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The hanger image below represents a balanced equation.
\newline
Write an equation to represent the image.
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Math Problems
Algebra 1
Identify direct variation and inverse variation
Full solution
Q.
The hanger image below represents a balanced equation.
\newline
Write an equation to represent the image.
Count Shapes for Balance:
Count the number of shapes on each side of the hanger to determine the balance.
Assign Values to Shapes:
Let's say each triangle represents '
x
x
x
' and each circle represents '
1
1
1
'.
Left Side Count:
On the left side of the hanger, there are
3
3
3
triangles and
2
2
2
circles.
Right Side Count:
On the right side of the hanger, there are
2
2
2
triangles and
4
4
4
circles.
Write Balance Equation:
Write the equation representing the balance:
3
x
+
2
=
2
x
+
4
3x + 2 = 2x + 4
3
x
+
2
=
2
x
+
4
.
Simplify Equation:
Subtract
2
x
2x
2
x
from both sides to simplify the equation:
x
+
2
=
4
x + 2 = 4
x
+
2
=
4
.
More problems from Identify direct variation and inverse variation
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Write an expression to represent:
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3
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2
2
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Write an expression to represent:
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Question
What happens to the value of the expression
35
+
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35+k
35
+
k
as
k
k
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decreases?
\newline
Choose
1
1
1
answer:
\newline
(A) It increases.
\newline
(B) It decreases.
\newline
(C) It stays the same.
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Question
Let
h
(
x
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=
x
−
5
h(x)=x^{-5}
h
(
x
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=
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h
′
(
2
)
=
h^{\prime}(2)=
h
′
(
2
)
=
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Question
D
=
[
4
−
1
2
−
1
]
\mathrm{D}=\left[\begin{array}{ll}4 & -1 \\ 2 & -1\end{array}\right]
D
=
[
4
2
−
1
−
1
]
and
A
=
[
3
1
0
2
1
−
2
]
A=\left[\begin{array}{rrr} 3 & 1 & 0 \\ 2 & 1 & -2 \end{array}\right]
A
=
[
3
2
1
1
0
−
2
]
\newline
Let
H
=
D
A
\mathrm{H}=\mathrm{DA}
H
=
DA
. Find
H
\mathrm{H}
H
.
\newline
H
=
\mathbf{H}=
H
=
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Posted 3 months ago
Question
B
=
[
4
4
1
0
−
2
1
]
and
F
=
[
0
3
0
1
]
B=\left[\begin{array}{rr} 4 & 4 \\ 1 & 0 \\ -2 & 1 \end{array}\right] \text { and } F=\left[\begin{array}{ll} 0 & 3 \\ 0 & 1 \end{array}\right]
B
=
⎣
⎡
4
1
−
2
4
0
1
⎦
⎤
and
F
=
[
0
0
3
1
]
\newline
Let
H
=
B
F
\mathrm{H}=\mathrm{BF}
H
=
BF
. Find
H
\mathrm{H}
H
.
\newline
H
=
\mathbf{H}=
H
=
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Question
F
=
[
2
3
0
5
−
1
−
1
]
F=\left[\begin{array}{rr}2 & 3 \\ 0 & 5 \\ -1 & -1\end{array}\right]
F
=
⎣
⎡
2
0
−
1
3
5
−
1
⎦
⎤
and
D
=
[
−
1
0
4
2
]
\mathrm{D}=\left[\begin{array}{rr} -1 & 0 \\ 4 & 2 \end{array}\right]
D
=
[
−
1
4
0
2
]
\newline
Let
H
=
F
D
\mathrm{H}=\mathrm{FD}
H
=
FD
. Find
H
\mathrm{H}
H
.
\newline
H
=
\mathbf{H}=
H
=
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Posted 3 months ago
Question
E
=
[
1
−
1
5
5
5
0
]
\mathrm{E}=\left[\begin{array}{rrr}1 & -1 & 5 \\ 5 & 5 & 0\end{array}\right]
E
=
[
1
5
−
1
5
5
0
]
and
F
=
[
−
2
−
1
5
2
5
−
2
]
F=\left[\begin{array}{rr}-2 & -1 \\ 5 & 2 \\ 5 & -2\end{array}\right]
F
=
⎣
⎡
−
2
5
5
−
1
2
−
2
⎦
⎤
\newline
Let
H
=
E
F
\mathrm{H}=\mathrm{EF}
H
=
EF
. Find
H
\mathrm{H}
H
.
\newline
H
=
\mathbf{H}=
H
=
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Posted 3 months ago
Question
C
=
[
−
1
−
2
2
]
and
D
=
[
2
1
]
\mathrm{C}=\left[\begin{array}{r} -1 \\ -2 \\ 2 \end{array}\right] \text { and } \mathrm{D}=\left[\begin{array}{ll} 2 & 1 \end{array}\right]
C
=
⎣
⎡
−
1
−
2
2
⎦
⎤
and
D
=
[
2
1
]
\newline
Let
H
=
C
D
\mathrm{H}=\mathrm{CD}
H
=
CD
. Find
H
\mathrm{H}
H
.
\newline
H
=
\mathbf{H}=
H
=
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