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Math Problems
Precalculus
Find the roots of factored polynomials
Find all angles,
0
∘
≤
θ
<
36
0
∘
0^{\circ} \leq \theta<360^{\circ}
0
∘
≤
θ
<
36
0
∘
, that satisfy the equation below, to the nearest tenth of a degree.
\newline
cot
2
θ
+
4
cot
θ
+
3
=
0
\cot ^{2} \theta+4 \cot \theta+3=0
cot
2
θ
+
4
cot
θ
+
3
=
0
\newline
Answer:
θ
=
\theta=
θ
=
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Find all angles,
0
∘
≤
θ
<
36
0
∘
0^{\circ} \leq \theta<360^{\circ}
0
∘
≤
θ
<
36
0
∘
, that satisfy the equation below, to the nearest tenth of a degree.
\newline
cos
2
θ
−
cos
θ
=
0
\cos ^{2} \theta-\cos \theta=0
cos
2
θ
−
cos
θ
=
0
\newline
Answer:
θ
=
\theta=
θ
=
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7
7
7
−
20
-20
−
20
. The, area of the rectangle below is
8
1
4
8 \frac{1}{4}
8
4
1
square inches. Find the perimeter. Show your work.
\newline
Width is
4
1
2
i
n
4 \frac{1}{2} \mathrm{in}
4
2
1
in
.
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Simplify the expression to a + bi form:
\newline
(
−
1
+
9
i
)
(
11
−
7
i
)
(-1+9 i)(11-7 i)
(
−
1
+
9
i
)
(
11
−
7
i
)
\newline
Answer:
Get tutor help
Simplify the expression to a + bi form:
\newline
(
−
8
−
9
i
)
(
10
−
2
i
)
(-8-9 i)(10-2 i)
(
−
8
−
9
i
)
(
10
−
2
i
)
\newline
Answer:
Get tutor help
Simplify the expression to a + bi form:
\newline
(
5
−
6
i
)
(
−
9
−
9
i
)
(5-6 i)(-9-9 i)
(
5
−
6
i
)
(
−
9
−
9
i
)
\newline
Answer:
Get tutor help
Simplify the expression to a + bi form:
\newline
(
−
9
−
7
i
)
(
3
+
6
i
)
(-9-7 i)(3+6 i)
(
−
9
−
7
i
)
(
3
+
6
i
)
\newline
Answer:
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Write
(
−
1
+
3
i
)
4
(-1+3 i)^{4}
(
−
1
+
3
i
)
4
in simplest
a
+
b
i
a+b i
a
+
bi
form.
\newline
Answer:
Get tutor help
Simplify the expression to a + bi form:
\newline
(
−
6
−
7
i
)
(
−
3
+
5
i
)
(-6-7 i)(-3+5 i)
(
−
6
−
7
i
)
(
−
3
+
5
i
)
\newline
Answer:
Get tutor help
Simplify the expression to a + bi form:
\newline
(
12
−
4
i
)
(
−
6
−
9
i
)
(12-4 i)(-6-9 i)
(
12
−
4
i
)
(
−
6
−
9
i
)
\newline
Answer:
Get tutor help
Simplify the expression to a + bi form:
\newline
(
−
5
−
9
i
)
2
(-5-9 i)^{2}
(
−
5
−
9
i
)
2
\newline
Answer:
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Write
(
−
1
+
3
i
)
3
(-1+3 i)^{3}
(
−
1
+
3
i
)
3
in simplest
a
+
b
i
a+b i
a
+
bi
form.
\newline
Answer:
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Write
(
−
3
+
i
)
4
(-3+i)^{4}
(
−
3
+
i
)
4
in simplest
a
+
b
i
a+b i
a
+
bi
form.
\newline
Answer:
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Write
(
4
+
5
i
)
2
(4+5 i)^{2}
(
4
+
5
i
)
2
in simplest
a
+
b
i
a+b i
a
+
bi
form.
\newline
Answer:
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Write
(
−
1
+
4
i
)
3
(-1+4 i)^{3}
(
−
1
+
4
i
)
3
in simplest
a
+
b
i
a+b i
a
+
bi
form.
\newline
Answer:
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Write
(
−
1
+
2
i
)
3
(-1+2 i)^{3}
(
−
1
+
2
i
)
3
in simplest
a
+
b
i
a+b i
a
+
bi
form.
\newline
Answer:
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Write
(
2
+
4
i
)
3
(2+4 i)^{3}
(
2
+
4
i
)
3
in simplest
a
+
b
i
a+b i
a
+
bi
form.
\newline
Answer:
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Write
(
−
1
+
2
i
)
4
(-1+2 i)^{4}
(
−
1
+
2
i
)
4
in simplest
a
+
b
i
a+b i
a
+
bi
form.
\newline
Answer:
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b
(
n
)
=
−
4
−
2
(
n
−
1
)
b(n) = -4 - 2(n - 1)
b
(
n
)
=
−
4
−
2
(
n
−
1
)
Get tutor help
Rewrite in simplest terms:
3
(
−
6
s
+
4
t
)
+
0.8
t
−
3
(
t
−
5
s
)
3(-6 s+4 t)+0.8 t-3(t-5 s)
3
(
−
6
s
+
4
t
)
+
0.8
t
−
3
(
t
−
5
s
)
\newline
Answer:
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Rewrite in simplest terms:
7
(
−
0.3
v
+
8
v
+
1
)
−
v
7(-0.3 v+8 v+1)-v
7
(
−
0.3
v
+
8
v
+
1
)
−
v
\newline
Answer:
Get tutor help
Find (if possible) the rational zeros of the function. (Enter your answers as a comma-separated list. If an answer does not exist, enter DNE.)
f
(
x
)
=
9
x
4
−
9
x
3
−
58
x
2
+
4
x
+
24
f(x) = 9x^4 - 9x^3 - 58x^2 + 4x + 24
f
(
x
)
=
9
x
4
−
9
x
3
−
58
x
2
+
4
x
+
24
x
=
x =
x
=
Get tutor help
Find (if possible) the rational zeros of the function.
\newline
(Enter your answers as a comma-separated list. If an answer does not exist, enter DNE.)
\newline
f
(
x
)
=
4
x
3
−
34
x
2
+
80
x
−
32
f(x) = 4x^3 - 34x^2 + 80x - 32
f
(
x
)
=
4
x
3
−
34
x
2
+
80
x
−
32
Get tutor help
Khan Academy
\newline
Quadratics by taking
\newline
FL.BEST.Math: MA.
912
912
912
.
\newline
Create a list of steps, in order, that
\newline
1
4
(
x
+
5
)
2
−
1
=
3
\frac{1}{4}(x+5)^{2}-1=3
4
1
(
x
+
5
)
2
−
1
=
3
\newline
Solution steps:
Get tutor help
comma-separated lists. If an answer does not exist, enter DNE.)
\newline
f
(
x
,
y
)
=
7
(
x
−
y
)
e
(
−
x
2
−
y
2
)
f(x,y)=7(x-y)e^{(-x^{2}-y^{2})}
f
(
x
,
y
)
=
7
(
x
−
y
)
e
(
−
x
2
−
y
2
)
\newline
local maximum vilue(s)
\newline
local minimum value(s)
\newline
saddle point(s)
\newline
(
x
,
y
)
=
(x,y)=
(
x
,
y
)
=
Get tutor help
comma-separated lists. If an answer does not exist, enter DNE.)
\newline
f
(
x
,
y
)
=
7
(
x
−
y
)
e
−
x
2
−
y
2
f(x, y)=7(x-y) e^{-x^{2}-y^{2}}
f
(
x
,
y
)
=
7
(
x
−
y
)
e
−
x
2
−
y
2
\newline
local maximum vislue(s)
\newline
local minimum value(s)
\newline
saddle point(s)
\newline
(
x
,
y
)
=
(x, y)=
(
x
,
y
)
=
Get tutor help
Perform the operation and reduce the answer fully. Make sure to express your answer as a simplified fraction.
\newline
2
3
÷
8
9
\frac{2}{3} \div \frac{8}{9}
3
2
÷
9
8
\newline
Answer:
Get tutor help
Perform the operation and reduce the answer fully. Make sure to express your answer as a simplified fraction.
\newline
1
10
÷
8
3
\frac{1}{10} \div \frac{8}{3}
10
1
÷
3
8
\newline
Answer:
Get tutor help
Approximate
A
(
1
x
,
1
≤
x
≤
5
)
A(\frac{1}{x},1 \leq x \leq 5)
A
(
x
1
,
1
≤
x
≤
5
)
using eight left endpoint rectangles. Use sigma notation to show the sum of the areas of the rectangles. answer is approximately
1.823
1.823
1.823
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x
2
−
10
x
+
14
=
0
x^{2}-10x+14=0
x
2
−
10
x
+
14
=
0
\newline
One solution to the given equation can be written as
x
=
5
+
n
x=5+\sqrt{n}
x
=
5
+
n
, where
n
n
n
is a constant. What is the value of
n
n
n
?
Get tutor help
a. Simplify the expression. Leave simplified answers in factored form.
\newline
(
x
2
−
16
x
+
64
)
(
x
+
2
)
(
x
2
−
64
)
(
x
2
−
6
x
−
16
)
\frac{\left(x^{2}-16 x+64\right)(x+2)}{\left(x^{2}-64\right)\left(x^{2}-6 x-16\right)}
(
x
2
−
64
)
(
x
2
−
6
x
−
16
)
(
x
2
−
16
x
+
64
)
(
x
+
2
)
\newline
+
−
x
÷
∣
□
□
[
□
□
∣
=
≠
<
>
≥
≤
∣
(प)
∣
π
+-x \div \left\lvert\, \frac{\square}{\square} \quad[\sqrt{\square} \sqrt{\square}|=\neq<>\geq \leq| \text { (प) } \mid \pi\right.
+
−
x
÷
∣
∣
□
□
[
□
□
∣
=
=
<>≥≤
∣
(
प
)
∣
π
\newline
Part B
\newline
b. State when the original expression is undefined. Write your answer in ascending order.
\newline
x
=
x=
x
=
Get tutor help
Find the difference quotient
\newline
(
f
(
x
+
h
)
−
f
(
x
)
)
/
(
h
)
(f(x+h)-f(x))/(h)
(
f
(
x
+
h
)
−
f
(
x
))
/
(
h
)
, where
\newline
h
≠
0
h\neq 0
h
=
0
, for the function below.
\newline
f
(
x
)
=
−
3
x
2
−
2
x
+
5
f(x)=-3x^{2}-2x+5
f
(
x
)
=
−
3
x
2
−
2
x
+
5
\newline
Simplify your answer as much as possible.
\newline
(
f
(
x
+
h
)
−
f
(
x
)
)
/
(
h
)
=
(f(x+h)-f(x))/(h)=
(
f
(
x
+
h
)
−
f
(
x
))
/
(
h
)
=
Get tutor help
Select all values for scale factor,
k
k
k
, that would create a reduced image.(\newline\)
k
=
13
12
k=\frac{13}{12}
k
=
12
13
(\newline\)
k
=
10
9
k=\frac{10}{9}
k
=
9
10
(\newline\)
k
=
15
30
k=\frac{15}{30}
k
=
30
15
(\newline\)
k
=
27
9
k=\frac{27}{9}
k
=
9
27
(\newline\)
k
=
1
8
k=\frac{1}{8}
k
=
8
1
(\newline\)
k
=
1
9
k=\frac{1}{9}
k
=
9
1
Get tutor help
For the polynomial below,
1
1
1
is a zero.
\newline
g
(
x
)
=
x
3
−
7
x
2
+
12
x
−
6
g(x)=x^{3}-7x^{2}+12x-6
g
(
x
)
=
x
3
−
7
x
2
+
12
x
−
6
\newline
Express
\newline
g
(
x
)
g(x)
g
(
x
)
as a product of linear factors.
\newline
g
(
x
)
=
g(x)=
g
(
x
)
=
Get tutor help
Exponential and Logarithmic Functions
\newline
Solving an exponential equation by using logarithms: Solve for
x
x
x
.
\newline
5
(
x
−
9
)
=
1
2
(
10
x
)
5^{(x-9)}=12^{(10x)}
5
(
x
−
9
)
=
1
2
(
10
x
)
\newline
Round your answer to the nearest thousandth.
\newline
Do not round any intermediate computations.
\newline
x
=
x=
x
=
Get tutor help
Solve for
x
x
x
.
\newline
5
(
x
−
4
)
=
6
(
9
x
)
5^{(x-4)}=6^{(9x)}
5
(
x
−
4
)
=
6
(
9
x
)
\newline
Round your answer to the nearest thousandth.
\newline
Do not round any intermediate computations.
\newline
x
=
x=
x
=
Get tutor help
For the polynomial below,
−
2
-2
−
2
is a zero.
\newline
h
(
x
)
=
x
3
+
x
2
−
4
x
−
4
h(x)=x^{3}+x^{2}-4x-4
h
(
x
)
=
x
3
+
x
2
−
4
x
−
4
\newline
Express
\newline
h
(
x
)
h(x)
h
(
x
)
as a product of linear factors.
\newline
h
(
x
)
=
h(x)=
h
(
x
)
=
Get tutor help
Using a graphing calculator to solve an exponential or logarithmic... Use the ALEKS graphing calculator to solve the equation.
\newline
e
2
−
3
x
=
5
−
3
x
e^{2-3x}=5-3x
e
2
−
3
x
=
5
−
3
x
\newline
Round to the nearest hundredth.
\newline
If there is more than one solution, separate them with commas.
\newline
x
=
x=
x
=
Get tutor help
For the polynomial below,
2
2
2
is a zero.
\newline
f
(
x
)
=
x
3
−
6
x
2
+
10
x
−
4
f(x)=x^{3}-6x^{2}+10x-4
f
(
x
)
=
x
3
−
6
x
2
+
10
x
−
4
\newline
Express
\newline
f
(
x
)
f(x)
f
(
x
)
as a product of linear factors.
\newline
f
(
x
)
=
f(x)=
f
(
x
)
=
Get tutor help
Quadratic and Polynomial Functions
\newline
Using a given zero to write a polynomial as a product of linear factors: Re...
\newline
For the polynomial below,
−
1
-1
−
1
is a zero.
\newline
f
(
x
)
=
x
3
−
7
x
−
6
f(x)=x^{3}-7x-6
f
(
x
)
=
x
3
−
7
x
−
6
\newline
Express
\newline
f
(
x
)
f(x)
f
(
x
)
as a product of linear factors.
\newline
f
(
x
)
=
f(x)=
f
(
x
)
=
Get tutor help
For the polynomial below,
−
1
-1
−
1
is a zero.
\newline
f
(
x
)
=
x
3
−
3
x
2
−
7
x
−
3
f(x)=x^{3}-3x^{2}-7x-3
f
(
x
)
=
x
3
−
3
x
2
−
7
x
−
3
\newline
Express
\newline
f
(
x
)
f(x)
f
(
x
)
as a product of linear factors.
\newline
f
(
x
)
=
f(x)=
f
(
x
)
=
Get tutor help
Find the sum of the first
7
7
7
terms of the following sequence. Round to the nearest hundredth if necessary.
\newline
125
,
100
,
80
,
…
125, \quad 100, \quad 80, \ldots
125
,
100
,
80
,
…
\newline
Sum of a finite geometric series:
\newline
S
n
=
a
1
−
a
1
r
n
1
−
r
S_{n}=\frac{a_{1}-a_{1} r^{n}}{1-r}
S
n
=
1
−
r
a
1
−
a
1
r
n
\newline
Answer:
Get tutor help
Find the sum of the first
7
7
7
terms of the following sequence. Round to the nearest hundredth if necessary.
\newline
27
,
−
54
,
108
,
…
27, \quad-54, \quad 108, \ldots
27
,
−
54
,
108
,
…
\newline
Sum of a finite geometric series:
\newline
S
n
=
a
1
−
a
1
r
n
1
−
r
S_{n}=\frac{a_{1}-a_{1} r^{n}}{1-r}
S
n
=
1
−
r
a
1
−
a
1
r
n
\newline
Answer:
Get tutor help
Evaluate:
\newline
∑
n
=
0
2
(
x
+
n
)
\sum_{n=0}^{2}(x+n)
n
=
0
∑
2
(
x
+
n
)
\newline
Answer:
Get tutor help
Find the numerical answer to the summation given below.
\newline
∑
n
=
0
92
(
6
n
+
3
)
\sum_{n=0}^{92}(6 n+3)
n
=
0
∑
92
(
6
n
+
3
)
\newline
Answer:
Get tutor help
Find the numerical answer to the summation given below.
\newline
∑
n
=
0
95
(
5
n
+
7
)
\sum_{n=0}^{95}(5 n+7)
n
=
0
∑
95
(
5
n
+
7
)
\newline
Answer:
Get tutor help
Find the numerical answer to the summation given below.
\newline
∑
n
=
2
61
(
5
n
+
9
)
\sum_{n=2}^{61}(5 n+9)
n
=
2
∑
61
(
5
n
+
9
)
\newline
Answer:
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Find the numerical answer to the summation given below.
\newline
∑
n
=
0
93
(
3
n
+
10
)
\sum_{n=0}^{93}(3 n+10)
n
=
0
∑
93
(
3
n
+
10
)
\newline
Answer:
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Find the numerical answer to the summation given below.
\newline
∑
n
=
0
68
(
6
n
+
3
)
\sum_{n=0}^{68}(6 n+3)
n
=
0
∑
68
(
6
n
+
3
)
\newline
Answer:
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Find the numerical answer to the summation given below.
\newline
∑
n
=
1
95
(
2
n
+
1
)
\sum_{n=1}^{95}(2 n+1)
n
=
1
∑
95
(
2
n
+
1
)
\newline
Answer:
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