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Math Problems
Algebra 2
Simplify variable expressions using properties
FIND
x
,
y
,
z
−
3
3
+
4
y
=
1
x
−
z
3
x
+
y
−
1
=
−
z
−
1
6
z
5
y
+
8
=
−
1
\begin{array}{l}\text { FIND } x, y, z \\ -\frac{3}{3+4 y}=\frac{1}{x-z} \\ \frac{3}{x+y-1}=-z^{-1} \\ \frac{6 z}{5 y+8}=-1\end{array}
FIND
x
,
y
,
z
−
3
+
4
y
3
=
x
−
z
1
x
+
y
−
1
3
=
−
z
−
1
5
y
+
8
6
z
=
−
1
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Дано:
\newline
1
1
1
)
u
(
x
0
)
=
4
i
u
′
(
x
0
)
=
−
3
u\left(x_{0}\right)=4 \mathrm{i} u^{\prime}\left(x_{0}\right)=-3
u
(
x
0
)
=
4
i
u
′
(
x
0
)
=
−
3
;
\newline
2
2
2
)
v
(
x
0
)
=
−
3
v\left(x_{0}\right)=-3
v
(
x
0
)
=
−
3
і
v
′
(
x
0
)
=
3
v^{\prime}\left(x_{0}\right)=3
v
′
(
x
0
)
=
3
;
\newline
3
3
3
)
f
(
x
)
=
u
(
x
)
v
(
x
)
f(x)=u(x) v(x)
f
(
x
)
=
u
(
x
)
v
(
x
)
\newline
Обчисли значення
f
′
(
x
0
)
f^{\prime}\left(x_{0}\right)
f
′
(
x
0
)
:
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Perform the operation and express your answer as a single fraction in simplest form.
\newline
4
+
1
3
x
4+\frac{1}{3 x}
4
+
3
x
1
\newline
Answer:
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Simplify the fraction completely. If the fraction does not simplify, submit the fraction in its current form.
\newline
6
x
4
7
x
3
\frac{6 x^{4}}{7 x^{3}}
7
x
3
6
x
4
\newline
Answer:
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Simplify the fraction completely. If the fraction does not simplify, submit the fraction in its current form.
\newline
24
x
2
30
\frac{24 x^{2}}{30}
30
24
x
2
\newline
Answer:
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Given the definitions of
f
(
x
)
f(x)
f
(
x
)
and
g
(
x
)
g(x)
g
(
x
)
below, find the value of
f
(
g
(
−
2
)
)
f(g(-2))
f
(
g
(
−
2
))
.
\newline
f
(
x
)
=
3
x
2
+
x
+
7
g
(
x
)
=
2
x
+
8
\begin{array}{l} f(x)=3 x^{2}+x+7 \\ g(x)=2 x+8 \end{array}
f
(
x
)
=
3
x
2
+
x
+
7
g
(
x
)
=
2
x
+
8
\newline
Answer:
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(a)
\newline
4
x
+
5
y
=
9
4
y
3
−
x
2
=
−
7
\begin{array}{l} 4 x+5 y=9 \\ \frac{4 y}{3}-\frac{x}{2}=-7 \end{array}
4
x
+
5
y
=
9
3
4
y
−
2
x
=
−
7
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3.9279
(
1
−
(
−
0.3086
)
)
2
8
−
1
8
−
2
=
3.9279 \sqrt{(1-(-0.3086))^{2} \frac{8-1}{8-2}}=
3.9279
(
1
−
(
−
0.3086
)
)
2
8
−
2
8
−
1
=
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Simplify the following fraction:
42
90
\frac{42}{90}
90
42
\newline
Answer:
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Simplify the following fraction:
24
88
\frac{24}{88}
88
24
\newline
Answer:
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Simplify the following fraction:
50
75
\frac{50}{75}
75
50
\newline
Answer:
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Simplify the following fraction:
24
60
\frac{24}{60}
60
24
\newline
Answer:
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Simplify the following fraction:
20
35
\frac{20}{35}
35
20
\newline
Answer:
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Simplify the following fraction:
25
50
\frac{25}{50}
50
25
\newline
Answer:
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Simplify the following fraction:
56
88
\frac{56}{88}
88
56
\newline
Answer:
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Simplify the following fraction:
30
40
\frac{30}{40}
40
30
\newline
Answer:
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Simplify the following fraction:
25
100
\frac{25}{100}
100
25
\newline
Answer:
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Simplify the following fraction:
40
90
\frac{40}{90}
90
40
\newline
Answer:
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Simplify the following fraction:
33
55
\frac{33}{55}
55
33
\newline
Answer:
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Simplify the expression to a + bi form:
\newline
(
1
−
6
i
)
(
6
−
3
i
)
(1-6 i)(6-3 i)
(
1
−
6
i
)
(
6
−
3
i
)
\newline
Answer:
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Simplify the expression to a + bi form:
\newline
(
6
−
5
i
)
2
(6-5 i)^{2}
(
6
−
5
i
)
2
\newline
Answer:
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Simplify the expression to a + bi form:
\newline
(
−
3
+
5
i
)
2
(-3+5 i)^{2}
(
−
3
+
5
i
)
2
\newline
Answer:
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Simplify the expression to a + bi form:
\newline
(
11
+
8
i
)
2
(11+8 i)^{2}
(
11
+
8
i
)
2
\newline
Answer:
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Simplify the expression to a + bi form:
\newline
(
7
+
2
i
)
(
−
8
−
3
i
)
(7+2 i)(-8-3 i)
(
7
+
2
i
)
(
−
8
−
3
i
)
\newline
Answer:
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Simplify the expression to a + bi form:
\newline
(
2
−
7
i
)
(
5
−
7
i
)
(2-7 i)(5-7 i)
(
2
−
7
i
)
(
5
−
7
i
)
\newline
Answer:
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Simplify the expression to a + bi form:
\newline
(
−
1
−
4
i
)
(
2
+
8
i
)
(-1-4 i)(2+8 i)
(
−
1
−
4
i
)
(
2
+
8
i
)
\newline
Answer:
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Simplify the expression to a + bi form:
\newline
(
−
3
−
i
)
2
(-3-i)^{2}
(
−
3
−
i
)
2
\newline
Answer:
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Simplify the expression to a + bi form:
\newline
(
−
9
+
2
i
)
2
(-9+2 i)^{2}
(
−
9
+
2
i
)
2
\newline
Answer:
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Simplify the expression to a + bi form:
\newline
(
10
+
2
i
)
2
(10+2 i)^{2}
(
10
+
2
i
)
2
\newline
Answer:
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Simplify the expression to a + bi form:
\newline
(
1
+
7
i
)
(
11
+
8
i
)
(1+7 i)(11+8 i)
(
1
+
7
i
)
(
11
+
8
i
)
\newline
Answer:
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Express as a complex number in simplest a+bi form:
\newline
8
+
3
i
−
9
−
7
i
\frac{8+3 i}{-9-7 i}
−
9
−
7
i
8
+
3
i
\newline
Answer:
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Express as a complex number in simplest a+bi form:
\newline
−
8
+
i
9
+
10
i
\frac{-8+i}{9+10 i}
9
+
10
i
−
8
+
i
\newline
Answer:
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Express as a complex number in simplest a+bi form:
\newline
−
10
+
6
i
5
−
7
i
\frac{-10+6 i}{5-7 i}
5
−
7
i
−
10
+
6
i
\newline
Answer:
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Express as a complex number in simplest a+bi form:
\newline
−
17
+
3
i
7
−
10
i
\frac{-17+3 i}{7-10 i}
7
−
10
i
−
17
+
3
i
\newline
Answer:
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Express as a complex number in simplest a+bi form:
\newline
4
−
2
i
9
−
8
i
\frac{4-2 i}{9-8 i}
9
−
8
i
4
−
2
i
\newline
Answer:
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Express as a complex number in simplest a+bi form:
\newline
9
−
7
i
−
3
−
2
i
\frac{9-7 i}{-3-2 i}
−
3
−
2
i
9
−
7
i
\newline
Answer:
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Simplify the expression:
\newline
(
2
z
)
(
3
)
=
(2z)(3) =
(
2
z
)
(
3
)
=
_____
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Simplify the expression:
\newline
2
(
2
t
)
=
2(2t) =
2
(
2
t
)
=
_____
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Simplify the expression:
\newline
2
(
2
c
)
=
2(2c) =
2
(
2
c
)
=
_____
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Simplify the expression:
\newline
5
(
5
p
)
=
5(5p) =
5
(
5
p
)
=
_____
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Simplify the expression:
\newline
2
(
2
d
)
=
2(2d) =
2
(
2
d
)
=
_____
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Simplify the expression:
\newline
2
(
3
x
)
=
2(3x) =
2
(
3
x
)
=
_____
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Simplify the expression:
\newline
3
(
3
k
)
=
3(3k) =
3
(
3
k
)
=
_____
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Simplify the expression:
\newline
(
4
c
)
(
5
)
=
(4c)(5) =
(
4
c
)
(
5
)
=
_____
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Simplify the expression:
\newline
2
(
3
z
)
=
2(3z) =
2
(
3
z
)
=
_____
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Simplify the expression:
\newline
3
(
2
z
)
=
3(2z) =
3
(
2
z
)
=
_____
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Simplify the expression:
\newline
7
(
2
v
)
=
7(2v) =
7
(
2
v
)
=
_____
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Simplify the expression:
\newline
3
(
3
n
)
=
3(3n) =
3
(
3
n
)
=
_____
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Simplify the expression:
\newline
2
(
6
m
)
=
2(6m) =
2
(
6
m
)
=
_____
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Simplify the expression:
\newline
4
(
2
z
)
=
4(2z) =
4
(
2
z
)
=
_____
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