Answer:
![\frac{f(x + h) - f(x)}{ h} = \frac{7}{2}](https://tex.z-dn.net/?f=%5Cfrac%7Bf%28x%20%2B%20h%29%20-%20f%28x%29%7D%7B%20h%7D%20%3D%20%5Cfrac%7B7%7D%7B2%7D)
Step-by-step explanation:
Given
![f(x) = \frac{7}{2}x - 16](https://tex.z-dn.net/?f=f%28x%29%20%3D%20%5Cfrac%7B7%7D%7B2%7Dx%20-%2016)
Required
The difference quotient for h
The difference quotient is calculated as:
![\frac{f(x + h) - f(x)}{ h}](https://tex.z-dn.net/?f=%5Cfrac%7Bf%28x%20%2B%20h%29%20-%20f%28x%29%7D%7B%20h%7D)
Calculate f(x + h)
![f(x) = \frac{7}{2}x - 16](https://tex.z-dn.net/?f=f%28x%29%20%3D%20%5Cfrac%7B7%7D%7B2%7Dx%20-%2016)
![f(x+h) = \frac{7}{2}(x+h) - 16](https://tex.z-dn.net/?f=f%28x%2Bh%29%20%3D%20%5Cfrac%7B7%7D%7B2%7D%28x%2Bh%29%20-%2016)
![f(x+h) = \frac{7}{2}x+ \frac{7}{2}h- 16](https://tex.z-dn.net/?f=f%28x%2Bh%29%20%3D%20%5Cfrac%7B7%7D%7B2%7Dx%2B%20%5Cfrac%7B7%7D%7B2%7Dh-%2016)
The numerator of
is:
![f(x + h) - f(x) = \frac{7}{2}x+ \frac{7}{2}h- 16 -(\frac{7}{2}x - 16)](https://tex.z-dn.net/?f=f%28x%20%2B%20h%29%20-%20f%28x%29%20%3D%20%20%5Cfrac%7B7%7D%7B2%7Dx%2B%20%5Cfrac%7B7%7D%7B2%7Dh-%2016%20-%28%5Cfrac%7B7%7D%7B2%7Dx%20-%2016%29)
![f(x + h) - f(x) = \frac{7}{2}x+ \frac{7}{2}h- 16 -\frac{7}{2}x + 16](https://tex.z-dn.net/?f=f%28x%20%2B%20h%29%20-%20f%28x%29%20%3D%20%20%5Cfrac%7B7%7D%7B2%7Dx%2B%20%5Cfrac%7B7%7D%7B2%7Dh-%2016%20-%5Cfrac%7B7%7D%7B2%7Dx%20%2B%2016)
Collect like terms
![f(x + h) - f(x) = \frac{7}{2}x -\frac{7}{2}x + \frac{7}{2}h- 16 + 16](https://tex.z-dn.net/?f=f%28x%20%2B%20h%29%20-%20f%28x%29%20%3D%20%20%5Cfrac%7B7%7D%7B2%7Dx%20%20-%5Cfrac%7B7%7D%7B2%7Dx%20%2B%20%5Cfrac%7B7%7D%7B2%7Dh-%2016%20%2B%2016)
![f(x + h) - f(x) = \frac{7}{2}h](https://tex.z-dn.net/?f=f%28x%20%2B%20h%29%20-%20f%28x%29%20%3D%20%5Cfrac%7B7%7D%7B2%7Dh)
So, we have:
![\frac{f(x + h) - f(x)}{ h} = \frac{7}{2}h \div h](https://tex.z-dn.net/?f=%5Cfrac%7Bf%28x%20%2B%20h%29%20-%20f%28x%29%7D%7B%20h%7D%20%3D%20%5Cfrac%7B7%7D%7B2%7Dh%20%5Cdiv%20h)
Rewrite as:
![\frac{f(x + h) - f(x)}{ h} = \frac{7}{2}h * \frac{1}{h}](https://tex.z-dn.net/?f=%5Cfrac%7Bf%28x%20%2B%20h%29%20-%20f%28x%29%7D%7B%20h%7D%20%3D%20%5Cfrac%7B7%7D%7B2%7Dh%20%2A%20%5Cfrac%7B1%7D%7Bh%7D)
![\frac{f(x + h) - f(x)}{ h} = \frac{7}{2}](https://tex.z-dn.net/?f=%5Cfrac%7Bf%28x%20%2B%20h%29%20-%20f%28x%29%7D%7B%20h%7D%20%3D%20%5Cfrac%7B7%7D%7B2%7D)
Answer:
1.
Volume= 729cm^3
Height= 9cm^2
Area of Base= 81cm^2
2.
Volume=450m^3
Height= 3m^2
Area of Base=150m^2
3.
Volume= 480 cm^2
Area of base=75cm^2
Height= 8cm^2
4.
Volume =120in^3
Area of Base=20in^2
Height= 6in^2
Step-by-step explanation:
Volume = (length) Times (Width) Times (Height)
Area os base = (Length) Times (width)
Answer:D ( if you add +4 to the (x + 3)^2)
Step-by-step explanation:
Parent function is f(x) = x^2
A translation 3 units left gives y = )x + 3)^2
- and 4 up gives y = (x + 3)^2 + 4 - vertex form.
Standard form :
y = x^2 + 6x + 9 + 4
= x^2 + 6x + 13.
Sum up the total number of votes.
So, 5+7+8=20 students
Answer:
-2
Step-by-step explanation:
6x+3y=-6
-6-6x=3y
divided by 3
-2-2x=y