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Math Problems
Precalculus
Find the roots of factored polynomials
Solve for
x
x
x
.
\newline
1
5
−
5
x
=
−
8
5
x
\frac{1}{5}-\frac{5}{x}=\frac{-8}{5 x}
5
1
−
x
5
=
5
x
−
8
\newline
Answer:
x
=
x=
x
=
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If
f
(
x
)
=
x
+
18
3
x
f(x)=\frac{\sqrt{x}+18}{3 x}
f
(
x
)
=
3
x
x
+
18
, what is the value of
f
(
5
)
f(5)
f
(
5
)
, to the nearest tenth (if necessary)?
\newline
Answer:
Get tutor help
Solve for
x
x
x
.
\newline
−
1
6
+
x
−
3
x
=
7
6
x
\frac{-1}{6}+\frac{x-3}{x}=\frac{7}{6 x}
6
−
1
+
x
x
−
3
=
6
x
7
\newline
Answer:
x
=
x=
x
=
Get tutor help
Solve for
x
x
x
.
\newline
−
1
x
+
2
9
=
5
9
x
\frac{-1}{x}+\frac{2}{9}=\frac{5}{9 x}
x
−
1
+
9
2
=
9
x
5
\newline
Answer:
x
=
x=
x
=
Get tutor help
Complete the square to re-write the quadratic function in vertex form:
\newline
y
=
x
2
−
9
x
−
3
y=x^{2}-9 x-3
y
=
x
2
−
9
x
−
3
\newline
Answer:
y
=
y=
y
=
Get tutor help
Solve the equation
2
x
2
+
8
x
−
10
=
−
3
x
2
2 x^{2}+8 x-10=-3 x^{2}
2
x
2
+
8
x
−
10
=
−
3
x
2
to the nearest tenth.
\newline
Answer:
x
=
x=
x
=
Get tutor help
Solve for all values of
x
x
x
.
\newline
x
−
7
x
−
3
=
−
2
x
\frac{x-7}{x-3}=\frac{-2}{x}
x
−
3
x
−
7
=
x
−
2
\newline
Answer:
x
=
x=
x
=
Get tutor help
Solve for all values of
x
x
x
.
\newline
x
−
8
x
+
4
=
−
2
x
\frac{x-8}{x+4}=\frac{-2}{x}
x
+
4
x
−
8
=
x
−
2
\newline
Answer:
x
=
x=
x
=
Get tutor help
Solve for all values of
x
x
x
.
\newline
x
+
3
x
−
4
=
−
5
x
\frac{x+3}{x-4}=\frac{-5}{x}
x
−
4
x
+
3
=
x
−
5
\newline
Answer:
x
=
x=
x
=
Get tutor help
Solve for all values of
x
x
x
.
\newline
x
−
5
x
+
3
=
−
1
x
\frac{x-5}{x+3}=\frac{-1}{x}
x
+
3
x
−
5
=
x
−
1
\newline
Answer:
x
=
x=
x
=
Get tutor help
Solve for all values of
x
x
x
.
\newline
−
1
13
x
=
x
−
13
\frac{-1}{13 x}=\frac{x}{-13}
13
x
−
1
=
−
13
x
\newline
Answer:
x
=
x=
x
=
Get tutor help
Solve for all values of
x
x
x
.
\newline
x
−
5
x
+
9
=
2
x
\frac{x-5}{x+9}=\frac{2}{x}
x
+
9
x
−
5
=
x
2
\newline
Answer:
x
=
x=
x
=
Get tutor help
Solve for all values of
x
x
x
.
\newline
x
−
7
x
+
3
=
4
x
\frac{x-7}{x+3}=\frac{4}{x}
x
+
3
x
−
7
=
x
4
\newline
Answer:
x
=
x=
x
=
Get tutor help
Solve for all values of
x
x
x
.
\newline
x
−
7
x
+
8
=
−
1
x
\frac{x-7}{x+8}=\frac{-1}{x}
x
+
8
x
−
7
=
x
−
1
\newline
Answer:
x
=
x=
x
=
Get tutor help
Solve for all values of
x
x
x
.
\newline
x
−
5
x
+
9
=
4
x
\frac{x-5}{x+9}=\frac{4}{x}
x
+
9
x
−
5
=
x
4
\newline
Answer:
x
=
x=
x
=
Get tutor help
Solve for all values of
x
x
x
.
\newline
x
−
3
x
+
2
=
4
x
\frac{x-3}{x+2}=\frac{4}{x}
x
+
2
x
−
3
=
x
4
\newline
Answer:
x
=
x=
x
=
Get tutor help
Rewrite the expression as a product of four linear factors:
\newline
(
x
2
+
3
x
)
2
−
16
(
x
2
+
3
x
)
−
36
\left(x^{2}+3 x\right)^{2}-16\left(x^{2}+3 x\right)-36
(
x
2
+
3
x
)
2
−
16
(
x
2
+
3
x
)
−
36
\newline
Answer:
Get tutor help
Rewrite the expression as a product of four linear factors:
\newline
(
x
2
−
5
x
)
2
−
2
(
x
2
−
5
x
)
−
24
\left(x^{2}-5 x\right)^{2}-2\left(x^{2}-5 x\right)-24
(
x
2
−
5
x
)
2
−
2
(
x
2
−
5
x
)
−
24
\newline
Answer:
Get tutor help
Rewrite the expression as a product of four linear factors:
\newline
(
x
2
+
5
x
)
2
−
2
(
x
2
+
5
x
)
−
24
\left(x^{2}+5 x\right)^{2}-2\left(x^{2}+5 x\right)-24
(
x
2
+
5
x
)
2
−
2
(
x
2
+
5
x
)
−
24
\newline
Answer:
Get tutor help
Rewrite the expression as a product of four linear factors:
\newline
(
x
2
+
4
x
)
2
−
9
(
x
2
+
4
x
)
−
36
\left(x^{2}+4 x\right)^{2}-9\left(x^{2}+4 x\right)-36
(
x
2
+
4
x
)
2
−
9
(
x
2
+
4
x
)
−
36
\newline
Answer:
Get tutor help
If
a
1
=
4
,
a
2
=
1
a_{1}=4, a_{2}=1
a
1
=
4
,
a
2
=
1
and
a
n
=
a
n
−
1
+
3
a
n
−
2
a_{n}=a_{n-1}+3 a_{n-2}
a
n
=
a
n
−
1
+
3
a
n
−
2
then find the value of
a
6
a_{6}
a
6
.
\newline
Answer:
Get tutor help
If
f
(
1
)
=
1
f(1)=1
f
(
1
)
=
1
and
f
(
n
)
=
−
2
f
(
n
−
1
)
+
3
f(n)=-2 f(n-1)+3
f
(
n
)
=
−
2
f
(
n
−
1
)
+
3
then find the value of
f
(
5
)
f(5)
f
(
5
)
.
\newline
Answer:
Get tutor help
Rewrite the expression as a product of four linear factors:
\newline
(
10
x
2
+
x
)
2
−
11
(
10
x
2
+
x
)
+
18
\left(10 x^{2}+x\right)^{2}-11\left(10 x^{2}+x\right)+18
(
10
x
2
+
x
)
2
−
11
(
10
x
2
+
x
)
+
18
\newline
Answer:
Get tutor help
Rewrite the expression as a product of four linear factors:
\newline
(
4
x
2
+
x
)
2
−
19
(
4
x
2
+
x
)
+
70
\left(4 x^{2}+x\right)^{2}-19\left(4 x^{2}+x\right)+70
(
4
x
2
+
x
)
2
−
19
(
4
x
2
+
x
)
+
70
\newline
Answer:
Get tutor help
Rewrite the expression as a product of four linear factors:
\newline
(
6
x
2
−
x
)
2
−
6
(
6
x
2
−
x
)
+
5
\left(6 x^{2}-x\right)^{2}-6\left(6 x^{2}-x\right)+5
(
6
x
2
−
x
)
2
−
6
(
6
x
2
−
x
)
+
5
\newline
Answer:
Get tutor help
Find a power series for
f
(
x
)
=
4
8
−
x
f(x)=\frac{4}{8-x}
f
(
x
)
=
8
−
x
4
centered at
2
2
2
and determine the interval of convergence. (
6
6
6
Get tutor help
Solve the proportion. If there is no solution, enter DNE.
\newline
p
p
−
12
=
11
8
\frac{p}{p-12}=\frac{11}{8}
p
−
12
p
=
8
11
\newline
Solution:
p
=
p=
p
=
\newline
If there is more than one solution to the equation, use a comma to separate solutions.
Get tutor help
Solve the rational equation. If there is no solution, enter DNE.
\newline
a
+
6
a
2
−
6
a
−
7
=
1
a
+
1
+
1
a
−
7
\frac{a+6}{a^{2}-6 a-7}=\frac{1}{a+1}+\frac{1}{a-7}
a
2
−
6
a
−
7
a
+
6
=
a
+
1
1
+
a
−
7
1
\newline
Solution:
a
=
a=
a
=
\newline
If there is more than one solution to the equation, use a comma to separate solutions.
Get tutor help
If
a
1
=
9
a_{1}=9
a
1
=
9
and
a
n
=
−
2
a
n
−
1
−
4
a_{n}=-2 a_{n-1}-4
a
n
=
−
2
a
n
−
1
−
4
then find the value of
a
5
a_{5}
a
5
.
\newline
Answer:
Get tutor help
If
a
1
=
9
a_{1}=9
a
1
=
9
and
a
n
=
3
a
n
−
1
−
3
a_{n}=3 a_{n-1}-3
a
n
=
3
a
n
−
1
−
3
then find the value of
a
5
a_{5}
a
5
.
\newline
Answer:
Get tutor help
If
a
1
=
6
a_{1}=6
a
1
=
6
and
a
n
=
−
4
a
n
−
1
−
5
a_{n}=-4 a_{n-1}-5
a
n
=
−
4
a
n
−
1
−
5
then find the value of
a
3
a_{3}
a
3
.
\newline
Answer:
Get tutor help
If
a
1
=
3
a_{1}=3
a
1
=
3
and
a
n
=
4
a
n
−
1
−
5
a_{n}=4 a_{n-1}-5
a
n
=
4
a
n
−
1
−
5
then find the value of
a
4
a_{4}
a
4
.
\newline
Answer:
Get tutor help
If
a
1
=
4
a_{1}=4
a
1
=
4
and
a
n
=
2
a
n
−
1
+
4
a_{n}=2 a_{n-1}+4
a
n
=
2
a
n
−
1
+
4
then find the value of
a
3
a_{3}
a
3
.
\newline
Answer:
Get tutor help
If
a
1
=
9
a_{1}=9
a
1
=
9
and
a
n
=
4
a
n
−
1
−
1
a_{n}=4 a_{n-1}-1
a
n
=
4
a
n
−
1
−
1
then find the value of
a
3
a_{3}
a
3
.
\newline
Answer:
Get tutor help
If
a
1
=
1
a_{1}=1
a
1
=
1
and
a
n
=
2
a
n
−
1
−
5
a_{n}=2 a_{n-1}-5
a
n
=
2
a
n
−
1
−
5
then find the value of
a
5
a_{5}
a
5
.
\newline
Answer:
Get tutor help
If
a
1
=
1
a_{1}=1
a
1
=
1
and
a
n
=
n
a
n
−
1
+
5
a_{n}=n a_{n-1}+5
a
n
=
n
a
n
−
1
+
5
then find the value of
a
4
a_{4}
a
4
.
\newline
Answer:
Get tutor help
If
a
1
=
9
a_{1}=9
a
1
=
9
and
a
n
=
n
a
n
−
1
+
4
a_{n}=n a_{n-1}+4
a
n
=
n
a
n
−
1
+
4
then find the value of
a
4
a_{4}
a
4
.
\newline
Answer:
Get tutor help
If
a
1
=
3
a_{1}=3
a
1
=
3
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:
Get tutor help
If
a
1
=
3
a_{1}=3
a
1
=
3
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
3
a_{3}
a
3
.
\newline
Answer:
Get tutor help
If
a
1
=
7
a_{1}=7
a
1
=
7
and
a
n
=
n
a
n
−
1
+
5
a_{n}=n a_{n-1}+5
a
n
=
n
a
n
−
1
+
5
then find the value of
a
4
a_{4}
a
4
.
\newline
Answer:
Get tutor help
If
a
1
=
7
a_{1}=7
a
1
=
7
and
a
n
=
n
a
n
−
1
+
1
a_{n}=n a_{n-1}+1
a
n
=
n
a
n
−
1
+
1
then find the value of
a
3
a_{3}
a
3
.
\newline
Answer:
Get tutor help
If
a
1
=
9
a_{1}=9
a
1
=
9
and
a
n
=
n
a
n
−
1
+
1
a_{n}=n a_{n-1}+1
a
n
=
n
a
n
−
1
+
1
then find the value of
a
5
a_{5}
a
5
.
\newline
Answer:
Get tutor help
If
a
1
=
6
a_{1}=6
a
1
=
6
and
a
n
=
n
a
n
−
1
+
5
a_{n}=n a_{n-1}+5
a
n
=
n
a
n
−
1
+
5
then find the value of
a
4
a_{4}
a
4
.
\newline
Answer:
Get tutor help
If
a
1
=
5
a_{1}=5
a
1
=
5
and
a
n
=
n
a
n
−
1
−
5
a_{n}=n a_{n-1}-5
a
n
=
n
a
n
−
1
−
5
then find the value of
a
3
a_{3}
a
3
.
\newline
Answer:
Get tutor help
If
a
1
=
5
a_{1}=5
a
1
=
5
and
a
n
=
n
a
n
−
1
−
2
a_{n}=n a_{n-1}-2
a
n
=
n
a
n
−
1
−
2
then find the value of
a
3
a_{3}
a
3
.
\newline
Answer:
Get tutor help
If
a
1
=
6
a_{1}=6
a
1
=
6
and
a
n
=
n
a
n
−
1
+
4
a_{n}=n a_{n-1}+4
a
n
=
n
a
n
−
1
+
4
then find the value of
a
4
a_{4}
a
4
.
\newline
Answer:
Get tutor help
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
3
a_{3}
a
3
.
\newline
Answer:
Get tutor help
If
a
1
=
8
a_{1}=8
a
1
=
8
and
a
n
=
−
5
a
n
−
1
−
3
a_{n}=-5 a_{n-1}-3
a
n
=
−
5
a
n
−
1
−
3
then find the value of
a
5
a_{5}
a
5
.
\newline
Answer:
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If
a
1
=
4
a_{1}=4
a
1
=
4
and
a
n
+
1
=
(
a
n
)
2
+
3
a_{n+1}=\left(a_{n}\right)^{2}+3
a
n
+
1
=
(
a
n
)
2
+
3
then find the value of
a
4
a_{4}
a
4
.
\newline
Answer:
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If
a
1
=
9
a_{1}=9
a
1
=
9
and
a
n
+
1
=
5
a
n
+
3
a_{n+1}=5 a_{n}+3
a
n
+
1
=
5
a
n
+
3
then find the value of
a
5
a_{5}
a
5
.
\newline
Answer:
Get tutor help
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