\newline
h
=
h =
h
=
_____
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Find
(
f
∘
g
)
(
0
)
(f \circ g)(0)
(
f
∘
g
)
(
0
)
.
\newline
f
(
x
)
=
6
x
f(x) = 6x
f
(
x
)
=
6
x
\newline
g
(
x
)
=
x
2
+
4
x
g(x) = x^2 + 4x
g
(
x
)
=
x
2
+
4
x
\newline
(
f
∘
g
)
(
0
)
=
(f \circ g)(0) =
(
f
∘
g
)
(
0
)
=
____
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