You would start by saying his budget is $80 so you start with 80= he pays an initial fee of $59.50 every month plus $5 per gigabyte so you would set it up like
80=59.50+5x
X being how many gigabytes he uses then you solve 80-59.50 is 20.5 divided by 5 gives you 4.1 but you round down cause you don’t want to pass the limit so therefor the most gigabytes he can use is 4
Answer: ![\displaystyle y= \frac{2\text{x}}{4\text{x} - 1}](https://tex.z-dn.net/?f=%5Cdisplaystyle%20y%3D%20%5Cfrac%7B2%5Ctext%7Bx%7D%7D%7B4%5Ctext%7Bx%7D%20-%201%7D)
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Work Shown:
![8\text{x}y= 2(2\text{x} + y)\\\\8\text{x}y= 4\text{x} + 2y\\\\8\text{x}y - 2y= 4\text{x}\\\\y(8\text{x} - 2)= 4\text{x}\\\\y= \frac{4\text{x}}{8\text{x} - 2}\\\\y= \frac{2*2\text{x}}{2(4\text{x} - 1)}\\\\y= \frac{2\text{x}}{4\text{x} - 1}\\\\](https://tex.z-dn.net/?f=8%5Ctext%7Bx%7Dy%3D%202%282%5Ctext%7Bx%7D%20%2B%20y%29%5C%5C%5C%5C8%5Ctext%7Bx%7Dy%3D%204%5Ctext%7Bx%7D%20%2B%202y%5C%5C%5C%5C8%5Ctext%7Bx%7Dy%20-%202y%3D%204%5Ctext%7Bx%7D%5C%5C%5C%5Cy%288%5Ctext%7Bx%7D%20-%202%29%3D%204%5Ctext%7Bx%7D%5C%5C%5C%5Cy%3D%20%5Cfrac%7B4%5Ctext%7Bx%7D%7D%7B8%5Ctext%7Bx%7D%20-%202%7D%5C%5C%5C%5Cy%3D%20%5Cfrac%7B2%2A2%5Ctext%7Bx%7D%7D%7B2%284%5Ctext%7Bx%7D%20-%201%29%7D%5C%5C%5C%5Cy%3D%20%5Cfrac%7B2%5Ctext%7Bx%7D%7D%7B4%5Ctext%7Bx%7D%20-%201%7D%5C%5C%5C%5C)
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Explanation:
The idea is to first get all the y terms to one side. I did this by subtracting 2y from both sides in the third step.
Then factor out y and divide both sides by (8x-2)
Afterward there's the optional steps of simplifying (as shown in the final two steps).
Given:
A(-5,4)
B(3,4)
C(3,-5)
So point D is:
so point D is (-5,-5)
For AB is
Distance between two point is:
![\begin{gathered} (x_1,y_1)and(x_2,y_2) \\ D=\sqrt[]{(x_2-x_1)^2+(y_2-y_1)^2} \end{gathered}](https://tex.z-dn.net/?f=%5Cbegin%7Bgathered%7D%20%28x_1%2Cy_1%29and%28x_2%2Cy_2%29%20%5C%5C%20D%3D%5Csqrt%5B%5D%7B%28x_2-x_1%29%5E2%2B%28y_2-y_1%29%5E2%7D%20%5Cend%7Bgathered%7D)
so distance between A(-5,4) and B(3,4) is:
![\begin{gathered} D=\sqrt[]{(3-(-5))^2+(4-4)^2} \\ =\sqrt[]{(8)^2+0^2} \\ =8 \end{gathered}](https://tex.z-dn.net/?f=%5Cbegin%7Bgathered%7D%20D%3D%5Csqrt%5B%5D%7B%283-%28-5%29%29%5E2%2B%284-4%29%5E2%7D%20%5C%5C%20%3D%5Csqrt%5B%5D%7B%288%29%5E2%2B0%5E2%7D%20%5C%5C%20%3D8%20%5Cend%7Bgathered%7D)
So AB is 8 unit apart.
For B(3,4) and C(3,-5).
![\begin{gathered} D=\sqrt[]{(3-3)^2+(-5-4)^2} \\ =\sqrt[]{0^2+(-9)^2} \\ =9 \end{gathered}](https://tex.z-dn.net/?f=%5Cbegin%7Bgathered%7D%20D%3D%5Csqrt%5B%5D%7B%283-3%29%5E2%2B%28-5-4%29%5E2%7D%20%5C%5C%20%3D%5Csqrt%5B%5D%7B0%5E2%2B%28-9%29%5E2%7D%20%5C%5C%20%3D9%20%5Cend%7Bgathered%7D)
So BC is 9 unit apart.
For fourth bush point is (-5,-5) it left of point C(3,-5) is:
![\begin{gathered} D=\sqrt[]{(3-(-5))^2+(-5-(-5))^2} \\ =\sqrt[]{(8)^2+0^2} \\ =8 \end{gathered}](https://tex.z-dn.net/?f=%5Cbegin%7Bgathered%7D%20D%3D%5Csqrt%5B%5D%7B%283-%28-5%29%29%5E2%2B%28-5-%28-5%29%29%5E2%7D%20%5C%5C%20%3D%5Csqrt%5B%5D%7B%288%29%5E2%2B0%5E2%7D%20%5C%5C%20%3D8%20%5Cend%7Bgathered%7D)
so fourth bush is 8 unit left of C.
For fourth bush(-5,-5) below to point A(-5,4)
![\begin{gathered} D=\sqrt[]{(-5-(-5))^2+(4-(-5))^2} \\ =\sqrt[]{0^2+9^2} \\ =9 \end{gathered}](https://tex.z-dn.net/?f=%5Cbegin%7Bgathered%7D%20D%3D%5Csqrt%5B%5D%7B%28-5-%28-5%29%29%5E2%2B%284-%28-5%29%29%5E2%7D%20%5C%5C%20%3D%5Csqrt%5B%5D%7B0%5E2%2B9%5E2%7D%20%5C%5C%20%3D9%20%5Cend%7Bgathered%7D)
so fourth bush 9 units below of A.
In order to solve the given expression follow these steps:
1. Take the square roots on both sides in order to get rid of the power on the left side:
√(x-5)² = ±√3
x - 5 = ±√3
2. add 5 on both sides:
x-5 + 5 = 5 ±√3
x = 5 ±√3
Then, the solution is x = 5 ±√3
Factor completely x³ + 6x² - 3x – 18
![- 6 + 6( - 6)^{2} - 3( - 6) - 18 \\ - 6 +6 \times 6 ^{2} + 18 - 18 \\ - 6 + 6 ^{3} + 18 - 18 \\ - 6 + 216 \\ 210](https://tex.z-dn.net/?f=%20-%206%20%2B%206%28%20-%206%29%5E%7B2%7D%20%20-%203%28%20-%206%29%20-%2018%20%5C%5C%20%20-%206%20%2B6%20%5Ctimes%206%20%5E%7B2%7D%20%20%2B%2018%20-%2018%20%5C%5C%20%20-%206%20%2B%206%20%5E%7B3%7D%20%20%2B%2018%20-%2018%20%5C%5C%20%20-%206%20%2B%20216%20%5C%5C%20210)
with a root of x = -6
the answer is 210