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Math Problems
Algebra 1
Evaluate integers raised to rational exponents
g
(
x
)
=
4
(
3
)
2
+
5
(
3
)
2
g(x)=\frac{4(3)^{2}+5}{(3)^{2}}
g
(
x
)
=
(
3
)
2
4
(
3
)
2
+
5
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5
5
5
. Найдите обьем тела, полученного при вращении вокруг оеи абецисе
11
11
11
main криволинейной трапеции, ограниченной линимми
\newline
y
=
4
x
;
y
=
1
4
x
2
y=\sqrt{4 x} ; y=\frac{1}{4} x^{2}
y
=
4
x
;
y
=
4
1
x
2
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f
(
x
)
=
3
x
+
6
x
5
−
4
x
3
+
1
f(x)=3^{x}+6 \sqrt[5]{x}-\frac{4}{\sqrt[3]{x}}+1
f
(
x
)
=
3
x
+
6
5
x
−
3
x
4
+
1
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f
(
x
)
=
x
−
1
x
2
+
2
x
+
1
f(x)=\frac{x-1}{x^{2}+2 x+1}
f
(
x
)
=
x
2
+
2
x
+
1
x
−
1
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f
′
(
x
)
f'(x)
f
′
(
x
)
=
12
e
x
12e^x
12
e
x
and
f
(
4
)
f(4)
f
(
4
)
=
−
16
+
12
e
4
-16 + 12e^4
−
16
+
12
e
4
. Find
f
(
0
)
f(0)
f
(
0
)
.
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Which of these expressions are equivalent to
−
7
1
2
-7 \frac{1}{2}
−
7
2
1
? Choose ALL the correct expressions.
\newline
−
8
+
(
−
1
2
)
7
+
(
−
1
2
)
−
8
+
1
2
-8+\left(-\frac{1}{2}\right) \quad 7+\left(-\frac{1}{2}\right) \quad-8+\frac{1}{2}
−
8
+
(
−
2
1
)
7
+
(
−
2
1
)
−
8
+
2
1
\newline
−
7
+
1
2
−
7
+
(
−
1
2
)
-7+\frac{1}{2} \quad-7+\left(-\frac{1}{2}\right)
−
7
+
2
1
−
7
+
(
−
2
1
)
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Complete each equation.
\newline
6
+
(
−
1
4
)
=
?
6+\left(-\frac{1}{4}\right)=\quad ?
6
+
(
−
4
1
)
=
?
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tan
(
−
4
π
3
)
\tan \left(-\frac{4 \pi}{3}\right)
tan
(
−
3
4
π
)
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Draw the number line and mark the following rational number on it :- b)
1
5
\frac{1}{5}
5
1
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x
−
6
≥
−
20
\dfrac{x}{-6}\geq-20
−
6
x
≥
−
20
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x
2
−
14
x
+
24
x
2
x
+
6
>
x
\frac{x^{2}-14 x+24 x}{2 x+6}>x
2
x
+
6
x
2
−
14
x
+
24
x
>
x
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Which of the following is equivalent to the expression
x
4
−
6
x
2
+
9
x^{4}-6 x^{2}+9
x
4
−
6
x
2
+
9
?
\newline
I.
(
x
+
3
)
2
(
x
−
3
)
2
(x+3)^{2}(x-3)^{2}
(
x
+
3
)
2
(
x
−
3
)
2
\newline
II.
(
x
2
−
3
)
2
\left(x^{2}-3\right)^{2}
(
x
2
−
3
)
2
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x
3
−
2
x
+
4
÷
x
−
2
x^{3}-2x+4\div x-2
x
3
−
2
x
+
4
÷
x
−
2
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f
(
x
)
=
4
x
3
+
x
−
1
f(x)=\frac{4}{x^{3}}+\sqrt{x}-1
f
(
x
)
=
x
3
4
+
x
−
1
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-
40
+
(
−
1
)
−
(
2
)
×
6
÷
3
−
2
40 +{ (-1)- (2)} \times 6 \div{ 3-2}
40
+
(
−
1
)
−
(
2
)
×
6
÷
3
−
2
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Perform the following operations in the proper order.
\newline
19
+
18
÷
(
−
3
)
−
6
(
5
)
19+18 \div(-3)-6(5)
19
+
18
÷
(
−
3
)
−
6
(
5
)
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What is the value of the expression shown below when
\newline
x
=
7
x=7
x
=
7
?
\newline
3
x
2
−
2
x
+
3
3x^{2}-2x+3
3
x
2
−
2
x
+
3
\newline
A
31
31
31
\newline
B
50
50
50
\newline
C
136
136
136
\newline
D
164
164
164
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1
−
cos
2
x
1
+
cos
x
\frac{1-\cos ^{2} x}{1+\cos x}
1
+
c
o
s
x
1
−
c
o
s
2
x
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Solve each of the following using factoring.
\newline
50
x
3
+
125
x
2
−
18
x
−
45
=
0
50x^{3}+125x^{2}-18x-45=0
50
x
3
+
125
x
2
−
18
x
−
45
=
0
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x
−
20
=
2
3
x
x-20=\frac{2}{3} x
x
−
20
=
3
2
x
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subtract
\newline
−
4
x
+
1
-4x+1
−
4
x
+
1
from
\newline
−
7
x
2
+
4
x
+
-7x^{2}+4x+
−
7
x
2
+
4
x
+
\newline
Answer Attempt
2
2
2
out of
2
2
2
\newline
◻
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∫
y
(
1
−
1
y
)
d
y
\int \sqrt{y}\left(1-\frac{1}{y}\right) d y
∫
y
(
1
−
y
1
)
d
y
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sin
x
+
tan
x
−
sin
2
x
cos
x
−
1
=
0
\sin x+\tan x-\frac{\sin ^{2} x}{\cos x}-1=0
sin
x
+
tan
x
−
c
o
s
x
s
i
n
2
x
−
1
=
0
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7
(
3
)
+
6
2
−
9
7(3)+\frac{6}{2}-9
7
(
3
)
+
2
6
−
9
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egin{equation}
−
9
-9
−
9
+(
2
2
2
-x)+
8
8
8
xegin{equation}
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What could be the value of
x
x
x
in the following equation? Select all that apply.
\newline
x
3
=
1
125
x^3 = \frac{1}{125}
x
3
=
125
1
\newline
Multi-select Choices:
\newline
(A)
−
1
125
3
-\sqrt[3]{\frac{1}{125}}
−
3
125
1
\newline
(B)
−
1
5
-\frac{1}{5}
−
5
1
\newline
(C)
1
5
\frac{1}{5}
5
1
\newline
(D)
1
125
3
\sqrt[3]{\frac{1}{125}}
3
125
1
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What could be the value of
x
x
x
in the following equation? Select all that apply.
\newline
x
3
=
1
27
x^3 = \frac{1}{27}
x
3
=
27
1
\newline
Multi-select Choices:
\newline
(A)
1
27
3
\sqrt[3]{\frac{1}{27}}
3
27
1
\newline
(B)
1
3
\frac{1}{3}
3
1
\newline
(C)
−
1
27
3
-\sqrt[3]{\frac{1}{27}}
−
3
27
1
\newline
(D)
−
1
3
-\frac{1}{3}
−
3
1
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cos
x
=
−
1
2
\cos x=-\frac{1}{2}
cos
x
=
−
2
1
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(vi)
2
2
3
+
3
1
2
2 \frac{2}{3}+3 \frac{1}{2}
2
3
2
+
3
2
1
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−
6
−
(
−
3
)
-6 - (-3)
−
6
−
(
−
3
)
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What is the value of
2
tan
−
1
(
1
2
)
2\tan^{-1} \left(\frac{1}{2}\right)
2
tan
−
1
(
2
1
)
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9
÷
9
7
9 \div \frac{9}{7}
9
÷
7
9
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9
÷
5
6
9 \div \frac{5}{6}
9
÷
6
5
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4
x
+
(
6
−
2
x
)
4x+(6-2x)
4
x
+
(
6
−
2
x
)
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Negative / Zero Exponents (Level
2
2
2
)
\newline
Score:
1
/
2
1 / 2
1/2
\newline
Penalty:
1
1
1
off
\newline
Question
\newline
Which expression is equivalent to
6
8
×
6
7
6
−
5
\frac{6^{8} \times 6^{7}}{6^{-5}}
6
−
5
6
8
×
6
7
?
\newline
Answer
\newline
6
10
6^{10}
6
10
\newline
6
20
6^{20}
6
20
\newline
6
−
20
6^{-20}
6
−
20
\newline
6
22
6^{22}
6
22
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x
=
−
16
±
1
6
2
−
4
(
−
6
)
(
−
8
)
−
12
x=\frac{-16 \pm \sqrt{16^{2}-4(-6)(-8)}}{-12}
x
=
−
12
−
16
±
1
6
2
−
4
(
−
6
)
(
−
8
)
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x
2
+
y
2
4
=
1
\frac{x^{2}+y^{2}}{4}=1
4
x
2
+
y
2
=
1
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−
3
x
−
1
-3 x^{-1}
−
3
x
−
1
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Convert each coordinate then graph on the given polar coordinate system. Label your point.
\newline
A.
(
−
2
,
−
π
3
)
\left(-2,-\frac{\pi}{3}\right)
(
−
2
,
−
3
π
)
\newline
B.
(
5
,
−
4
π
3
)
\left(5,-\frac{4 \pi}{3}\right)
(
5
,
−
3
4
π
)
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55
55
55
.
\newline
x
−
6
x
2
−
5
x
+
6
=
A
x
−
2
+
B
x
−
3
⇒
5
A
−
B
=
?
\begin{array}{l} \frac{x-6}{x^{2}-5 x+6}=\frac{A}{x-2}+\frac{B}{x-3} \\ \Rightarrow 5 A-B=? \end{array}
x
2
−
5
x
+
6
x
−
6
=
x
−
2
A
+
x
−
3
B
⇒
5
A
−
B
=
?
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cos
(
7
π
2
)
\cos \left(\frac{7 \pi}{2}\right)
cos
(
2
7
π
)
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3
x
4
−
1
=
7
3 \frac{x}{4}-1=7
3
4
x
−
1
=
7
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f
(
x
)
=
x
2
+
3
x
+
2
x
−
1
f(x)=\frac{x^{2}+3 x+2}{x-1}
f
(
x
)
=
x
−
1
x
2
+
3
x
+
2
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e
−
i
−
i
⋅
(
−
2
i
)
\frac{e^{-i}}{-i \cdot(-2 i)}
−
i
⋅
(
−
2
i
)
e
−
i
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2
+
3
4
2+\frac{3}{4}
2
+
4
3
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−
∣
3
11
−
3
2
∣
-\left|\frac{3}{11}-3^{2}\right|
−
∣
∣
11
3
−
3
2
∣
∣
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8
5
÷
8
3
)
×
8
−
2
\left.8^{5} \div 8^{3}\right) \times 8^{-2}
8
5
÷
8
3
)
×
8
−
2
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Factor the expression below.
\newline
(
6
x
3
+
12
x
2
)
(
−
x
−
2
y
)
\left(6 x^{3}+12 x^{2}\right)(-x-2 y)
(
6
x
3
+
12
x
2
)
(
−
x
−
2
y
)
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7
−
24
/
8
∗
4
+
6
7-24/8*4+6
7
−
24/8
∗
4
+
6
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x
−
7
4
=
5
6
x-\frac{7}{4}=\frac{5}{6}
x
−
4
7
=
6
5
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1
2
3
...
5
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