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Math Problems
Algebra 2
Evaluate exponential functions
Rewrite the expression in the form
y
n
y^{n}
y
n
.
\newline
y
5
4
y
1
4
=
\frac{y^{\frac{5}{4}}}{y^{\frac{1}{4}}}=
y
4
1
y
4
5
=
Get tutor help
Rewrite the expression in the form
a
n
a^{n}
a
n
.
\newline
a
5
a
5
2
=
□
−
+
x
\frac{a^{5}}{a^{\frac{5}{2}}}=\square^{-+x}
a
2
5
a
5
=
□
−+
x
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Rewrite the expression in the form
y
n
y^{n}
y
n
.
\newline
y
3
4
⋅
y
1
3
=
y^{\frac{3}{4}} \cdot y^{\frac{1}{3}}=
y
4
3
⋅
y
3
1
=
Get tutor help
Rewrite the expression in the form
b
n
b^{n}
b
n
.
\newline
b
4
⋅
b
−
1
4
=
b^{4} \cdot b^{-\frac{1}{4}}=
b
4
⋅
b
−
4
1
=
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Rewrite the expression in the form
z
n
z^{n}
z
n
.
\newline
z
3
4
⋅
z
2
=
z^{\frac{3}{4}} \cdot z^{2}=
z
4
3
⋅
z
2
=
Get tutor help
Rewrite the expression in the form
x
n
x^{n}
x
n
.
\newline
(
x
2
3
)
5
2
=
□
\left(x^{\frac{2}{3}}\right)^{\frac{5}{2}}=\square
(
x
3
2
)
2
5
=
□
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Rewrite the expression in the form
a
n
a^{n}
a
n
.
\newline
(
a
2
3
)
−
1
=
□
\left(a^{\frac{2}{3}}\right)^{-1}=\square
(
a
3
2
)
−
1
=
□
Get tutor help
Solve the exponential equation for
x
x
x
.
\newline
6
4
7
x
−
8
=
1
x
=
\begin{array}{l} 64^{7 x-8}=1 \\ x= \end{array}
6
4
7
x
−
8
=
1
x
=
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Solve the exponential equation for
x
x
x
.
\newline
(
9
8
)
3
x
+
12
=
1
x
=
□
\begin{array}{l} \left(\frac{9}{8}\right)^{3 x+12}=1 \\ x=\square \end{array}
(
8
9
)
3
x
+
12
=
1
x
=
□
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Solve the exponential equation for
x
x
x
.
\newline
3
2
x
5
=
(
1
16
)
4
x
−
3
x
=
□
\begin{array}{l} 32^{\frac{x}{5}}=\left(\frac{1}{16}\right)^{4 x-3} \\ x=\square \end{array}
3
2
5
x
=
(
16
1
)
4
x
−
3
x
=
□
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Find
lim
x
→
−
3
g
(
x
)
\lim _{x \rightarrow-3} g(x)
lim
x
→
−
3
g
(
x
)
for
\newline
g
(
x
)
=
x
2
−
x
−
1
.
g(x)=x^{2}-x-1 \text {. }
g
(
x
)
=
x
2
−
x
−
1
.
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Find
lim
x
→
−
5
(
x
+
1
)
2
8
−
x
\lim _{x \rightarrow-5} \frac{(x+1)^{2}}{8-x}
lim
x
→
−
5
8
−
x
(
x
+
1
)
2
.
\newline
Choose
1
1
1
answer:
\newline
(A)
16
13
\frac{16}{13}
13
16
\newline
(B)
2
2
2
\newline
(C)
12
12
12
\newline
(D) The limit doesn't exist
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Find
lim
x
→
3
f
(
x
)
\lim _{x \rightarrow 3} f(x)
lim
x
→
3
f
(
x
)
for
\newline
f
(
x
)
=
x
2
−
4
11
−
2
x
.
f(x)=\frac{x^{2}-4}{11-2 x} \text {. }
f
(
x
)
=
11
−
2
x
x
2
−
4
.
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f
(
x
)
=
2
x
−
4
f(x)=2^{x-4}
f
(
x
)
=
2
x
−
4
\newline
g
(
x
)
=
5
x
g(x)=\frac{5}{x}
g
(
x
)
=
x
5
\newline
Evaluate.
\newline
g
(
f
(
2
)
)
=
g(f(2))=
g
(
f
(
2
))
=
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What is the inverse of the function
\newline
g
(
x
)
=
−
3
(
x
+
6
)
?
g
−
1
(
x
)
=
\begin{array}{l} g(x)=-3(x+6) ? \\ g^{-1}(x)= \end{array}
g
(
x
)
=
−
3
(
x
+
6
)?
g
−
1
(
x
)
=
Get tutor help
Find the following trigonometric values.
\newline
Express your answers exactly.
\newline
cos
(
31
5
∘
)
=
sin
(
31
5
∘
)
=
\begin{array}{l} \cos \left(315^{\circ}\right)= \\ \sin \left(315^{\circ}\right)= \end{array}
cos
(
31
5
∘
)
=
sin
(
31
5
∘
)
=
Get tutor help
Find the following trigonometric values.
\newline
Express your answers exactly.
\newline
cos
(
24
0
∘
)
=
sin
(
24
0
∘
)
=
\begin{array}{l} \cos \left(240^{\circ}\right)= \\ \sin \left(240^{\circ}\right)= \end{array}
cos
(
24
0
∘
)
=
sin
(
24
0
∘
)
=
Get tutor help
Find the following trigonometric values.
\newline
Express your answers exactly.
\newline
cos
(
22
5
∘
)
=
sin
(
22
5
∘
)
=
\begin{array}{l} \cos \left(225^{\circ}\right)= \\ \sin \left(225^{\circ}\right)= \end{array}
cos
(
22
5
∘
)
=
sin
(
22
5
∘
)
=
Get tutor help
Find the following trigonometric values.
\newline
Express your answers exactly.
\newline
cos
(
13
5
∘
)
=
sin
(
13
5
∘
)
=
\begin{array}{l} \cos \left(135^{\circ}\right)= \\ \sin \left(135^{\circ}\right)= \end{array}
cos
(
13
5
∘
)
=
sin
(
13
5
∘
)
=
Get tutor help
Find the following trigonometric values.
\newline
Express your answers exactly.
\newline
cos
(
4
π
3
)
=
□
sin
(
4
π
3
)
=
□
\begin{array}{l} \cos \left(\frac{4 \pi}{3}\right)=\square \\ \sin \left(\frac{4 \pi}{3}\right)=\square \end{array}
cos
(
3
4
π
)
=
□
sin
(
3
4
π
)
=
□
Get tutor help
Find the following trigonometric values.
\newline
Express your answers exactly.
\newline
cos
(
33
0
∘
)
=
sin
(
33
0
∘
)
=
\begin{array}{l} \cos \left(330^{\circ}\right)= \\ \sin \left(330^{\circ}\right)= \end{array}
cos
(
33
0
∘
)
=
sin
(
33
0
∘
)
=
Get tutor help
Find the zeros of the function. Enter the solutions from least to greatest.
\newline
f
(
x
)
=
(
x
+
8
)
2
−
1
f(x)=(x+8)^{2}-1
f
(
x
)
=
(
x
+
8
)
2
−
1
\newline
lesser
x
=
x=
x
=
\newline
greater
x
=
x=
x
=
Get tutor help
Solve for
x
x
x
. Enter the solutions from least to greatest.
\newline
(
x
−
1
)
2
−
9
=
0
lesser
x
=
□
greater
x
=
□
\begin{array}{l} (x-1)^{2}-9=0 \\ \text { lesser } x=\square \\ \text { greater } x=\square \end{array}
(
x
−
1
)
2
−
9
=
0
lesser
x
=
□
greater
x
=
□
Get tutor help
Solve for
x
x
x
. Enter the solutions from least to greatest.
\newline
(
x
+
1
)
2
−
36
=
0
lesser
x
=
□
greater
x
=
□
\begin{array}{l} (x+1)^{2}-36=0 \\ \text { lesser } x=\square \\ \text { greater } x=\square \end{array}
(
x
+
1
)
2
−
36
=
0
lesser
x
=
□
greater
x
=
□
Get tutor help
Find the zeros of the function. Enter the solutions from least to greatest.
\newline
f
(
x
)
=
(
x
−
2
)
2
−
9
f(x)=(x-2)^{2}-9
f
(
x
)
=
(
x
−
2
)
2
−
9
\newline
lesser
x
=
x=
x
=
\newline
greater
x
=
x=
x
=
Get tutor help
Find the zeros of the function. Enter the solutions from least to greatest.
\newline
f
(
x
)
=
(
x
+
6
)
2
−
16
f(x)=(x+6)^{2}-16
f
(
x
)
=
(
x
+
6
)
2
−
16
\newline
lesser
x
=
x=
x
=
\newline
greater
x
=
x=
x
=
Get tutor help
Solve for
x
x
x
. Enter the solutions from least to greatest.
\newline
(
x
+
7
)
2
−
49
=
0
lesser
x
=
□
greater
x
=
□
\begin{array}{l} (x+7)^{2}-49=0 \\ \text { lesser } x=\square \\ \text { greater } x=\square \end{array}
(
x
+
7
)
2
−
49
=
0
lesser
x
=
□
greater
x
=
□
Get tutor help
Find the zeros of the function. Enter the solutions from least to greatest.
\newline
f
(
x
)
=
(
x
+
2
)
2
−
16
f(x)=(x+2)^{2}-16
f
(
x
)
=
(
x
+
2
)
2
−
16
\newline
lesser
x
=
x=
x
=
\newline
greater
x
=
x=
x
=
Get tutor help
Solve for
x
x
x
. Enter the solutions from least to greatest.
\newline
(
x
−
7
)
2
−
25
=
0
lesser
x
=
□
greater
x
=
□
\begin{array}{l} (x-7)^{2}-25=0 \\ \text { lesser } x=\square \\ \text { greater } x=\square \end{array}
(
x
−
7
)
2
−
25
=
0
lesser
x
=
□
greater
x
=
□
Get tutor help
Find the zeros of the function. Enter the solutions from least to greatest.
\newline
f
(
x
)
=
(
x
−
8
)
2
−
9
f(x)=(x-8)^{2}-9
f
(
x
)
=
(
x
−
8
)
2
−
9
\newline
lesser
x
=
x=
x
=
\newline
greater
x
=
x=
x
=
Get tutor help
Solve for
x
x
x
. Enter the solutions from least to greatest.
\newline
(
x
+
3
)
2
−
4
=
0
lesser
x
=
□
greater
x
=
□
\begin{array}{l} (x+3)^{2}-4=0 \\ \text { lesser } x=\square \\ \text { greater } x=\square \end{array}
(
x
+
3
)
2
−
4
=
0
lesser
x
=
□
greater
x
=
□
Get tutor help
Solve for
x
x
x
. Enter the solutions from least to greatest.
\newline
(
x
+
6
)
2
−
16
=
0
lesser
x
=
□
greater
x
=
□
\begin{array}{l} (x+6)^{2}-16=0 \\ \text { lesser } x=\square \\ \text { greater } x=\square \end{array}
(
x
+
6
)
2
−
16
=
0
lesser
x
=
□
greater
x
=
□
Get tutor help
Solve for
x
x
x
. Enter the solutions from least to greatest.
\newline
(
x
+
5
)
2
−
64
=
0
lesser
x
=
□
greater
x
=
□
\begin{array}{l} (x+5)^{2}-64=0 \\ \text { lesser } x=\square \\ \text { greater } x=\square \end{array}
(
x
+
5
)
2
−
64
=
0
lesser
x
=
□
greater
x
=
□
Get tutor help
Solve for
x
x
x
. Enter the solutions from least to greatest.
\newline
(
x
−
3
)
2
−
81
=
0
lesser
x
=
□
greater
x
=
□
\begin{array}{l} (x-3)^{2}-81=0 \\ \text { lesser } x=\square \\ \text { greater } x=\square \end{array}
(
x
−
3
)
2
−
81
=
0
lesser
x
=
□
greater
x
=
□
Get tutor help
Find the zeros of the function. Enter the solutions from least to greatest.
\newline
f
(
x
)
=
(
x
+
3
)
2
−
4
f(x)=(x+3)^{2}-4
f
(
x
)
=
(
x
+
3
)
2
−
4
\newline
lesser
x
=
x=
x
=
\newline
greater
x
=
x=
x
=
Get tutor help
Find the zeros of the function. Enter the solutions from least to greatest.
\newline
f
(
x
)
=
(
x
−
4
)
2
−
16
f(x)=(x-4)^{2}-16
f
(
x
)
=
(
x
−
4
)
2
−
16
\newline
lesser
x
=
x=
x
=
\newline
greater
x
=
x=
x
=
Get tutor help
If
h
(
x
)
=
x
3
−
4
x
+
3
h(x)=x^{3}-4 x+3
h
(
x
)
=
x
3
−
4
x
+
3
, what is the value of
h
(
h
(
2
)
)
h(h(2))
h
(
h
(
2
))
?
Get tutor help
Which of the following is the value of
tan
(
0
∘
)
\tan \left(0^{\circ}\right)
tan
(
0
∘
)
?
\newline
Choose
1
1
1
answer:
\newline
(A)
1
1
1
\newline
(B)
0
0
0
\newline
(C)
−
1
-1
−
1
\newline
(D)
tan
(
0
∘
)
\tan \left(0^{\circ}\right)
tan
(
0
∘
)
is undefined.
Get tutor help
If
y
=
(
x
−
2
)
(
x
−
1
)
(
2
x
2
+
3
)
+
4
y=(x-2)(x-1)\left(2 x^{2}+3\right)+4
y
=
(
x
−
2
)
(
x
−
1
)
(
2
x
2
+
3
)
+
4
what is the value of
y
y
y
when
x
=
1
x=1
x
=
1
?
Get tutor help
y
=
(
x
−
5
)
2
+
1
y=(x-5)^{2}+1
y
=
(
x
−
5
)
2
+
1
\newline
y
−
5
3
=
15
\frac{y-5}{3}=15
3
y
−
5
=
15
\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
?
Get tutor help
If
f
(
x
)
=
1.
5
x
+
1
f(x)=1.5^{x}+1
f
(
x
)
=
1.
5
x
+
1
, what is the value of
f
(
2
)
f(2)
f
(
2
)
?
Get tutor help
What is the
x
x
x
-intercept of the graph of
y
=
(
x
−
5
)
2
y=(x-5)^{2}
y
=
(
x
−
5
)
2
?
\newline
Choose
1
1
1
answer:
\newline
(A)
−
25
-25
−
25
\newline
(B)
−
5
-5
−
5
\newline
(C)
5
5
5
\newline
(D)
25
25
25
Get tutor help
What is the inverse of the function
\newline
g
(
x
)
=
5
(
x
−
2
)
?
g(x)=5(x-2) ?
g
(
x
)
=
5
(
x
−
2
)?
\newline
g
−
1
(
x
)
=
g^{-1}(x)=
g
−
1
(
x
)
=
Get tutor help
What is the inverse of the function
\newline
f
(
x
)
=
8
x
+
1
f(x)=8x+1
f
(
x
)
=
8
x
+
1
?
\newline
f
−
1
(
x
)
=
f^{-1}(x)=
f
−
1
(
x
)
=
Get tutor help
Use the following function rule to find
f
(
1
)
f(1)
f
(
1
)
.
\newline
f
(
x
)
=
12
(
7
)
x
+
8
f(x) = 12(7)^x + 8
f
(
x
)
=
12
(
7
)
x
+
8
Get tutor help
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