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Math Problems
Algebra 2
Composition of linear and quadratic functions: find a value
Given
f
(
x
)
=
−
x
2
−
3
x
+
19
f(x)=-x^{2}-3 x+19
f
(
x
)
=
−
x
2
−
3
x
+
19
, find
f
(
−
9
)
f(-9)
f
(
−
9
)
\newline
Answer:
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Given
f
(
x
)
=
−
x
2
+
2
x
f(x)=-x^{2}+2 x
f
(
x
)
=
−
x
2
+
2
x
, find
f
(
−
9
)
f(-9)
f
(
−
9
)
\newline
Answer:
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Given
f
(
x
)
=
−
x
2
+
4
x
+
16
f(x)=-x^{2}+4 x+16
f
(
x
)
=
−
x
2
+
4
x
+
16
, find
f
(
−
9
)
f(-9)
f
(
−
9
)
\newline
Answer:
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Given
f
(
x
)
=
−
x
2
−
3
x
+
20
f(x)=-x^{2}-3 x+20
f
(
x
)
=
−
x
2
−
3
x
+
20
, find
f
(
6
)
f(6)
f
(
6
)
\newline
Answer:
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Factor completely:
\newline
(
5
x
−
1
)
2
(
4
x
+
5
)
+
(
x
+
7
)
(
5
x
−
1
)
(5 x-1)^{2}(4 x+5)+(x+7)(5 x-1)
(
5
x
−
1
)
2
(
4
x
+
5
)
+
(
x
+
7
)
(
5
x
−
1
)
\newline
Answer:
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Factor completely:
\newline
5
c
12
+
4
c
6
s
4
−
9
s
8
5 c^{12}+4 c^{6} s^{4}-9 s^{8}
5
c
12
+
4
c
6
s
4
−
9
s
8
\newline
Answer:
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Factor completely:
\newline
9
u
2
+
21
u
s
3
+
10
s
6
9 u^{2}+21 u s^{3}+10 s^{6}
9
u
2
+
21
u
s
3
+
10
s
6
\newline
Answer:
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Factor completely:
\newline
3
x
2
(
3
x
−
5
)
+
4
(
3
x
−
5
)
3 x^{2}(3 x-5)+4(3 x-5)
3
x
2
(
3
x
−
5
)
+
4
(
3
x
−
5
)
\newline
Answer:
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Factor completely:
\newline
x
2
(
x
+
8
)
−
3
x
(
x
+
8
)
−
10
(
x
+
8
)
x^{2}(x+8)-3 x(x+8)-10(x+8)
x
2
(
x
+
8
)
−
3
x
(
x
+
8
)
−
10
(
x
+
8
)
\newline
Answer:
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Factor completely:
\newline
x
2
(
5
x
2
−
6
)
−
9
x
(
5
x
2
−
6
)
−
10
(
5
x
2
−
6
)
x^{2}\left(5 x^{2}-6\right)-9 x\left(5 x^{2}-6\right)-10\left(5 x^{2}-6\right)
x
2
(
5
x
2
−
6
)
−
9
x
(
5
x
2
−
6
)
−
10
(
5
x
2
−
6
)
\newline
Answer:
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Solve for all values of
x
x
x
:
\newline
4
x
2
(
x
−
10
)
−
(
x
−
10
)
=
0
4 x^{2}(x-10)-(x-10)=0
4
x
2
(
x
−
10
)
−
(
x
−
10
)
=
0
\newline
Answer:
x
=
x=
x
=
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Solve for all values of
x
x
x
:
\newline
(
x
+
3
)
2
−
(
x
+
3
)
=
0
(x+3)^{2}-(x+3)=0
(
x
+
3
)
2
−
(
x
+
3
)
=
0
\newline
Answer:
x
=
x=
x
=
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Solve for all values of
x
x
x
:
\newline
(
3
x
−
2
)
2
+
5
(
3
x
−
2
)
=
0
(3 x-2)^{2}+5(3 x-2)=0
(
3
x
−
2
)
2
+
5
(
3
x
−
2
)
=
0
\newline
Answer:
x
=
x=
x
=
Get tutor help
Factor completely:
\newline
(
8
x
+
3
)
2
+
(
8
x
+
3
)
(8 x+3)^{2}+(8 x+3)
(
8
x
+
3
)
2
+
(
8
x
+
3
)
\newline
Answer:
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Solve for all values of
x
x
x
:
\newline
(
x
−
5
)
2
+
(
x
−
5
)
=
0
(x-5)^{2}+(x-5)=0
(
x
−
5
)
2
+
(
x
−
5
)
=
0
\newline
Answer:
x
=
x=
x
=
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Solve for all values of
x
x
x
:
\newline
x
2
(
x
+
8
)
+
4
x
(
x
+
8
)
+
3
(
x
+
8
)
=
0
x^{2}(x+8)+4 x(x+8)+3(x+8)=0
x
2
(
x
+
8
)
+
4
x
(
x
+
8
)
+
3
(
x
+
8
)
=
0
\newline
Answer:
x
=
x=
x
=
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Solve for all values of
x
x
x
:
\newline
3
(
2
x
+
9
)
+
(
2
x
+
9
)
2
=
0
3(2 x+9)+(2 x+9)^{2}=0
3
(
2
x
+
9
)
+
(
2
x
+
9
)
2
=
0
\newline
Answer:
x
=
x=
x
=
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Solve for all values of
x
x
x
:
\newline
(
9
x
−
2
)
−
(
9
x
−
2
)
2
=
0
(9 x-2)-(9 x-2)^{2}=0
(
9
x
−
2
)
−
(
9
x
−
2
)
2
=
0
\newline
Answer:
x
=
x=
x
=
Get tutor help
Solve for all values of
x
x
x
:
\newline
(
4
x
+
9
)
2
+
(
4
x
+
9
)
=
0
(4 x+9)^{2}+(4 x+9)=0
(
4
x
+
9
)
2
+
(
4
x
+
9
)
=
0
\newline
Answer:
x
=
x=
x
=
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The sum of a number and
15
15
15
is
−
23
-23
−
23
. Find the number. (Simplify your answer.)
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Li Juan solves the equation below by first squaring both sides of the equation.
3
−
2
w
=
w
+
6
\sqrt{3-2w}=w+6
3
−
2
w
=
w
+
6
What extraneous solution does Li Juan obtain?
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evaluate
9
−
8
s
9 - \frac{8}{s}
9
−
s
8
when
S
=
4
S=4
S
=
4
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If
4
x
+
5
=
13
x
+
4
−
x
−
9
4x + 5 = 13x + 4 - x - 9
4
x
+
5
=
13
x
+
4
−
x
−
9
, then
x
=
?
x = ?
x
=
?
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If
a
1
=
1
a_{1}=1
a
1
=
1
and
a
n
=
(
a
n
−
1
)
2
+
3
a_{n}=\left(a_{n-1}\right)^{2}+3
a
n
=
(
a
n
−
1
)
2
+
3
then find the value of
a
3
a_{3}
a
3
.
\newline
Answer:
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If
a
1
=
4
a_{1}=4
a
1
=
4
and
a
n
=
(
a
n
−
1
)
2
+
2
a_{n}=\left(a_{n-1}\right)^{2}+2
a
n
=
(
a
n
−
1
)
2
+
2
then find the value of
a
3
a_{3}
a
3
.
\newline
Answer:
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If
a
1
=
4
a_{1}=4
a
1
=
4
and
a
n
=
(
a
n
−
1
)
2
+
3
a_{n}=\left(a_{n-1}\right)^{2}+3
a
n
=
(
a
n
−
1
)
2
+
3
then find the value of
a
3
a_{3}
a
3
.
\newline
Answer:
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Determine the value of
y
y
y
, if
x
x
x
is
−
8
-8
−
8
.
\newline
y
=
x
2
+
8
y=x^{2}+8
y
=
x
2
+
8
\newline
Answer:
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Find the missing factor that makes the equality true.
21
y
4
=
(
B
)
(
7
y
3
)
21y^4 = (B)(7y^3)
21
y
4
=
(
B
)
(
7
y
3
)
B
=
B =
B
=
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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
)
=
Get tutor help
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
Get tutor help
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
=
Get tutor help
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
=
Get tutor help
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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