Root are also known as what x is equal to. So, to find x you would need to set (x-4)=0 and (x+7)=0
X=4. X=-7
Answer:
![\displaystyle y=-0.927x+13.63](https://tex.z-dn.net/?f=%5Cdisplaystyle%20y%3D-0.927x%2B13.63)
Step-by-step explanation:
<u>Simple Linear Regression
</u>
It a function that represents the relationship between two or more variables in a given data set. It uses the method of the least-squares regression line which minimizes the error between the estimate function and the real data.
Let's compute the best-fit line for the data
![x=\{1,5,6,12,15\}](https://tex.z-dn.net/?f=x%3D%5C%7B1%2C5%2C6%2C12%2C15%5C%7D)
![y=\{14,11,4,2,1\}](https://tex.z-dn.net/?f=y%3D%5C%7B14%2C11%2C4%2C2%2C1%5C%7D)
First, we find the sums
![\displaystyle \sum x=1+5+6+12+15=39](https://tex.z-dn.net/?f=%5Cdisplaystyle%20%5Csum%20x%3D1%2B5%2B6%2B12%2B15%3D39)
![\displaystyle \sum y=14+11+4+2+1=32](https://tex.z-dn.net/?f=%5Cdisplaystyle%20%5Csum%20y%3D14%2B11%2B4%2B2%2B1%3D32)
Then, we compute the averages values
![\displaystyle \bar{x}=\frac{39}{5}=7.8](https://tex.z-dn.net/?f=%5Cdisplaystyle%20%5Cbar%7Bx%7D%3D%5Cfrac%7B39%7D%7B5%7D%3D7.8)
![\displaystyle \bar{y}=\frac{32}{5}=6.4](https://tex.z-dn.net/?f=%5Cdisplaystyle%20%5Cbar%7By%7D%3D%5Cfrac%7B32%7D%7B5%7D%3D6.4)
We will also compute the sums of the cross-products and the sum of the squares
![\displaystyle \sum xy=(1)(14)+(5)(11)+(6)(4)+(12)(2)+(15)(1)=137](https://tex.z-dn.net/?f=%5Cdisplaystyle%20%5Csum%20xy%3D%281%29%2814%29%2B%285%29%2811%29%2B%286%29%284%29%2B%2812%29%282%29%2B%2815%29%281%29%3D137)
![\displaystyle \sum x^2=1^2+5^2+6^2+12^2+15^2=1+25+36+144+225](https://tex.z-dn.net/?f=%5Cdisplaystyle%20%5Csum%20x%5E2%3D1%5E2%2B5%5E2%2B6%5E2%2B12%5E2%2B15%5E2%3D1%2B25%2B36%2B144%2B225)
![\displaystyle \sum x^2=431](https://tex.z-dn.net/?f=%5Cdisplaystyle%20%5Csum%20x%5E2%3D431)
We will compute Sxy and Sxx
![\displaystyle S_{xy}=\sum xy-\frac{\sum x\ \sum y}{n}](https://tex.z-dn.net/?f=%5Cdisplaystyle%20S_%7Bxy%7D%3D%5Csum%20xy-%5Cfrac%7B%5Csum%20x%5C%20%5Csum%20y%7D%7Bn%7D)
![\displaystyle S_{xy}=137-\frac{(39)(32)}{5}](https://tex.z-dn.net/?f=%5Cdisplaystyle%20S_%7Bxy%7D%3D137-%5Cfrac%7B%2839%29%2832%29%7D%7B5%7D)
![\displaystyle S_{xy}=-117.6](https://tex.z-dn.net/?f=%5Cdisplaystyle%20S_%7Bxy%7D%3D-117.6)
![\displaystyle S_{xx}=\sum x^2-\frac{(\sum x)^2}{n}](https://tex.z-dn.net/?f=%5Cdisplaystyle%20S_%7Bxx%7D%3D%5Csum%20x%5E2-%5Cfrac%7B%28%5Csum%20x%29%5E2%7D%7Bn%7D)
![\displaystyle S_{xx}=431-\frac{39}{5}^2=126.8](https://tex.z-dn.net/?f=%5Cdisplaystyle%20S_%7Bxx%7D%3D431-%5Cfrac%7B39%7D%7B5%7D%5E2%3D126.8)
The slope of the linear regression function is given by
![\displaystyle m=\frac{S_{xy}}{S_{xx}}=\frac{-117.6}{126.8}=-0.927](https://tex.z-dn.net/?f=%5Cdisplaystyle%20m%3D%5Cfrac%7BS_%7Bxy%7D%7D%7BS_%7Bxx%7D%7D%3D%5Cfrac%7B-117.6%7D%7B126.8%7D%3D-0.927)
The y-intercept ot the linear function is
![\displaystyle b=\bar{y}-b\bar{x}=6.4-(-0.927)(7.8)](https://tex.z-dn.net/?f=%5Cdisplaystyle%20b%3D%5Cbar%7By%7D-b%5Cbar%7Bx%7D%3D6.4-%28-0.927%29%287.8%29)
![\displaystyle b=13.63](https://tex.z-dn.net/?f=%5Cdisplaystyle%20b%3D13.63)
Thus the best-fit line is
![\displaystyle y=-0.927x+13.63](https://tex.z-dn.net/?f=%5Cdisplaystyle%20y%3D-0.927x%2B13.63)
The correct option is the last one
Step-by-step explanation:
step 1. an example of difference of squares (dos) is (x + y)(x - y) = x^2 - y^2.
step 2. dos must have only 2 square rootable terms and a "-" between them.
step 3. 196x^2 - 121y^2 = (14x + 11y)(14x - 11y) works!
step 4. 5x^2 - 245 = 5(x^2 - 49) = 5(x + 7)(x - 7) works!
step 5. 27w^5 - 75w = 3w(9w^4 - 25) = 3w(3w^2 + 5)(3w^2 - 5) works!
step 6. x^4 - 100y^2 = (x^2 - 10y)(x^2 + 10y) works!
Answer:
Any numbers above -5 make this inequality true. Values that will make the inequality true: -4, -3, -2, -1, 0, 1...
It would take 20 hours
300/15= 20