Answer:
Step-by-step explanation:
Here is the set up:
x
x + 2
x + 4
x^2 + (x + 2) + (x + 4)^2 = 170
Take it from here.
Answer:
The required equation is: ![\mathbf{f(x)=\frac{3}{4}x-\frac{29}{4}}](https://tex.z-dn.net/?f=%5Cmathbf%7Bf%28x%29%3D%5Cfrac%7B3%7D%7B4%7Dx-%5Cfrac%7B29%7D%7B4%7D%7D)
Step-by-step explanation:
We need to find equation from the table given
x f(x)
3 -5
7 -2
11 1
15 4
We can write equation in the form of ![y=mx+b](https://tex.z-dn.net/?f=y%3Dmx%2Bb)
where m is slope and b is y-intercept.
Finding Slope
We can used the slope formula to find slope: ![Slope=\frac{y_2-y_1}{x_2-x_1}](https://tex.z-dn.net/?f=Slope%3D%5Cfrac%7By_2-y_1%7D%7Bx_2-x_1%7D)
From the table we have: ![x_1=3, y_1=-5, x_2=7, y_2=-2](https://tex.z-dn.net/?f=x_1%3D3%2C%20y_1%3D-5%2C%20x_2%3D7%2C%20y_2%3D-2)
Putting values and finding slope
![Slope=\frac{y_2-y_1}{x_2-x_1}\\Slope=\frac{-2-(-5)}{7-3} \\Slope=\frac{-2+5}{7-3}\\Slope=\frac{3}{4}](https://tex.z-dn.net/?f=Slope%3D%5Cfrac%7By_2-y_1%7D%7Bx_2-x_1%7D%5C%5CSlope%3D%5Cfrac%7B-2-%28-5%29%7D%7B7-3%7D%20%5C%5CSlope%3D%5Cfrac%7B-2%2B5%7D%7B7-3%7D%5C%5CSlope%3D%5Cfrac%7B3%7D%7B4%7D)
So, we get slope ![m=\frac{3}{4}](https://tex.z-dn.net/?f=m%3D%5Cfrac%7B3%7D%7B4%7D)
Now, finding y-intercept
Using the slope
and point (3,-5) we can find y-intercept
![y=mx+b\\-5=\frac{3}{4}(3)+b\\-5=\frac{9}{4}+b\\b=-5-\frac{9}{4}\\b=\frac{-5*4-9}{4}\\b=\frac{-20-9}{4}\\b=\frac{-29}{4}](https://tex.z-dn.net/?f=y%3Dmx%2Bb%5C%5C-5%3D%5Cfrac%7B3%7D%7B4%7D%283%29%2Bb%5C%5C-5%3D%5Cfrac%7B9%7D%7B4%7D%2Bb%5C%5Cb%3D-5-%5Cfrac%7B9%7D%7B4%7D%5C%5Cb%3D%5Cfrac%7B-5%2A4-9%7D%7B4%7D%5C%5Cb%3D%5Cfrac%7B-20-9%7D%7B4%7D%5C%5Cb%3D%5Cfrac%7B-29%7D%7B4%7D)
The y-intercept is ![b=\frac{-29}{4}](https://tex.z-dn.net/?f=b%3D%5Cfrac%7B-29%7D%7B4%7D)
So, the equation having slope
and y-intercept
will be:
![y=mx+b\\y=\frac{3}{4}x-\frac{29}{4}](https://tex.z-dn.net/?f=y%3Dmx%2Bb%5C%5Cy%3D%5Cfrac%7B3%7D%7B4%7Dx-%5Cfrac%7B29%7D%7B4%7D)
The required equation is: ![\mathbf{f(x)=\frac{3}{4}x-\frac{29}{4}}](https://tex.z-dn.net/?f=%5Cmathbf%7Bf%28x%29%3D%5Cfrac%7B3%7D%7B4%7Dx-%5Cfrac%7B29%7D%7B4%7D%7D)
Answer:
2 & 20
Step-by-step explanation:
100 x 2= 200
20 x 10= 200
Answer:
1728
Step-by-step explanation:
12*12*12