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Math Problems
Algebra 2
Sum of finite series not start from 1
What is a different way to represent
2
×
3
8
2\times\frac{3}{8}
2
×
8
3
?
\newline
A.
2
+
3
8
2+\frac{3}{8}
2
+
8
3
\newline
B.
2
×
8
3
2\times\frac{8}{3}
2
×
3
8
\newline
C.
8
×
2
3
8\times\frac{2}{3}
8
×
3
2
\newline
D.
3
8
+
3
8
\frac{3}{8}+\frac{3}{8}
8
3
+
8
3
\newline
E.
3
8
×
3
8
\frac{3}{8}\times\frac{3}{8}
8
3
×
8
3
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Solve:
log
(
2
x
+
8
)
+
1
log
(
2
x
+
8
)
=
2
\log(2^{x}+8)+\frac{1}{\log(2^{x}+8)}=2
lo
g
(
2
x
+
8
)
+
l
o
g
(
2
x
+
8
)
1
=
2
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y
=
−
16
x
2
+
180
x
+
93
y=-16 x^{2}+180 x+93
y
=
−
16
x
2
+
180
x
+
93
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A tomato has a mass of
100
100
100
grams. The mass of an ant is
4.0
×
1
0
−
3
g
r
a
m
4.0 \times 10^{-3} \mathrm{gram}
4.0
×
1
0
−
3
gram
. The mass of the tomato is how many times greater than the mass of the ant?
\newline
2.5
×
1
0
−
2
2.5 \times 10^{-2}
2.5
×
1
0
−
2
\newline
2.5
×
1
0
5
2.5 \times 10^{5}
2.5
×
1
0
5
\newline
2.5
×
1
0
4
2.5 \times 10^{4}
2.5
×
1
0
4
\newline
2.5
×
1
0
−
1
2.5 \times 10^{-1}
2.5
×
1
0
−
1
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Use partial fractions to find the power series of the function:
9
x
2
+
184
(
x
2
+
16
)
(
x
2
+
36
)
\frac{9 x^{2}+184}{\left(x^{2}+16\right)\left(x^{2}+36)\right.}
(
x
2
+
16
)
(
x
2
+
36
)
9
x
2
+
184
\newline
∑
n
=
0
∞
\sum_{n=0}^{\infty}
∑
n
=
0
∞
____________
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Select all the rational numbers.
\newline
Multi-select Choices:
\newline
(A)
2
\sqrt{2}
2
\newline
(B)
64
\sqrt{64}
64
\newline
(C)
64
3
\sqrt[3]{64}
3
64
\newline
(D)
27
3
\sqrt[3]{27}
3
27
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Find the area of a rectangle with a length of
5
1
3
5 \frac{1}{3}
5
3
1
inches and a width of
2
3
\frac{2}{3}
3
2
inches
\newline
(A)
9
16
i
n
2
\frac{9}{16} \mathrm{in}^{2}
16
9
in
2
\newline
(B)
16
9
i
n
2
\frac{16}{9} \mathrm{in}^{2}
9
16
in
2
\newline
(C)
32
9
i
n
2
\frac{32}{9} \mathrm{in}^{2}
9
32
in
2
\newline
(D)
5
2
i
n
2
\frac{5}{2} \mathrm{in}^{2}
2
5
in
2
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Find the limit of the expression
lim
x
→
0
(
5
+
x
)
2
−
3
(
5
+
x
)
−
10
x
\lim _{x \rightarrow 0} \frac{(5+x)^{2}-3(5+x)-10}{x}
lim
x
→
0
x
(
5
+
x
)
2
−
3
(
5
+
x
)
−
10
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Find the sum of the first
25
25
25
terms in this geometric series:
\newline
8
+
6
+
4.5
…
8+6+4.5 \ldots
8
+
6
+
4.5
…
\newline
Choose
1
1
1
answer:
\newline
(A)
0
0
0
.
03
03
03
\newline
(B)
4
4
4
.
57
57
57
\newline
(C)
29
29
29
.
91
91
91
\newline
(D)
31
31
31
.
98
98
98
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(
10
×
9.258
,
484
)
−
(
9.619
,
98
)
2
1
0
2
×
(
10
−
1
)
\sqrt{\frac{(10 \times 9.258,484)-(9.619,98)^{2}}{10^{2} \times(10-1)}}
1
0
2
×
(
10
−
1
)
(
10
×
9.258
,
484
)
−
(
9.619
,
98
)
2
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x
4
−
20
x
3
+
94
x
2
−
34
x
−
23
=
0
x^4 -20x^3 +94x^2 -34x-23=0
x
4
−
20
x
3
+
94
x
2
−
34
x
−
23
=
0
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Find the sum of the following series. Round to the nearest hundredth if necessary.
\newline
5
+
15
+
45
+
…
+
7971615
5+15+45+\ldots+7971615
5
+
15
+
45
+
…
+
7971615
\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
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Which of the following numbers are not perfect squares? Give reasons.
\newline
(A)
841
841
841
\newline
(B)
753
753
753
\newline
(C)
1
1
1
,
285
285
285
\newline
(D)
1296
1296
1296
\newline
(E)
325
325
325
\newline
(F)
5
5
5
,
625
625
625
\newline
(G)
164
164
164
\newline
(H)
625
625
625
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The following geometric series has a sum to infinity as shown:
\newline
16
log
x
64
+
8
log
x
64
+
4
log
x
64
+
…
=
64
3
.
16 \log _{\sqrt{x}} 64+8 \log _{\sqrt{x}} 64+4 \log _{\sqrt{x}} 64+\ldots=\frac{64}{3} .
16
lo
g
x
64
+
8
lo
g
x
64
+
4
lo
g
x
64
+
…
=
3
64
.
\newline
Calculate the value of
x
x
x
.
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1
3
×
2
5
+
4
5
×
1
5
−
1
2
×
3
5
\frac{1}{3} \times \frac{2}{5}+\frac{4}{5} \times \frac{1}{5}-\frac{1}{2} \times \frac{3}{5}
3
1
×
5
2
+
5
4
×
5
1
−
2
1
×
5
3
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C
=
2
×
10.000
×
20.000.000
1.5
%
C=\sqrt{\frac{2 \times 10.000 \times 20.000 .000}{1.5 \%}}
C
=
1.5%
2
×
10.000
×
20.000.000
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Ed is drawing stars in his notebook. He draws
335
335
335
stars on the first page,
349
349
349
stars on the second page,
361
361
361
stars on the third page, and
371
371
371
stars on the fourth page. What kind of sequence is this?
\newline
Choices:
\newline
(A) arithmetic
\newline
(B) geometric
\newline
(C) both
\newline
(D) neither
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What is the value of
k
k
k
that makes
49
x
4
−
k
x
2
y
2
+
36
y
4
49x^{4}-kx^{2}y^{2}+36y^{4}
49
x
4
−
k
x
2
y
2
+
36
y
4
a perfect square trinomial?
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lim
x
→
0
4
x
3
−
2
x
2
+
x
3
x
2
+
2
x
\lim _{x \rightarrow 0} \frac{4 x^{3}-2 x^{2}+x}{3 x^{2}+2 x}
lim
x
→
0
3
x
2
+
2
x
4
x
3
−
2
x
2
+
x
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Using synthetic division, determine the quotient of the expression below.
\newline
(
1
+
4
x
2
−
x
−
x
4
)
(
2
−
x
)
\frac{(1+4x^{2}-x-x^{4})}{(2-x)}
(
2
−
x
)
(
1
+
4
x
2
−
x
−
x
4
)
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Find the PRODUCT of the solutions to
\newline
2
(
x
+
2
)
4
−
6
=
156
2(x+2)^{4}-6=156
2
(
x
+
2
)
4
−
6
=
156
\newline
A)
−
5
-5
−
5
\newline
B)
2
2
2
\newline
C)
−
2
-2
−
2
\newline
D)
3
3
3
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What is the simplest form of the following fraction?
\newline
32
40
\frac{32}{40}
40
32
\newline
A.
4
6
\frac{4}{6}
6
4
\newline
B.
4
7
\frac{4}{7}
7
4
\newline
C.
4
5
\frac{4}{5}
5
4
\newline
D.
8
9
\frac{8}{9}
9
8
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Find the sum of the first
6
6
6
terms of the following sequence. Round to the nearest hundredth if necessary.
\newline
8
,
12
,
18
,
…
8, \quad 12, \quad 18, \ldots
8
,
12
,
18
,
…
\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:
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Find the sum of the first
10
10
10
terms of the following sequence. Round to the nearest hundredth if necessary.
\newline
27
,
18
,
12
,
…
27, \quad 18, \quad 12, \ldots
27
,
18
,
12
,
…
\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
8
8
8
terms of the following sequence. Round to the nearest hundredth if necessary.
\newline
9
,
−
12
,
16
,
…
9, \quad-12, \quad 16, \ldots
9
,
−
12
,
16
,
…
\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
10
10
10
terms of the following sequence. Round to the nearest hundredth if necessary.
\newline
28
,
35
,
43.75
,
…
28, \quad 35, \quad 43.75, \ldots
28
,
35
,
43.75
,
…
\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
8
8
8
terms of the following sequence. Round to the nearest hundredth if necessary.
\newline
50
,
44
,
38.72
,
…
50, \quad 44, \quad 38.72, \ldots
50
,
44
,
38.72
,
…
\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
9
9
9
terms of the following sequence. Round to the nearest hundredth if necessary.
\newline
75
,
66
,
58.08
,
…
75, \quad 66, \quad 58.08, \ldots
75
,
66
,
58.08
,
…
\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
7
,
−
35
,
175
,
…
7, \quad-35, \quad 175, \ldots
7
,
−
35
,
175
,
…
\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
8
8
8
terms of the following sequence. Round to the nearest hundredth if necessary.
\newline
64
,
80
,
100
,
…
64, \quad 80, \quad 100, \ldots
64
,
80
,
100
,
…
\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
10
10
10
terms of the following sequence. Round to the nearest hundredth if necessary.
\newline
25
,
19.5
,
15.21
,
…
25, \quad 19.5, \quad 15.21, \ldots
25
,
19.5
,
15.21
,
…
\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
6
6
6
terms of the following sequence. Round to the nearest hundredth if necessary.
\newline
32
,
16
,
8
,
…
32, \quad 16, \quad 8, \ldots
32
,
16
,
8
,
…
\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
Solve the equation by factoring:
\newline
168
x
+
3
x
2
−
3
x
3
=
0
168 x+3 x^{2}-3 x^{3}=0
168
x
+
3
x
2
−
3
x
3
=
0
\newline
Answer:
x
=
x=
x
=
Get tutor help
Solve the equation by factoring:
\newline
34
x
2
−
140
x
−
2
x
3
=
0
34 x^{2}-140 x-2 x^{3}=0
34
x
2
−
140
x
−
2
x
3
=
0
\newline
Answer:
x
=
x=
x
=
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Solve the equation by factoring:
\newline
2
x
3
+
2
x
2
−
112
x
=
0
2 x^{3}+2 x^{2}-112 x=0
2
x
3
+
2
x
2
−
112
x
=
0
\newline
Answer:
x
=
x=
x
=
Get tutor help
Evaluate:
∫
0
1
[
e
−
t
i
+
1
t
+
1
j
]
d
t
\int_{0}^{1} \left[ e^{-t} \mathbf{i} + \frac{1}{t+1} \mathbf{j} \right] dt
∫
0
1
[
e
−
t
i
+
t
+
1
1
j
]
d
t
Get tutor help
Find the sum of the first
25
25
25
terms in this geometric series:
\newline
8
+
6
+
4.5
8+6+4.5
8
+
6
+
4.5
.
\newline
Choose
1
1
1
answer:
\newline
(A)
0.03
0.03
0.03
\newline
(B)
4.57
4.57
4.57
\newline
(C)
29.91
29.91
29.91
\newline
(D)
31.98
31.98
31.98
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Find the sum of the first
25
25
25
terms in this geometric series:
\newline
8
+
6
+
4.5
+
.
.
.
8+6+4.5+...
8
+
6
+
4.5
+
...
\newline
Choose
1
1
1
answer:
\newline
(A)
0.03
0.03
0.03
\newline
(B)
4.57
4.57
4.57
\newline
(C)
29.91
29.91
29.91
\newline
(D)
31.98
31.98
31.98
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lim
x
→
0
(
1
−
2
x
)
1
x
\lim_{x \to 0}(1-2x)^{\frac{1}{x}}
x
→
0
lim
(
1
−
2
x
)
x
1
Get tutor help
Find the sum of the finite series.
\newline
∑
i
=
3
120
i
(
i
−
5
)
\sum_{i=3}^{120} i(i-5)
∑
i
=
3
120
i
(
i
−
5
)
\newline
______
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