Answer:
The answer is 2.375.
Step-by-step explanation:
17 / 8 = 2.125.
2 / 8 = 0.25.
2.125 + 0.25 = 2.375.
Answer:
The function is:
![y=\frac{5}{4}(x-3) +2\\](https://tex.z-dn.net/?f=y%3D%5Cfrac%7B5%7D%7B4%7D%28x-3%29%20%2B2%5C%5C)
Step-by-step explanation:
If we have a function f(x) and we want to compress its graph vertically c units then we must do the transformation
Where
.
If we want to make a transformation that moves horizontally h units the graph of f(x) then we must do:
![y = f (x + h)](https://tex.z-dn.net/?f=y%20%3D%20f%20%28x%20%2B%20h%29)
If
the graph of f(x) shifts h units to the left
If
the graph of f(x) shifts h units to the right.
If we want to make a transformation that moves vertically k units the graph of f(x) then we must do
![y = f (x) + k](https://tex.z-dn.net/?f=y%20%3D%20f%20%28x%29%20%2B%20k)
If
the graph of f(x) moves k units up
If
the graph of f(x) shifts k units down
In this case ![f (x) =5x](https://tex.z-dn.net/?f=f%20%28x%29%20%3D5x)
If the transformation vertically compresses the function by a factor of
and moves the function 3 units to the right and 2 units up then the transformation is:
![y=\frac{1}{4}f(x-3)+2](https://tex.z-dn.net/?f=y%3D%5Cfrac%7B1%7D%7B4%7Df%28x-3%29%2B2)
The function is:
![y=\frac{5}{4}(x-3) +2\\](https://tex.z-dn.net/?f=y%3D%5Cfrac%7B5%7D%7B4%7D%28x-3%29%20%2B2%5C%5C)
For this case we have by definition, that the volume of a cone is given by:
![V = \frac {1} {3} * \pi * r ^ 2 * h](https://tex.z-dn.net/?f=V%20%3D%20%5Cfrac%20%7B1%7D%20%7B3%7D%20%2A%20%5Cpi%20%2A%20r%20%5E%202%20%2A%20h)
Where:
A: It is the cone radius
h: It's the height
They tell us that the diameter is 21 m, then the radius is half the diameter, that is: 10.5m. The height is 4m. Substituting the data:
.
Finally, the volume of the cube is![147 \pi \ m ^ 3](https://tex.z-dn.net/?f=147%20%5Cpi%20%5C%20m%20%5E%203)
ANswer:
Option B
Hi there!
Let's solve this problem step by step!
![7x + 3y = - 1](https://tex.z-dn.net/?f=7x%20%2B%203y%20%3D%20%20-%201)
To convert this formula to slope-intercept form, we must isolate y.
First bring 7x to the left by subtracting 7x from both sides of the equation.
![3y = - 7x - 1](https://tex.z-dn.net/?f=3y%20%3D%20%20-%207x%20-%201)
Finally we need to divide both sides of the equation by 3.
![\frac{3y}{3} = \frac{ - 7x - 1}{3}](https://tex.z-dn.net/?f=%20%5Cfrac%7B3y%7D%7B3%7D%20%20%3D%20%20%5Cfrac%7B%20-%207x%20-%201%7D%7B3%7D%20)
Do some simple algebra and we find:
![y = - \frac{7}{3} x - \frac{1}{3} \\ y = - 2 \frac{1}{3} x - \frac{1}{3}](https://tex.z-dn.net/?f=y%20%3D%20%20-%20%20%5Cfrac%7B7%7D%7B3%7D%20x%20-%20%20%5Cfrac%7B1%7D%7B3%7D%20%20%20%5C%5C%20y%20%3D%20%20-%202%20%5Cfrac%7B1%7D%7B3%7D%20x%20-%20%20%5Cfrac%7B1%7D%7B3%7D%20)
~ Hope this helps you!