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Math Problems
Algebra 2
Evaluate expression when a complex numbers and a variable term is given
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
′
(
−
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, 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, 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
)
=
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
)
=
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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
)
=
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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:
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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.
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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
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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
)
=
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Let
h
(
x
)
=
x
−
11
h(x)=x^{-11}
h
(
x
)
=
x
−
11
.
\newline
h
′
(
x
)
=
h^{\prime}(x)=
h
′
(
x
)
=
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Let
g
(
x
)
=
x
−
12
g(x)=x^{-12}
g
(
x
)
=
x
−
12
.
\newline
g
′
(
x
)
=
g^{\prime}(x)=
g
′
(
x
)
=
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y
′
=
2
x
+
3
y
−
1
y^{\prime}=2 x+3 y-1
y
′
=
2
x
+
3
y
−
1
\newline
Is
y
=
−
2
3
x
+
1
9
y=-\frac{2}{3} x+\frac{1}{9}
y
=
−
3
2
x
+
9
1
a solution to the above equation?
\newline
Choose
1
1
1
answer:
\newline
(A) Yes
\newline
(B) No
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Let
y
=
5
−
3
x
x
2
+
3
x
y=\frac{5-3 x}{x^{2}+3 x}
y
=
x
2
+
3
x
5
−
3
x
.
\newline
d
y
d
x
=
\frac{d y}{d x}=
d
x
d
y
=
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Let
h
(
x
)
=
−
x
3
+
4
h(x)=-x^{3}+4
h
(
x
)
=
−
x
3
+
4
.
\newline
What is the absolute maximum value of
h
h
h
over the closed interval
[
−
2
,
2
]
[-2,2]
[
−
2
,
2
]
?
\newline
Choose
1
1
1
answer:
\newline
(A)
12
\mathbf{1 2}
12
\newline
(B)
4
4
4
\newline
(C)
−
16
-16
−
16
\newline
(D)
16
\mathbf{1 6}
16
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Let
h
(
x
)
=
−
x
3
+
4
h(x)=-x^{3}+4
h
(
x
)
=
−
x
3
+
4
.
\newline
What is the absolute maximum value of
h
h
h
over the closed interval
[
−
2
,
2
]
[-2,2]
[
−
2
,
2
]
?
\newline
Choose
1
1
1
answer:
\newline
(A)
12
\mathbf{1 2}
12
\newline
(B)
16
\mathbf{1 6}
16
\newline
(C)
4
4
4
\newline
(D)
−
16
-16
−
16
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