Answer:
3/2 < x < 2
Step-by-step explanation:
We assume the problem is ...
[tek]\dfrac{1}{x-2}<-2[/tex]
This will not be true for x-2 > 0 because that would make the left side positive. So, we must have x < 2, which makes the denominator negative. Multiplying by (x-2), we get ...
1 > -2(x -2)
1 > -2x +4
2x > 3 . . . . . . add 2x-1
x > 3/2
From above, we also have x < 2, so the solution set is ...
3/2 < x < 2
Answer:
a). y = 0.25x + 15
b). x = 480 cups
Step-by-step explanation:
(a). Let the equation of the linear function passing through a point (x', y') is,
y - y' = m(x - x')
'm' = slope of the line
b = y-intercept
Two points lying on the linear function will be (200, 65) and (250, 77.5).
Slope of the line 'm' =
m =
=
= 0.25
Therefore, equation of the line passing through (200, 65) and slope 0.25 will be,
y - 65 = 0.25(x - 200)
y - 65 = 0.25x - 50
y = 0.25x + 15
(b). For y = $135 we have to calculate the number of cups of coffee produced.
135 = 0.25x + 15
0.25x = 135 - 15
0.25x = 120
x = 480 cups
Therefore, 480 cups of coffee will be produced.