<span>Z $ xy then Z = Kxy. When x = 2 and y = 3, and Z = 60, our constant of variation becomes
60 = K * 2 * 3
K = 10. Our constant of proportionality equals 10. We would need that in the second part of the equation.
When x = 4 and y = 9, we have
Z = 10 * 4 * 9 = 360</span>
Move all terms not containing
|
5
−
8
x
|
|
5
-
8
x
|
to the right side of the inequality.
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Add
7
7
to both sides of the inequality.
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5
−
8
x
|
<
8
+
7
|
5
-
8
x
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<
8
+
7
Add
8
8
and
7
7
.
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5
−
8
x
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<
15
|
5
-
8
x
|
<
15
Remove the absolute value term. This creates a
±
±
on the right side of the inequality because
|
x
|
=
±
x
|
x
|
=
±
x
.
5
−
8
x
<
±
15
5
-
8
x
<
±
15
Set up the positive portion of the
±
±
solution.
5
−
8
x
<
15
5
-
8
x
<
15
Solve the first inequality for
x
x
.
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x
>
−
5
4
x
>
-
5
4
Set up the negative portion of the
±
±
solution. When solving the negative portion of an inequality, flip the direction of the inequality sign.
5
−
8
x
>
−
15
5
-
8
x
>
-
15
Solve the second inequality for
x
x
.
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x
<
5
2
x
<
5
2
Set up the intersection.
x
>
−
5
4
x
>
-
5
4
and
x
<
5
2
x
<
5
2
Find the intersection between the sets.
−
5
4
<
x
<
5
2
-
5
4
<
x
<
5
2
The result can be shown in multiple forms.
Inequality Form:
−
5
4
<
x
<
5
2
-
5
4
<
x
<
5
2
Interval Notation:
(
−
5
4
,
5
2
)
(
-
5
4
,
5
2
)
Fraction of the total was seen=(number of people were seen ) /(Total number of people)
Data:
number of people were seen=440
Total number of people=people saw +people didn´t see=440+360=800
Fraction of the toatal was seen=440/800=11/20
Answer: 11/20.
X+12y=68
x=8y-12
(8y-12) +12y=68
20y-12=68
20y=80
y=40
x=8(40)-12
x=320-12
x=308
