Answer:
![\dfrac{1}{2}](https://tex.z-dn.net/?f=%5Cdfrac%7B1%7D%7B2%7D)
Step-by-step explanation:
Given the function ![h(x)=\dfrac{1}{8}x^3-x^2](https://tex.z-dn.net/?f=h%28x%29%3D%5Cdfrac%7B1%7D%7B8%7Dx%5E3-x%5E2)
The average rate of change of the function h(x) over the interval
can be calculated using formula
![\dfrac{h(b)-h(a)}{b-a}](https://tex.z-dn.net/?f=%5Cdfrac%7Bh%28b%29-h%28a%29%7D%7Bb-a%7D)
In your case,
![a=-2,\\ \\b=2,](https://tex.z-dn.net/?f=a%3D-2%2C%5C%5C%20%5C%5Cb%3D2%2C)
so the average rate of change is
![\dfrac{h(2)-h(-2)}{2-(-2)}\\ \\=\dfrac{(\frac{1}{8}\cdot 2^3-2^2)-(\frac{1}{8}\cdot (-2)^3-(-2)^2)}{4}\\ \\=\dfrac{(1-4)-(-1-4)}{4}\\ \\=\dfrac{-3+5}{4}\\ \\=\dfrac{2}{4}\\ \\=\dfrac{1}{2}](https://tex.z-dn.net/?f=%5Cdfrac%7Bh%282%29-h%28-2%29%7D%7B2-%28-2%29%7D%5C%5C%20%5C%5C%3D%5Cdfrac%7B%28%5Cfrac%7B1%7D%7B8%7D%5Ccdot%202%5E3-2%5E2%29-%28%5Cfrac%7B1%7D%7B8%7D%5Ccdot%20%28-2%29%5E3-%28-2%29%5E2%29%7D%7B4%7D%5C%5C%20%5C%5C%3D%5Cdfrac%7B%281-4%29-%28-1-4%29%7D%7B4%7D%5C%5C%20%5C%5C%3D%5Cdfrac%7B-3%2B5%7D%7B4%7D%5C%5C%20%5C%5C%3D%5Cdfrac%7B2%7D%7B4%7D%5C%5C%20%5C%5C%3D%5Cdfrac%7B1%7D%7B2%7D)
Answer:
1) -2.13
2) 2.57
3) 33
Step-by-step explanation:
1)
3(8 + 5h) = -28 Distribute the 3
24 + 15h = -28 Subtract 24 from both sides of the equation
15h = -32 Divide both sides by 15 and round
h = - 2.13
2)
19 = 7(3n - 5) Distribute the 7
19 = 21n - 35 Add 35 to both sides of the equation
54 = 21n Divide both sides of the equation by 21
2.57 = n
3)
6s - 7s = -33 Combine the s's
-s = -33 Multiply both sides by -1
s = 33
Answer:
Dependent variable: y because you get the points by doing the quiz.
Independent variable: x because you don’t know how many questions you answered correctly.
Total points you score: Unknown until you know how many you got right also the same as y.
Number of questions you answer correctly: Unknown until you get your paper back, also the same as x.