Well I'm not sure what the answer would be since I'm not that smart but I did get the answer of 90, I did this by dividing 72 by 80 which equals .9 and I multiplied that by 100 and got 90.
Equation would be b = 14m
Answer:
The average rate of change of the function over the interval is of 6.
Step-by-step explanation:
Average rate of change:
The average rate of change of a function h(x) over an interval [a,b] is given by:
![A = \frac{h(b)-h(a)}{b-a}](https://tex.z-dn.net/?f=A%20%3D%20%5Cfrac%7Bh%28b%29-h%28a%29%7D%7Bb-a%7D)
In this question:
Over the interval [-9,-2], so ![a = -9, b = -2, b - a = -2 -(-9) = 7](https://tex.z-dn.net/?f=a%20%3D%20-9%2C%20b%20%3D%20-2%2C%20b%20-%20a%20%3D%20-2%20-%28-9%29%20%3D%207)
The function is:
![h(x) = -x^2 - 5x + 14](https://tex.z-dn.net/?f=h%28x%29%20%3D%20-x%5E2%20-%205x%20%2B%2014)
![h(-9) = -9^2 -5(-9) + 14 = -81 + 45 + 14 = -22](https://tex.z-dn.net/?f=h%28-9%29%20%3D%20-9%5E2%20-5%28-9%29%20%2B%2014%20%3D%20-81%20%2B%2045%20%2B%2014%20%3D%20-22)
![h(-2) = -2^2 -5(-2) + 14 = -4 + 10 + 14 = 20](https://tex.z-dn.net/?f=h%28-2%29%20%3D%20-2%5E2%20-5%28-2%29%20%2B%2014%20%3D%20-4%20%2B%2010%20%2B%2014%20%3D%2020)
Then
![A = \frac{h(-2)-h(-9)}{7} = \frac{20-(-22)}{7} = \frac{42}{7} = 6](https://tex.z-dn.net/?f=A%20%3D%20%5Cfrac%7Bh%28-2%29-h%28-9%29%7D%7B7%7D%20%3D%20%5Cfrac%7B20-%28-22%29%7D%7B7%7D%20%3D%20%5Cfrac%7B42%7D%7B7%7D%20%3D%206)
The average rate of change of the function over the interval is of 6.