3x^2+7x
18x^2-12x
-12x^3-8x^2
6x^3-18x^2+6x
Answer:
![k= \frac{-34}{3}](https://tex.z-dn.net/?f=k%3D%20%5Cfrac%7B-34%7D%7B3%7D)
Step-by-step explanation:
<u>Step 1 :</u>-
<u>Perpendicular condition :-</u>
<u>Step 1:-</u>
Two non-vertical lines are perpendicular to each other if and only if their slopes are negative reciprocals of each other.
![m_{2} = \frac{-1}{m_{1} }](https://tex.z-dn.net/?f=m_%7B2%7D%20%3D%20%5Cfrac%7B-1%7D%7Bm_%7B1%7D%20%7D)
![m_{1} m_{2} = -1](https://tex.z-dn.net/?f=m_%7B1%7D%20m_%7B2%7D%20%3D%20-1)
<u>Step 2:-</u>
The given points are (-8,k) and (-4,-8)
![m_{1} = \frac{y_{2}-y_{1} }{x_{2}-x_{1} }](https://tex.z-dn.net/?f=m_%7B1%7D%20%3D%20%5Cfrac%7By_%7B2%7D-y_%7B1%7D%20%20%7D%7Bx_%7B2%7D-x_%7B1%7D%20%20%7D)
finding slope of the first line is ![m_{1}](https://tex.z-dn.net/?f=m_%7B1%7D)
using formula ![m_{1} = \frac{-8-k}{-4+8}](https://tex.z-dn.net/?f=m_%7B1%7D%20%3D%20%5Cfrac%7B-8-k%7D%7B-4%2B8%7D)
= ![\frac{-8-k}{4}](https://tex.z-dn.net/?f=%5Cfrac%7B-8-k%7D%7B4%7D)
finding slope of the second line is ![m_{2}](https://tex.z-dn.net/?f=m_%7B2%7D)
using formula ![m_{2} = \frac{--5+11}{5-10}](https://tex.z-dn.net/?f=m_%7B2%7D%20%3D%20%5Cfrac%7B--5%2B11%7D%7B5-10%7D)
= ![\frac{6}{-5}](https://tex.z-dn.net/?f=%5Cfrac%7B6%7D%7B-5%7D)
<u>Step 3:</u>-
using perpendicular condition
The two lines are perpendicular and their slopes are
![m_{1} m_{2} = -1](https://tex.z-dn.net/?f=m_%7B1%7D%20m_%7B2%7D%20%3D%20-1)
![(\frac{-k-8}{4} )(\frac{-6}{5} )= -1](https://tex.z-dn.net/?f=%28%5Cfrac%7B-k-8%7D%7B4%7D%20%29%28%5Cfrac%7B-6%7D%7B5%7D%20%29%3D%20-1)
simplification,we get solution is
![\frac{6(k+8)}{20} =-1](https://tex.z-dn.net/?f=%5Cfrac%7B6%28k%2B8%29%7D%7B20%7D%20%3D-1)
![6 k+48 =-20](https://tex.z-dn.net/?f=6%20k%2B48%20%3D-20)
![6 k = -20 -48](https://tex.z-dn.net/?f=6%20k%20%3D%20-20%20-48)
![6 k = -68](https://tex.z-dn.net/?f=6%20k%20%3D%20-68)
![\frac{-68}{6}](https://tex.z-dn.net/?f=%5Cfrac%7B-68%7D%7B6%7D)
![k= \frac{-34}{3}](https://tex.z-dn.net/?f=k%3D%20%5Cfrac%7B-34%7D%7B3%7D)
<u>Final answer is </u>
![k= \frac{-34}{3}](https://tex.z-dn.net/?f=k%3D%20%5Cfrac%7B-34%7D%7B3%7D)
Brad is correct.
Polynomials do not include negative exponents; this means there can be no variables in the denominator. If two polynomials do not divide evenly, the remainder is written as a fraction with the divisor (which can include a variable) in the denominator. This is not a polynomial.
Well there’s 24 hours in a rotation.. and one rotation is approximately 40075km
40075km to miles is 24901.451 miles
And we need miles per hour
So divide 24901.451 by 24
= 1037.56 mph (rounded to nearest tenth)
36 is the number that makes it completely factored