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Math Problems
Algebra 2
Evaluate expression when a complex numbers and a variable term is given
\large{-n + (
−
3
-3
−
3
) +
3
3
3
n +
5
5
5
}
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Select the expressions that are equivalent to
9
a
+
3
a
9a + 3a
9
a
+
3
a
.
\newline
Multi-select Choices:
\newline
(A)
4
a
+
9
a
4a + 9a
4
a
+
9
a
\newline
(B)
12
a
12a
12
a
\newline
(C)
a
12
a^{12}
a
12
\newline
(D)
a
+
12
a
a + 12a
a
+
12
a
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1
1
1
. Let
a
,
b
>
0
a, b>0
a
,
b
>
0
satisfy
a
3
+
b
3
=
a
−
b
a^{3}+b^{3}=a-b
a
3
+
b
3
=
a
−
b
, then
\newline
(a)
a
2
+
b
2
=
1
a^{2}+b^{2}=1
a
2
+
b
2
=
1
\newline
(b)
a
2
+
a
b
+
b
2
<
1
a^{2}+a b+b^{2}<1
a
2
+
ab
+
b
2
<
1
\newline
(c)
a
2
+
b
2
>
1
a^{2}+b^{2}>1
a
2
+
b
2
>
1
\newline
(d) none of these
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Let
u
=
(
5
,
−
12
)
u=(5,-12)
u
=
(
5
,
−
12
)
and
c
=
−
3
c=-3
c
=
−
3
. What is
∣
∣
c
u
∣
∣
||cu||
∣∣
c
u
∣∣
?
\newline
a)
51
51
51
\newline
b)
−
39
-39
−
39
\newline
c)
21
21
21
\newline
d)
39
39
39
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Which expression is equivalent to
3
m
+
9
m
3m + 9m
3
m
+
9
m
?
\newline
Choices:
\newline
(A)
11
m
11m
11
m
\newline
(B)
m
+
12
m + 12
m
+
12
\newline
(C)
m
12
m^{12}
m
12
\newline
(D)
12
m
12m
12
m
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If
5
2
x
−
1
−
100
=
2
5
x
−
1
5^{2x-1}-100=25^{x-1}
5
2
x
−
1
−
100
=
2
5
x
−
1
, then the value of
6
x
6^{x}
6
x
.
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If
x
=
x =
x
=
6
3
\frac{6}{3}
3
6
,
y
=
y =
y
=
−
1
5
\frac{-1}{5}
5
−
1
\newline
Find:
(
x
−
y
)
(x-y)
(
x
−
y
)
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If
x
=
2
y
x=2y
x
=
2
y
, then which of the following is equivalent to
2
y
+
2
2y+2
2
y
+
2
?
?
?
\newline
A)
x
2
+
2
\frac{x}{2}+2
2
x
+
2
\newline
B)
x
+
2
x+2
x
+
2
\newline
C)
2
x
+
2
2x+2
2
x
+
2
\newline
D)
4
x
+
2
4x+2
4
x
+
2
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6
6
6
Consider the points
P
(
4
,
7
)
,
Q
(
8
,
4
)
,
R
(
7
,
0
)
\mathrm{P}(4,7), \mathrm{Q}(8,4), \mathrm{R}(7,0)
P
(
4
,
7
)
,
Q
(
8
,
4
)
,
R
(
7
,
0
)
, and
S
(
−
1
,
t
)
\mathrm{S}(-1, t)
S
(
−
1
,
t
)
. Find
t
t
t
given that
P
Q
∥
S
R
\mathrm{PQ} \| \mathrm{SR}
PQ
∥
SR
.
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If
A
=
[
2
−
3
−
4
1
]
A=\left[\begin{array}{cc}2 & -3 \ -4 & 1\end{array}\right]
A
=
[
2
−
3
−
4
1
]
, then
adj
(
3
A
2
+
12
A
)
\text{adj}(3A^{2}+12 A)
adj
(
3
A
2
+
12
A
)
is equal to
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Given the definitions of
f
(
x
)
f(x)
f
(
x
)
and
g
(
x
)
g(x)
g
(
x
)
below, find the value of
g
(
f
(
2
)
)
g(f(2))
g
(
f
(
2
))
.
\newline
f
(
x
)
=
3
x
2
−
6
x
−
9
g
(
x
)
=
5
x
−
8
\begin{array}{l} f(x)=3 x^{2}-6 x-9 \\ g(x)=5 x-8 \end{array}
f
(
x
)
=
3
x
2
−
6
x
−
9
g
(
x
)
=
5
x
−
8
\newline
Answer:
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If
P
(
B
)
=
0.55
,
P
(
A
∣
B
)
=
0.80
,
P
(
B
′
)
=
0.45
P(B)=0.55, P(A \mid B)=0.80, P\left(B^{\prime}\right)=0.45
P
(
B
)
=
0.55
,
P
(
A
∣
B
)
=
0.80
,
P
(
B
′
)
=
0.45
, and
P
(
A
∣
B
′
)
=
0.40
P\left(A \mid B^{\prime}\right)=0.40
P
(
A
∣
B
′
)
=
0.40
, find
P
(
B
∣
A
)
P(B \mid A)
P
(
B
∣
A
)
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Given the functions
f
(
x
)
=
5
x
+
3
f(x)=5 x+3
f
(
x
)
=
5
x
+
3
and
g
(
x
)
=
x
2
−
7
g(x)=x^{2}-7
g
(
x
)
=
x
2
−
7
, what is
f
(
g
(
−
3
)
)
?
f(g(-3)) ?
f
(
g
(
−
3
))?
\newline
A.
−
77
-77
−
77
\newline
B.
−
12
-12
−
12
\newline
C.
3
3
3
\newline
D.
13
13
13
\newline
E.
137
137
137
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Given that
1
+
2
i
1+2i
1
+
2
i
is a zero of
k
(
x
)
=
x
4
−
6
x
3
+
26
x
2
−
46
x
+
65
k(x)=x^{4}-6x^{3}+26x^{2}-46x+65
k
(
x
)
=
x
4
−
6
x
3
+
26
x
2
−
46
x
+
65
, find the remaining zeroes
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If
3
x
2
−
18
x
−
15
=
0
3x^{2}-18x-15=0
3
x
2
−
18
x
−
15
=
0
, what is the value of
x
2
−
6
x
x^{2}-6x
x
2
−
6
x
?
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If
f
(
1
)
=
1
f(1)=1
f
(
1
)
=
1
and
f
(
n
)
=
f
(
n
−
1
)
2
+
n
f(n)=f(n-1)^{2}+n
f
(
n
)
=
f
(
n
−
1
)
2
+
n
then find the value of
f
(
4
)
f(4)
f
(
4
)
.
\newline
Answer:
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Given that
f
(
x
)
=
x
−
5
,
g
(
x
)
=
−
5
x
f(x)=x-5, \quad g(x)=-5 x
f
(
x
)
=
x
−
5
,
g
(
x
)
=
−
5
x
and
h
(
x
)
=
−
3
f
(
x
)
+
3
g
(
x
+
2
)
h(x)=-3 f(x)+3 g(x+2)
h
(
x
)
=
−
3
f
(
x
)
+
3
g
(
x
+
2
)
, then what is the value of
h
(
6
)
h(6)
h
(
6
)
?
\newline
Answer:
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If
f
(
1
)
=
4
f(1)=4
f
(
1
)
=
4
and
f
(
n
)
=
f
(
n
−
1
)
2
+
n
f(n)=f(n-1)^{2}+n
f
(
n
)
=
f
(
n
−
1
)
2
+
n
then find the value of
f
(
4
)
f(4)
f
(
4
)
.
\newline
Answer:
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If
f
(
1
)
=
2
f(1)=2
f
(
1
)
=
2
and
f
(
n
)
=
f
(
n
−
1
)
2
+
n
f(n)=f(n-1)^{2}+n
f
(
n
)
=
f
(
n
−
1
)
2
+
n
then find the value of
f
(
4
)
f(4)
f
(
4
)
.
\newline
Answer:
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If
f
(
1
)
=
1
f(1)=1
f
(
1
)
=
1
and
f
(
n
)
=
f
(
n
−
1
)
2
+
n
f(n)=f(n-1)^{2}+n
f
(
n
)
=
f
(
n
−
1
)
2
+
n
then find the value of
f
(
3
)
f(3)
f
(
3
)
.
\newline
Answer:
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Simplify the following expression completely.
\newline
x
2
+
5
x
−
50
x
2
+
6
x
−
40
\frac{x^{2}+5 x-50}{x^{2}+6 x-40}
x
2
+
6
x
−
40
x
2
+
5
x
−
50
\newline
Answer:
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Given
f
(
x
)
=
−
2
x
2
+
9
x
f(x)=-2 x^{2}+9 x
f
(
x
)
=
−
2
x
2
+
9
x
, find
f
(
−
4
)
f(-4)
f
(
−
4
)
\newline
Answer:
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Given
f
(
x
)
=
−
3
x
2
+
16
f(x)=-3 x^{2}+16
f
(
x
)
=
−
3
x
2
+
16
, find
f
(
−
1
)
f(-1)
f
(
−
1
)
\newline
Answer:
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Given
f
(
x
)
=
−
x
2
+
5
x
−
6
f(x)=-x^{2}+5 x-6
f
(
x
)
=
−
x
2
+
5
x
−
6
, find
f
(
−
9
)
f(-9)
f
(
−
9
)
\newline
Answer:
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Given
f
(
x
)
=
4
x
2
+
10
x
f(x)=4 x^{2}+10 x
f
(
x
)
=
4
x
2
+
10
x
, find
f
(
−
4
)
f(-4)
f
(
−
4
)
\newline
Answer:
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Given
f
(
x
)
=
−
x
2
−
10
x
−
15
f(x)=-x^{2}-10 x-15
f
(
x
)
=
−
x
2
−
10
x
−
15
, find
f
(
2
)
f(2)
f
(
2
)
\newline
Answer:
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Given
f
(
x
)
=
2
x
2
−
7
x
−
18
f(x)=2 x^{2}-7 x-18
f
(
x
)
=
2
x
2
−
7
x
−
18
, find
f
(
−
1
)
f(-1)
f
(
−
1
)
\newline
Answer:
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Given
f
(
x
)
=
2
x
2
+
7
x
+
1
f(x)=2 x^{2}+7 x+1
f
(
x
)
=
2
x
2
+
7
x
+
1
, find
f
(
−
5
)
f(-5)
f
(
−
5
)
\newline
Answer:
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If
f
(
1
)
=
1
f(1)=1
f
(
1
)
=
1
and
f
(
n
)
=
f
(
n
−
1
)
2
+
3
f(n)=f(n-1)^{2}+3
f
(
n
)
=
f
(
n
−
1
)
2
+
3
then find the value of
f
(
3
)
f(3)
f
(
3
)
.
\newline
Answer:
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If
f
(
1
)
=
2
f(1)=2
f
(
1
)
=
2
and
f
(
n
)
=
f
(
n
−
1
)
2
+
1
f(n)=f(n-1)^{2}+1
f
(
n
)
=
f
(
n
−
1
)
2
+
1
then find the value of
f
(
4
)
f(4)
f
(
4
)
.
\newline
Answer:
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If
f
(
x
)
=
3
x
−
1
f(x)=3x-1
f
(
x
)
=
3
x
−
1
and
g
(
x
)
=
x
2
+
1
g(x)=x^{2}+1
g
(
x
)
=
x
2
+
1
, what is the value of
g
(
f
(
3
)
)
g(f(3))
g
(
f
(
3
))
?
\newline
Choose
1
1
1
answer:
\newline
(A)
8
8
8
\newline
(B)
10
10
10
\newline
(C)
29
29
29
\newline
(D)
65
65
65
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If
a
1
=
2
a_{1}=2
a
1
=
2
and
a
n
=
(
a
n
−
1
)
2
+
n
a_{n}=\left(a_{n-1}\right)^{2}+n
a
n
=
(
a
n
−
1
)
2
+
n
then find the value of
a
4
a_{4}
a
4
.
\newline
Answer:
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If
a
1
=
4
a_{1}=4
a
1
=
4
and
a
n
=
(
a
n
−
1
)
2
+
n
a_{n}=\left(a_{n-1}\right)^{2}+n
a
n
=
(
a
n
−
1
)
2
+
n
then find the value of
a
4
a_{4}
a
4
.
\newline
Answer:
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If
a
1
=
3
a_{1}=3
a
1
=
3
and
a
n
+
1
=
(
a
n
)
2
+
2
a_{n+1}=\left(a_{n}\right)^{2}+2
a
n
+
1
=
(
a
n
)
2
+
2
then find the value of
a
4
a_{4}
a
4
.
\newline
Answer:
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If
a
1
=
2
a_{1}=2
a
1
=
2
and
a
n
+
1
=
(
a
n
)
2
+
2
a_{n+1}=\left(a_{n}\right)^{2}+2
a
n
+
1
=
(
a
n
)
2
+
2
then find the value of
a
4
a_{4}
a
4
.
\newline
Answer:
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If
(
x
−
5
a
)
(
x
+
5
a
)
(x-5 \sqrt{a})(x+5 \sqrt{a})
(
x
−
5
a
)
(
x
+
5
a
)
is equivalent to
x
2
−
375
x^{2}-375
x
2
−
375
, what must be the value of
a
a
a
?
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Given the function
\newline
y
=
3
−
x
4
1
−
2
x
4
,
y=\frac{3-x^{4}}{1-2x^{4}},
y
=
1
−
2
x
4
3
−
x
4
,
find
\newline
d
y
d
x
\frac{dy}{dx}
d
x
d
y
in simplified form.
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If
7
x
−
8
y
=
−
10
\mathbf{7 x}-\mathbf{8 y}=-\mathbf{1 0}
7x
−
8y
=
−
10
and
10
x
+
4
y
=
6
\mathbf{1 0 x}+\mathbf{4 y}=\mathbf{6}
10x
+
4y
=
6
are true equations, what would be the value of
17
x
−
4
y
17 x-4 y
17
x
−
4
y
?
\newline
Answer:
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y
=
6
x
−
30
y
=
x
2
−
18
x
+
114
\begin{align*} y &= 6x-30 \\ y &= x^{2}-18x+114 \end{align*}
y
y
=
6
x
−
30
=
x
2
−
18
x
+
114
\newline
If
(
a
,
b
)
(a,b)
(
a
,
b
)
is the solution to the system of equations shown, what is the value of
b
b
b
?
\newline
□
\square
□
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For the following equation, evaluate
f
′
(
2
)
f^{\prime}(2)
f
′
(
2
)
.
\newline
f
(
x
)
=
−
x
4
+
5
x
f(x)=-x^{4}+5 x
f
(
x
)
=
−
x
4
+
5
x
\newline
Answer:
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For the following equation, evaluate
f
′
(
−
3
)
f^{\prime}(-3)
f
′
(
−
3
)
.
\newline
f
(
x
)
=
−
3
x
2
+
4
x
f(x)=-3 x^{2}+4 x
f
(
x
)
=
−
3
x
2
+
4
x
\newline
Answer:
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For the following equation, evaluate
f
′
(
1
)
f^{\prime}(1)
f
′
(
1
)
.
\newline
f
(
x
)
=
−
4
x
5
+
4
x
f(x)=-4 x^{5}+4 x
f
(
x
)
=
−
4
x
5
+
4
x
\newline
Answer:
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For the following equation, find
d
y
d
x
\frac{d y}{d x}
d
x
d
y
.
\newline
y
=
−
5
x
3
+
7
x
+
6
y=-5 x^{3}+7 x+6
y
=
−
5
x
3
+
7
x
+
6
\newline
Answer:
d
y
d
x
=
\frac{d y}{d x}=
d
x
d
y
=
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For the following equation, find
f
′
(
x
)
f^{\prime}(x)
f
′
(
x
)
.
\newline
f
(
x
)
=
−
4
x
4
−
8
f(x)=-4 x^{4}-8
f
(
x
)
=
−
4
x
4
−
8
\newline
Answer:
f
′
(
x
)
=
f^{\prime}(x)=
f
′
(
x
)
=
Get tutor help
For the following equation, find
f
′
(
x
)
f^{\prime}(x)
f
′
(
x
)
.
\newline
f
(
x
)
=
8
x
3
+
5
x
+
4
f(x)=8 x^{3}+5 x+4
f
(
x
)
=
8
x
3
+
5
x
+
4
\newline
Answer:
f
′
(
x
)
=
f^{\prime}(x)=
f
′
(
x
)
=
Get tutor help
Given that
w
=
y
3
+
5
w=y^{3}+5
w
=
y
3
+
5
, find
d
d
y
(
5
w
4
+
4
cos
y
)
\frac{d}{d y}\left(5 w^{4}+4 \cos y\right)
d
y
d
(
5
w
4
+
4
cos
y
)
in terms of only
y
y
y
.
\newline
Answer:
Get tutor help
If
a
=
2
a=2
a
=
2
and
b
=
2
i
b=2i
b
=
2
i
, then find the value of the
a
b
3
ab^{3}
a
b
3
in fully simplified form.
Get tutor help
If
x
=
2
3
y
x=\frac{2}{3}y
x
=
3
2
y
and
y
=
18
y=18
y
=
18
, what is the value of
2
x
−
3
2x-3
2
x
−
3
?
\newline
A)
21
21
21
\newline
B)
15
15
15
\newline
C)
12
12
12
\newline
D)
10
10
10
Get tutor help
Given the function
f
(
x
)
=
2
−
x
3
2
+
5
x
3
f(x)=\frac{2-x^{3}}{2+5 x^{3}}
f
(
x
)
=
2
+
5
x
3
2
−
x
3
, find
f
′
(
x
)
f^{\prime}(x)
f
′
(
x
)
in simplified form.
\newline
Answer:
f
′
(
x
)
=
f^{\prime}(x)=
f
′
(
x
)
=
Get tutor help
Let
h
(
x
)
=
x
−
11
h(x)=x^{-11}
h
(
x
)
=
x
−
11
.
\newline
h
′
(
x
)
=
h^{\prime}(x)=
h
′
(
x
)
=
Get tutor help
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