We are given the points
<span>E (0, 27)
</span><span>F (5,−8)
and we need to calculate the rate of change and the initial value:
To determine the rate of change, we will apply the slope formula:
m = (-8 - 27) / (5 - 0) = -7
Thus, the rate of change is -7
The initial value refers to the y-coordinate when x equals 0, which corresponds to point E. Therefore, the initial value is 27.</span>
Answer: x ≥ 3.2 OR x ≤ -0.75
Here's how to solve the compound inequality step-by-step: start by separating it into two inequalities. For the first one, 5x - 4 ≥ 12, add 4 to both sides to remove the constant, leaving 5x ≥ 16. Then divide both sides by 5 to isolate x, resulting in x ≥ 3.2.
Now for the second part, 12x + 5 ≤ -4, subtract 5 from both sides to obtain 12x ≤ -9. Dividing both sides by 12 gives x ≤ -9/12, which simplifies to x ≤ -0.75. So, combining both, the solution is x ≥ 3.2 OR x ≤ -0.75.