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Serggg [28]
3 years ago
9

Write the interval (5, 100] as an inequality and using set notation

Mathematics
1 answer:
Arada [10]3 years ago
7 0
An inequality is a statement that shows relation between two values, when the two values are not equal.
The inequality is opposite than equality.
So, the interval (5,100] means that it contains all number from number 5 (not and 5)  till 100, including 100. We can see this from the bracket's type. 
For a value x in this interval we can write the inequality:
5<x<=100
x is bigger than 5 , and smaller or equal 100
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Answer:

\large\boxed{y=-\dfrac{3}{2}x+16\dfrac{1}{2}\to y=-1.5x+16.5}

Step-by-step explanation:

The slope-intercept form of an equation of a line:

y=mx+b

<em>m</em><em> - slope</em>

<em>b</em><em> - y-intercept</em>

The formula of a slope:

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We have the points (3, 12) and (5, 9).

Substitute:

m=\dfrac{9-12}{5-3}=\dfrac{-3}{2}=-\dfrac{3}{2}

Put the value of a slope and coordinates of the point (3, 12) to the equation of a line:

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12=-4\dfrac{1}{2}+b          <em>add 4\dfrac{1}{2} to both sides</em>

16\dfrac{1}{2}=b\to b=16\dfrac{1}{2}

Finally:

y=-\dfrac{3}{2}x+16\dfrac{1}{2}

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Step-by-step explanation:

The answer with explanation is in the image.

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