Answer:
see explanation
Step-by-step explanation:
x - 2 | x² - x - 12
------------------------
x³ - 3x² - 10x + 24
x³ - 2x² ↓ ↓ ← subtract terms from terms above
--------------------------
- x² - 10x + 24
- x² + 2x ↓ ← subtract terms from terms above
----------------------------
- 12x + 24
- 12x + 24 ← subtract terms from above terms
----------------------------
0 ← remainder
Since remainder is zero then (x - 2) is a factor
and quotient = x² - x - 12 , thus
x³ - 3x² - 10x + 24 = (x - 2)(x² - x - 12) = (x - 2)(x - 4)(x + 3)
Step-by-step explanation:
Points are (8,5) and (-12,-9)
The equation of a line passing through two points is given by :
![y-y_1=m(x-x_1)\ \text{m is slope}\\\\y-5=\dfrac{y_2-y_1}{x_2-x_1}(x-8)\\\\y-5=\dfrac{-9-5}{-12-8}\times (x-8)\\\\y-5=\dfrac{7}{10}\times (x-8)\\\\10y-50=7x-56](https://tex.z-dn.net/?f=y-y_1%3Dm%28x-x_1%29%5C%20%5Ctext%7Bm%20is%20slope%7D%5C%5C%5C%5Cy-5%3D%5Cdfrac%7By_2-y_1%7D%7Bx_2-x_1%7D%28x-8%29%5C%5C%5C%5Cy-5%3D%5Cdfrac%7B-9-5%7D%7B-12-8%7D%5Ctimes%20%28x-8%29%5C%5C%5C%5Cy-5%3D%5Cdfrac%7B7%7D%7B10%7D%5Ctimes%20%28x-8%29%5C%5C%5C%5C10y-50%3D7x-56)
or
![-50+56=7x-10y\\\\7x-10y=6](https://tex.z-dn.net/?f=-50%2B56%3D7x-10y%5C%5C%5C%5C7x-10y%3D6)
But he writes the equation 7x – 10y = 3 which is not matching with the one we have calculated. It means that model calculated by Devon is not good.
Answer:
D, or the last graph.
Step-by-step explanation:
I got it right when I was doing the assignment :)
Answer:
, ![y=\frac{32}{5}x](https://tex.z-dn.net/?f=y%3D%5Cfrac%7B32%7D%7B5%7Dx)
, ![y=6.4x](https://tex.z-dn.net/?f=y%3D6.4x)
Step-by-step explanation:
we know that
A relationship between two variables, x, and y, represent a proportional variation if it can be expressed in the form
or ![y=kx](https://tex.z-dn.net/?f=y%3Dkx)
Find the value of the constant of proportionality k
take any ordered pair from the data
For x=25, y=160
![k=\frac{y}{x}](https://tex.z-dn.net/?f=k%3D%5Cfrac%7By%7D%7Bx%7D)
substitute the values of x and y
![k=\frac{160}{25}](https://tex.z-dn.net/?f=k%3D%5Cfrac%7B160%7D%7B25%7D)
simplify
![k=\frac{32}{5}](https://tex.z-dn.net/?f=k%3D%5Cfrac%7B32%7D%7B5%7D)
The linear equation is equal to
![y=\frac{32}{5}x](https://tex.z-dn.net/?f=y%3D%5Cfrac%7B32%7D%7B5%7Dx)
or
![y=6.4x](https://tex.z-dn.net/?f=y%3D6.4x)