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Math Problems
Algebra 2
Evaluate rational expressions II
Evaluate:
\newline
∑
n
=
2
5
(
−
3
x
−
4
n
)
\sum_{n=2}^{5}(-3 x-4 n)
n
=
2
∑
5
(
−
3
x
−
4
n
)
\newline
Answer:
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Evaluate:
\newline
∑
n
=
3
5
(
n
x
−
3
)
\sum_{n=3}^{5}(n x-3)
n
=
3
∑
5
(
n
x
−
3
)
\newline
Answer:
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Evaluate:
\newline
∑
n
=
3
6
(
n
x
−
3
)
\sum_{n=3}^{6}(n x-3)
n
=
3
∑
6
(
n
x
−
3
)
\newline
Answer:
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Given the function
f
(
x
)
=
5
8
x
2
+
3
f(x)=\frac{5}{8} x^{2}+3
f
(
x
)
=
8
5
x
2
+
3
, find the value of
f
(
−
2
)
f(-2)
f
(
−
2
)
in simplest form.
\newline
Answer:
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Given the function
f
(
x
)
=
−
3
4
x
+
1
f(x)=-\frac{3}{4} x+1
f
(
x
)
=
−
4
3
x
+
1
, find the value of
f
(
2
)
f(2)
f
(
2
)
in simplest form.
\newline
Answer:
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Assuming
x
x
x
and
y
y
y
are both positive, write the following expression in simplest radical form.
\newline
6
x
y
2
28
x
6
y
2
6 x y^{2} \sqrt{28 x^{6} y^{2}}
6
x
y
2
28
x
6
y
2
\newline
Answer:
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If
a
1
=
4
a_{1}=4
a
1
=
4
and
a
n
=
(
a
n
−
1
)
2
−
2
a_{n}=\left(a_{n-1}\right)^{2}-2
a
n
=
(
a
n
−
1
)
2
−
2
then find the value of
a
4
a_{4}
a
4
.
\newline
Answer:
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If
a
1
=
2
a_{1}=2
a
1
=
2
and
a
n
=
(
a
n
−
1
)
2
−
3
a_{n}=\left(a_{n-1}\right)^{2}-3
a
n
=
(
a
n
−
1
)
2
−
3
then find the value of
a
4
a_{4}
a
4
.
\newline
Answer:
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If
a
1
=
1
a_{1}=1
a
1
=
1
and
a
n
=
(
a
n
−
1
)
2
+
1
a_{n}=\left(a_{n-1}\right)^{2}+1
a
n
=
(
a
n
−
1
)
2
+
1
then find the value of
a
4
a_{4}
a
4
.
\newline
Answer:
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If
a
1
=
3
a_{1}=3
a
1
=
3
and
a
n
=
(
a
n
−
1
)
2
−
1
a_{n}=\left(a_{n-1}\right)^{2}-1
a
n
=
(
a
n
−
1
)
2
−
1
then find the value of
a
3
a_{3}
a
3
.
\newline
Answer:
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If
a
1
=
3
a_{1}=3
a
1
=
3
and
a
n
=
(
a
n
−
1
)
2
−
5
a_{n}=\left(a_{n-1}\right)^{2}-5
a
n
=
(
a
n
−
1
)
2
−
5
then find the value of
a
4
a_{4}
a
4
.
\newline
Answer:
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If
a
1
=
4
a_{1}=4
a
1
=
4
and
a
n
=
(
a
n
−
1
)
2
−
1
a_{n}=\left(a_{n-1}\right)^{2}-1
a
n
=
(
a
n
−
1
)
2
−
1
then find the value of
a
3
a_{3}
a
3
.
\newline
Answer:
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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
4
a_{4}
a
4
.
\newline
Answer:
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If
a
1
=
1
a_{1}=1
a
1
=
1
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:
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If
a
1
=
1
a_{1}=1
a
1
=
1
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
=
2
a_{1}=2
a
1
=
2
and
a
n
+
1
=
(
a
n
)
2
+
5
a_{n+1}=\left(a_{n}\right)^{2}+5
a
n
+
1
=
(
a
n
)
2
+
5
then find the value of
a
4
a_{4}
a
4
.
\newline
Answer:
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Solve for
x
x
x
and write your answer in simplest form.
\newline
2
(
−
2
x
−
4
5
)
−
2
5
=
−
(
−
10
x
−
1
)
+
7
2\left(-2 x-\frac{4}{5}\right)-\frac{2}{5}=-(-10 x-1)+7
2
(
−
2
x
−
5
4
)
−
5
2
=
−
(
−
10
x
−
1
)
+
7
\newline
Answer:
x
=
x=
x
=
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Solve for
x
x
x
and write your answer in simplest form.
\newline
−
2
=
−
1
+
6
(
−
2
5
x
−
3
5
)
-2=-1+6\left(-\frac{2}{5} x-\frac{3}{5}\right)
−
2
=
−
1
+
6
(
−
5
2
x
−
5
3
)
\newline
Answer:
x
=
x=
x
=
Get tutor help
Factor the expression completely.
\newline
x
4
+
x
2
−
20
x^{4}+x^{2}-20
x
4
+
x
2
−
20
\newline
Answer:
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Solve for
x
\mathrm{x}
x
in simplest form.
\newline
12
=
4
3
(
x
+
6
)
12=\frac{4}{3}(x+6)
12
=
3
4
(
x
+
6
)
\newline
Answer:
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Rewrite in simplest terms:
−
10
(
−
9
v
+
2
)
−
7
(
−
9
v
+
10
)
-10(-9 v+2)-7(-9 v+10)
−
10
(
−
9
v
+
2
)
−
7
(
−
9
v
+
10
)
\newline
Answer:
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Rewrite in simplest terms:
−
7
d
−
8
(
−
7
d
+
5
)
-7 d-8(-7 d+5)
−
7
d
−
8
(
−
7
d
+
5
)
\newline
Answer:
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Rewrite in simplest terms:
−
3
(
8
p
−
q
)
+
8
q
−
2
(
6
q
−
7
p
)
-3(8 p-q)+8 q-2(6 q-7 p)
−
3
(
8
p
−
q
)
+
8
q
−
2
(
6
q
−
7
p
)
\newline
Answer:
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Rewrite in simplest terms:
−
7
(
4
h
−
4
k
)
−
k
−
6
(
10
k
+
6
h
)
-7(4 h-4 k)-k-6(10 k+6 h)
−
7
(
4
h
−
4
k
)
−
k
−
6
(
10
k
+
6
h
)
\newline
Answer:
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Given that
y
=
u
5
−
2
y=u^{5}-2
y
=
u
5
−
2
, find
d
d
u
(
2
u
3
−
3
sin
y
)
\frac{d}{d u}\left(2 u^{3}-3 \sin y\right)
d
u
d
(
2
u
3
−
3
sin
y
)
in terms of only
u
u
u
.
\newline
Answer:
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Given that
x
=
u
2
+
2
x=u^{2}+2
x
=
u
2
+
2
, find
d
d
u
(
2
x
3
−
3
sin
u
)
\frac{d}{d u}\left(2 x^{3}-3 \sin u\right)
d
u
d
(
2
x
3
−
3
sin
u
)
in terms of only
u
u
u
.
\newline
Answer:
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Evaluate
∫
0
6
(
3
e
0.5
x
−
2
x
)
d
x
\int_{0}^{6}\left(3 e^{0.5 x}-2 x\right) d x
∫
0
6
(
3
e
0.5
x
−
2
x
)
d
x
and express the answer in simplest form.
\newline
Answer:
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Evaluate
∫
0
8
(
8
e
−
0.25
x
−
6
)
d
x
\int_{0}^{8}\left(8 e^{-0.25 x}-6\right) d x
∫
0
8
(
8
e
−
0.25
x
−
6
)
d
x
and express the answer in simplest form.
\newline
Answer:
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Evaluate
∫
3
4
2
x
2
−
15
x
+
22
x
−
5
d
x
\int_{3}^{4} \frac{2 x^{2}-15 x+22}{x-5} d x
∫
3
4
x
−
5
2
x
2
−
15
x
+
22
d
x
. Write your answer in simplest form with all logs condensed into a single logarithm (if necessary).
\newline
Submit Answer
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Evaluate
∫
3
4
4
x
2
−
9
x
+
1
x
−
2
d
x
\int_{3}^{4} \frac{4 x^{2}-9 x+1}{x-2} d x
∫
3
4
x
−
2
4
x
2
−
9
x
+
1
d
x
. Write your answer in simplest form with all logs condensed into a single logarithm (if necessary).
\newline
Submit Answer
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What is
y
=
−
2
9
x
+
2
y=-\frac{2}{9} x+2
y
=
−
9
2
x
+
2
written in standard form?
\newline
Choose
1
1
1
answer:
\newline
(A)
2
x
+
y
=
18
2 x+y=18
2
x
+
y
=
18
\newline
(B)
2
x
+
9
y
=
2
2 x+9 y=2
2
x
+
9
y
=
2
\newline
(C)
2
x
+
9
y
=
18
2 x+9 y=18
2
x
+
9
y
=
18
\newline
(D)
2
x
+
y
=
2
2 x+y=2
2
x
+
y
=
2
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What is
y
+
4
=
−
6
(
x
+
6
)
y+4=-6(x+6)
y
+
4
=
−
6
(
x
+
6
)
written in standard form?
\newline
Choose
1
1
1
answer:
\newline
(A)
y
=
−
6
x
+
2
y=-6 x+2
y
=
−
6
x
+
2
\newline
(B)
6
x
+
y
=
−
40
6 x+y=-40
6
x
+
y
=
−
40
\newline
(C)
6
x
+
y
=
2
6 x+y=2
6
x
+
y
=
2
\newline
(D)
y
=
−
6
x
−
40
y=-6 x-40
y
=
−
6
x
−
40
Get tutor help
What is
y
=
6
5
x
+
9
y=\frac{6}{5} x+9
y
=
5
6
x
+
9
written in standard form?
\newline
Choose
1
1
1
answer:
\newline
(A)
−
6
x
+
y
=
9
-6 x+y=9
−
6
x
+
y
=
9
\newline
(B)
−
6
x
+
5
y
=
9
-6 x+5 y=9
−
6
x
+
5
y
=
9
\newline
(C)
−
6
x
+
y
=
45
-6 x+y=45
−
6
x
+
y
=
45
\newline
(D)
−
6
x
+
5
y
=
45
-6 x+5 y=45
−
6
x
+
5
y
=
45
Get tutor help
What is
y
+
4
=
−
6
(
x
+
6
)
y+4=-6(x+6)
y
+
4
=
−
6
(
x
+
6
)
written in standard form?
\newline
Choose
1
1
1
answer:
\newline
(A)
y
=
−
6
x
−
40
y=-6 x-40
y
=
−
6
x
−
40
\newline
(B)
6
x
+
y
=
−
40
6 x+y=-40
6
x
+
y
=
−
40
\newline
(C)
6
x
+
y
=
2
6 x+y=2
6
x
+
y
=
2
\newline
(D)
y
=
−
6
x
+
2
y=-6 x+2
y
=
−
6
x
+
2
Get tutor help
What is
y
=
6
5
x
+
9
y=\frac{6}{5} x+9
y
=
5
6
x
+
9
written in standard form?
\newline
Choose
1
1
1
answer:
\newline
(A)
−
6
x
+
y
=
45
-6 x+y=45
−
6
x
+
y
=
45
\newline
(B)
−
6
x
+
5
y
=
9
-6 x+5 y=9
−
6
x
+
5
y
=
9
\newline
(C)
−
6
x
+
y
=
9
-6 x+y=9
−
6
x
+
y
=
9
\newline
(D)
−
6
x
+
5
y
=
45
-6 x+5 y=45
−
6
x
+
5
y
=
45
Get tutor help
What is
y
=
2
3
x
+
4
y=\frac{2}{3} x+4
y
=
3
2
x
+
4
written in standard form?
\newline
Choose
1
1
1
answer:
\newline
(A)
y
=
2
3
(
x
+
6
)
y=\frac{2}{3}(x+6)
y
=
3
2
(
x
+
6
)
\newline
(B)
−
2
x
+
3
y
=
12
-2 x+3 y=12
−
2
x
+
3
y
=
12
\newline
(C)
3
y
=
2
x
+
12
3 y=2 x+12
3
y
=
2
x
+
12
\newline
(D)
y
−
2
3
x
−
4
=
0
y-\frac{2}{3} x-4=0
y
−
3
2
x
−
4
=
0
Get tutor help
Evaluate the expression for
t
=
−
4.4
t = -4.4
t
=
−
4.4
.
\newline
Write your answer in simplest form.
\newline
` frac{t - 4}{t - 2} =` ____
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