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Math Problems
Algebra 1
Evaluate piecewise-defined functions
Find the equation of the quadratic function
g
g
g
whose graph is shown below.
\newline
g
(
x
)
=
g(x)=
g
(
x
)
=
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Compare the numbers. Pick the correct sign.
\newline
−
4
?
−
2
-4 \,?\, -2
−
4
?
−
2
\newline
You can use the number line to help.
\newline
Choices:
\newline
(
A
)
>
(A) >
(
A
)
>
\newline
(
B
)
<
(B) <
(
B
)
<
\newline
(
C
)
=
(C) =
(
C
)
=
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Compare the numbers. Pick the correct sign.
\newline
−
2
?
−
10
-2 \,?\, -10
−
2
?
−
10
\newline
\newline
You can use the number line to help.
\newline
\newline
Choices:
\newline
(A)
>
>
>
\newline
(B)
<
<
<
\newline
(C)
=
=
=
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Compare the numbers. Pick the correct sign.
\newline
−
5
?
−
5
-5 \,?\, -5
−
5
?
−
5
\newline
\newline
You can use the number line to help.
\newline
\newline
Choices:
\newline
(A)
>
>
>
\newline
(B)
<
<
<
\newline
(C)
=
=
=
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Compare the numbers. Pick the correct sign.
\newline
−
3
?
−
7
-3 \,?\, -7
−
3
?
−
7
\newline
\newline
You can use the number line to help.
\newline
\newline
Choices:
\newline
(A)
>
>
>
\newline
(B)
<
<
<
\newline
(C)
=
=
=
Get tutor help
Compare the numbers. Pick the correct sign.
\newline
−
5
?
−
7
-5 \,?\, -7
−
5
?
−
7
\newline
\newline
You can use the number line to help.
\newline
\newline
Choices:
\newline
(A)
>
>
>
\newline
(B)
<
<
<
\newline
(C)
=
=
=
Get tutor help
4
4
4
. Describe a possible scenario for each graph. Tell what each axis represents in each case.
\newline
a)
\newline
b)
\newline
c)
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b)
D
E
\mathrm{DE}
DE
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(b)
\newline
6
6
6
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P
(
x
)
=
x
4
−
2
x
3
+
k
x
−
4
P(x)=x^4-2 x^3+k x-4
P
(
x
)
=
x
4
−
2
x
3
+
k
x
−
4
\newline
where
k
k
k
is an unknown integer.
\newline
P
(
x
)
P(x)
P
(
x
)
divided by
(
x
−
1
)
(x-1)
(
x
−
1
)
has a remainder of
0
0
0
.
\newline
What is the value of
k
k
k
?
\newline
k
=
k=
k
=
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If L'Hospital's Rule applies, use it to evaluate the limit.
\newline
(Use symbolic notation and fractions where needed.)
\newline
lim
x
→
−
29
x
2
−
841
725
−
4
x
−
x
2
=
\lim_{x \to -29}\frac{x^{2}-841}{725-4x-x^{2}}=
lim
x
→
−
29
725
−
4
x
−
x
2
x
2
−
841
=
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Use L'Hôpital's Rule (possibly more than once) to evaluate the following limit. (Use symbolic notation and fractions where needed.)
\newline
lim
x
→
0
sin
(
7
x
)
−
7
x
cos
(
7
x
)
7
x
−
sin
(
7
x
)
=
\lim_{x \to 0}\frac{\sin(7x)-7x \cos(7x)}{7x-\sin(7x)}=
lim
x
→
0
7
x
−
s
i
n
(
7
x
)
s
i
n
(
7
x
)
−
7
x
c
o
s
(
7
x
)
=
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Solve for
x
x
x
and write your answer in simplest form.
\newline
−
5
4
−
(
3
4
x
+
5
)
+
7
x
=
−
10
x
-\frac{5}{4}-\left(\frac{3}{4} x+5\right)+7 x=-10 x
−
4
5
−
(
4
3
x
+
5
)
+
7
x
=
−
10
x
\newline
Answer:
x
=
x=
x
=
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Solve the following equation for
a
a
a
. Be sure to take into account whether a letter is capitalized or not.
\newline
a
q
+
N
=
h
\frac{a}{q}+N=h
q
a
+
N
=
h
\newline
Answer:
a
=
a=
a
=
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Solve the following equation for
a
a
a
. Be sure to take into account whether a letter is capitalized or not.
\newline
h
+
a
n
=
U
h+\frac{a}{n}=U
h
+
n
a
=
U
\newline
Answer:
a
=
a=
a
=
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Solve the following equation for
a
a
a
. Be sure to take into account whether a letter is capitalized or not.
\newline
q
=
a
d
+
g
q=\frac{a}{d+g}
q
=
d
+
g
a
\newline
Answer:
a
=
a=
a
=
Get tutor help
Solve the following equation for
a
a
a
. Be sure to take into account whether a letter is capitalized or not.
\newline
G
=
a
f
G=\frac{a}{f}
G
=
f
a
\newline
Answer:
a
=
a=
a
=
Get tutor help
Solve the following equation for
a
a
a
. Be sure to take into account whether a letter is capitalized or not.
\newline
a
B
=
d
\frac{a}{B}=d
B
a
=
d
\newline
Answer:
a
=
a=
a
=
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Solve the following equation for
G
G
G
. Be sure to take into account whether a letter is capitalized or not.
\newline
G
n
=
8
\frac{G}{n}=8
n
G
=
8
\newline
Answer:
G
=
G=
G
=
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Solve the following equation for
A
A
A
. Be sure to take into account whether a letter is capitalized or not.
\newline
f
=
A
b
f=\frac{A}{b}
f
=
b
A
\newline
Answer:
A
=
A=
A
=
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Solve the following equation for
A
A
A
. Be sure to take into account whether a letter is capitalized or not.
\newline
A
g
=
m
\frac{A}{g}=m
g
A
=
m
\newline
Answer:
A
=
A=
A
=
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Solve the following equation for
a
a
a
. Be sure to take into account whether a letter is capitalized or not.
\newline
a
D
=
7
\frac{a}{D}=7
D
a
=
7
\newline
Answer:
a
=
a=
a
=
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Given the function
f
(
x
)
=
1
x
3
4
f(x)=\frac{1}{\sqrt[4]{x^{3}}}
f
(
x
)
=
4
x
3
1
, find
f
′
(
x
)
f^{\prime}(x)
f
′
(
x
)
. Express your answer in radical form without using negative exponents, simplifying all fractions.
\newline
Answer:
f
′
(
x
)
=
f^{\prime}(x)=
f
′
(
x
)
=
Get tutor help
Given the function
y
=
x
6
5
3
y=\frac{\sqrt[5]{x^{6}}}{3}
y
=
3
5
x
6
, find
d
y
d
x
\frac{d y}{d x}
d
x
d
y
. Express your answer in radical form without using negative exponents, simplifying all fractions.
\newline
Answer:
d
y
d
x
=
\frac{d y}{d x}=
d
x
d
y
=
Get tutor help
Find the value of
x
x
x
in the equation below.
\newline
x
9
=
8
\frac{x}{9}=8
9
x
=
8
\newline
Answer:
x
=
x=
x
=
Get tutor help
Find the value of
x
x
x
in the equation below.
\newline
x
7
=
8
\frac{x}{7}=8
7
x
=
8
\newline
Answer:
x
=
x=
x
=
Get tutor help
Solve for
a
a
a
. Express your answer as a proper or improper fraction in simplest terms.
\newline
−
5
6
−
1
5
a
=
−
5
8
-\frac{5}{6}-\frac{1}{5} a=-\frac{5}{8}
−
6
5
−
5
1
a
=
−
8
5
\newline
Answer:
a
=
a=
a
=
Get tutor help
Rewrite the expression in the form
x
n
x^{n}
x
n
.
\newline
Write the exponent as an integer, fraction, or an exact decimal (not a mixed number).
\newline
x
3
4
x
−
1
=
□
\sqrt{x^{\frac{3}{4}} x^{-1}}=\square
x
4
3
x
−
1
=
□
Get tutor help
Vector
u
⃗
\vec{u}
u
has an initial point
(
5
,
1
)
(5,1)
(
5
,
1
)
and a terminal point
(
−
3
,
4
)
(-3,4)
(
−
3
,
4
)
.
\newline
Find the magnitude of
u
⃗
\vec{u}
u
.
\newline
Enter an exact answer as an expression with a square root symbol or enter an approximate answer as a decimal rounded to the nearest hundredth.
\newline
∥
u
⃗
∥
=
□
\|\vec{u}\|=\square
∥
u
∥
=
□
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Vector
u
⃗
\vec{u}
u
has an initial point
(
4
,
8
)
(4,8)
(
4
,
8
)
and a terminal point
(
2
,
4
)
(2,4)
(
2
,
4
)
.
\newline
Find the magnitude of
u
⃗
\vec{u}
u
.
\newline
Enter an exact answer as an expression with a square root symbol or enter an approximate answer as a decimal rounded to the nearest hundredth.
\newline
∥
u
⃗
∥
=
□
\|\vec{u}\|=\square
∥
u
∥
=
□
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The graph of a sinusoidal function intersects its midline at
(
0
,
−
3
)
(0,-3)
(
0
,
−
3
)
and then has a maximum point at
(
2
,
−
1.5
)
(2,-1.5)
(
2
,
−
1.5
)
.
\newline
Write the formula of the function, where
x
x
x
is entered in radians.
\newline
f
(
x
)
=
□
f(x)=\square
f
(
x
)
=
□
Get tutor help
