Question

HELP ME NOW PLEASE IM BEGGING YOU PLEASE IM CRYING IM GOING INSANE I NEED HELP WITH THIS QUESTION IM TIRED OF ASKING THE SAME QUESTION OVER AND OVER AGAIN PLEASE HELP IF YOU ARE GOOD AT MATH

Answer 1

Answer:

-4

Step-by-step explanation:

Average rate of change: y / x = (f(x₁) - f(x₂)) / (x₁ - x₂)

Note: it does not matter which goes first- x₁ or x₂. Just keep them in the same order for both parts (just like when you find slope)

For example, if we were conducting a lab experiment and there was 40 rats in week 2 and 80 rats in week 4, then to find the average rate of change:

(40 - 80) / (2 - 4) = -40 / -2 = 20 rats per week

Now, let's apply this to the equation we have.

h(x) = -x² + 3x + 1 when x=2 and x= 5

When x = 2,

-x² + 3x + 1 = - 2² + 3*2 + 1 = -4 + 6 + 1 = 3

When x = 5,

-x² + 3x + 1 = -5² + 3*5 + 1 = -25 + 15 + 1 = -9

Now, plug these into the equation (f(x₁) - f(x₂)) / (x₁ - x₂)

Let's set x₁ as 2 and x₂ as 5. So,

(h(2) - h(5)) / (2 - 5)

Then, substitute h(2) and h(5) with the numbers we already know.

(3 - (-9)) / (2 - 5)

12 / (-3)  = -4

Thus, the answer is -4

I hope this helps! Feel free to ask any questions!