Hello,
The correct answer is 4... This is the correct exact answer
The slope is 3
I am not that shure on the y intercept
The answer is for part A) 50(1.07(a) )
Answer:
![2t^3+15t^2+19t+6](https://tex.z-dn.net/?f=2t%5E3%2B15t%5E2%2B19t%2B6)
Step-by-step explanation:
Height of the Rectangle![=t^2+7t+6](https://tex.z-dn.net/?f=%3Dt%5E2%2B7t%2B6)
Width of the Rectangle![=2t+1](https://tex.z-dn.net/?f=%3D2t%2B1)
Area of the Rectangle = Height X Width
![=(2t+1)(t^2+7t+6)\\=2t(t^2+7t+6)+1(t^2+7t+6)\\=2t^3+14t^2+12t+t^2+7t+6\\$Collect like terms\\=2t^3+14t^2+t^2+12t+7t+6\\Area=2t^3+15t^2+19t+6\\](https://tex.z-dn.net/?f=%3D%282t%2B1%29%28t%5E2%2B7t%2B6%29%5C%5C%3D2t%28t%5E2%2B7t%2B6%29%2B1%28t%5E2%2B7t%2B6%29%5C%5C%3D2t%5E3%2B14t%5E2%2B12t%2Bt%5E2%2B7t%2B6%5C%5C%24Collect%20like%20terms%5C%5C%3D2t%5E3%2B14t%5E2%2Bt%5E2%2B12t%2B7t%2B6%5C%5CArea%3D2t%5E3%2B15t%5E2%2B19t%2B6%5C%5C)
The area of the rectangle is ![2t^3+15t^2+19t+6](https://tex.z-dn.net/?f=2t%5E3%2B15t%5E2%2B19t%2B6)
For this case we have that by definition, the equation of the line of the slope-intersection form is given by:
![y = mx + b](https://tex.z-dn.net/?f=y%20%3D%20mx%20%2B%20b)
Where:
m: It is the slope of the line
b: It is the cut-off point with the y axis.
According to the data of the statement we have the following points:
![(x_ {1}, y_ {1}): (- 9, -9)\\(x_ {2}, y_ {2}): (- 6,0)](https://tex.z-dn.net/?f=%28x_%20%7B1%7D%2C%20y_%20%7B1%7D%29%3A%20%28-%209%2C%20-9%29%5C%5C%28x_%20%7B2%7D%2C%20y_%20%7B2%7D%29%3A%20%28-%206%2C0%29)
We found the slope:
![m = \frac {y_ {2} -y_ {1}} {x_ {2} -x_ {1}} = \frac {0 - (- 9)} {- 6 - (- 9)} = \frac { 9} {- 6 + 9} = \frac {9} {3} = 3](https://tex.z-dn.net/?f=m%20%3D%20%5Cfrac%20%7By_%20%7B2%7D%20-y_%20%7B1%7D%7D%20%7Bx_%20%7B2%7D%20-x_%20%7B1%7D%7D%20%3D%20%5Cfrac%20%7B0%20-%20%28-%209%29%7D%20%7B-%206%20-%20%28-%209%29%7D%20%3D%20%5Cfrac%20%7B%209%7D%20%7B-%206%20%2B%209%7D%20%3D%20%5Cfrac%20%7B9%7D%20%7B3%7D%20%3D%203)
Thus, the equation is of the form:
![y = 3x + b](https://tex.z-dn.net/?f=y%20%3D%203x%20%2B%20b)
We substitute one of the points and find b:
![0 = 3 (-6) + b\\0 = -18 + b\\b = 18](https://tex.z-dn.net/?f=0%20%3D%203%20%28-6%29%20%2B%20b%5C%5C0%20%3D%20-18%20%2B%20b%5C%5Cb%20%3D%2018)
Finally, the equation is:
![y = 3x + 18](https://tex.z-dn.net/?f=y%20%3D%203x%20%2B%2018)
Answer:
![y = 3x + 18](https://tex.z-dn.net/?f=y%20%3D%203x%20%2B%2018)