A school vending machine sells cartons of milk and juice. On a typical day:
No cartons are sold between 7 A. M. and
8 A. M., or from 5 P. M. onward.
The machine has a capacity of 100 cartons.
At 7 A. M., it is three-quarters full.
From 8 A. M. to 10 A. M., 10:15 A. M. to noon, and
from 1
1 p. M. to 3 P. M. the students are in class.
The machine is filled at 11 A. M. and at 4 P. M.
Sketch a graph of the number of cartons in the
vending machine as a function of time. Explain
what each section of the graph represents.

so firstly, we need to isolate the y variables to be able to solve these inequalities. firstly, add 0.5x on both sides of the first inequality and subtract 1.5x on both sides of the second inequality:

now since the slope is positive for the first inequality, this means that the line going upwards belongs to the first inequality, and the line going downwards belongs to the second inequality.

next, since y ≥ in the first inequality, this means that the shaded region will be above the first inequality's line, thus shading regions a and b.

next, since y ≤ in the second inequality, this means that the shaded region is going to be below this line, thus shading regions a and c.

since both lines shade region a, this means that region a is the solution.

step-by-step explanation:

mark brainliest!