Could you get a picture that's clear ? I would like to help
I think it’s the 3rd one because quotient is the result of division so it couldn’t be in the front and all the other ones just don’t make since so 3
It helps them when they have either really big numbers or really small numbers and so they don't have to use so many zeroes
Answer:
![x = \frac{17}{18}](https://tex.z-dn.net/?f=x%20%3D%20%5Cfrac%7B17%7D%7B18%7D)
![y = \frac{23}{6}](https://tex.z-dn.net/?f=y%20%3D%20%5Cfrac%7B23%7D%7B6%7D)
Step-by-step explanation:
Given
![y = 3x + 1](https://tex.z-dn.net/?f=y%20%3D%203x%20%2B%201)
![Points = (0,0)\ to\ (-3,4)](https://tex.z-dn.net/?f=Points%20%3D%20%280%2C0%29%5C%20to%5C%20%28-3%2C4%29)
Required
Determine (x,y) equidistant from the equation and the given point
This question will be answered using distance formula;
![d = \sqrt{(x_1 - x_2)^2 + (y_1 - y_2)^2}](https://tex.z-dn.net/?f=d%20%3D%20%5Csqrt%7B%28x_1%20-%20x_2%29%5E2%20%2B%20%28y_1%20-%20y_2%29%5E2%7D)
Considering The first Point ![(0,0)\ to\ (x,y)](https://tex.z-dn.net/?f=%280%2C0%29%5C%20to%5C%20%28x%2Cy%29)
![(x_1 ,y_1) = (0,0)](https://tex.z-dn.net/?f=%28x_1%20%2Cy_1%29%20%3D%20%280%2C0%29)
![(x_2,y_2) = (x,y)](https://tex.z-dn.net/?f=%28x_2%2Cy_2%29%20%3D%20%28x%2Cy%29)
The distance is:
![d = \sqrt{(x_1 - x_2)^2 + (y_1 - y_2)^2}](https://tex.z-dn.net/?f=d%20%3D%20%5Csqrt%7B%28x_1%20-%20x_2%29%5E2%20%2B%20%28y_1%20-%20y_2%29%5E2%7D)
![d = \sqrt{0 - x)^2 + (0 - y)^2}](https://tex.z-dn.net/?f=d%20%3D%20%5Csqrt%7B0%20-%20x%29%5E2%20%2B%20%280%20-%20y%29%5E2%7D)
![d = \sqrt{(- x)^2 + (- y)^2}](https://tex.z-dn.net/?f=d%20%3D%20%5Csqrt%7B%28-%20x%29%5E2%20%2B%20%28-%20y%29%5E2%7D)
![d = \sqrt{x^2 + y^2}](https://tex.z-dn.net/?f=d%20%3D%20%5Csqrt%7Bx%5E2%20%2B%20y%5E2%7D)
Considering the second point: ![(x,y)\ to\ (-3,4)](https://tex.z-dn.net/?f=%28x%2Cy%29%5C%20to%5C%20%28-3%2C4%29)
![(x_1,y_1) = (x,y)](https://tex.z-dn.net/?f=%28x_1%2Cy_1%29%20%3D%20%28x%2Cy%29)
![(x_2,y_2) = (-3,4)](https://tex.z-dn.net/?f=%28x_2%2Cy_2%29%20%3D%20%28-3%2C4%29)
The distance is:
![d = \sqrt{(x_1 - x_2)^2 + (y_1 - y_2)^2}](https://tex.z-dn.net/?f=d%20%3D%20%5Csqrt%7B%28x_1%20-%20x_2%29%5E2%20%2B%20%28y_1%20-%20y_2%29%5E2%7D)
![d = \sqrt{(x - (-3))^2 + (y - 4)^2}](https://tex.z-dn.net/?f=d%20%3D%20%5Csqrt%7B%28x%20-%20%28-3%29%29%5E2%20%2B%20%28y%20-%204%29%5E2%7D)
![d = \sqrt{(x + 3)^2 + (y- 4)^2}](https://tex.z-dn.net/?f=d%20%3D%20%5Csqrt%7B%28x%20%2B%203%29%5E2%20%2B%20%28y-%204%29%5E2%7D)
![d = \sqrt{x^2 + 6x + 9 + y^2- 8y + 16}](https://tex.z-dn.net/?f=d%20%3D%20%5Csqrt%7Bx%5E2%20%2B%206x%20%2B%209%20%2B%20y%5E2-%208y%20%2B%2016%7D)
![d = \sqrt{x^2 + 6x + y^2- 8y + 16 + 9}](https://tex.z-dn.net/?f=d%20%3D%20%5Csqrt%7Bx%5E2%20%2B%206x%20%2B%20y%5E2-%208y%20%2B%2016%20%2B%209%7D)
![d = \sqrt{x^2 + 6x + y^2- 8y + 25}](https://tex.z-dn.net/?f=d%20%3D%20%5Csqrt%7Bx%5E2%20%2B%206x%20%2B%20y%5E2-%208y%20%2B%2025%7D)
Equate both values of d
![\sqrt{x^2 + 6x + y^2- 8y + 25} = \sqrt{x^2 + y^2}](https://tex.z-dn.net/?f=%5Csqrt%7Bx%5E2%20%2B%206x%20%2B%20y%5E2-%208y%20%2B%2025%7D%20%3D%20%20%5Csqrt%7Bx%5E2%20%2B%20y%5E2%7D)
Square both sides
![x^2 + 6x + y^2- 8y + 25 = x^2 + y^2](https://tex.z-dn.net/?f=x%5E2%20%2B%206x%20%2B%20y%5E2-%208y%20%2B%2025%20%3D%20x%5E2%20%2B%20y%5E2)
Collect Like Terms
![6x - 8y + 25 = x^2 -x^2+ y^2 -y^2](https://tex.z-dn.net/?f=6x%20-%208y%20%2B%2025%20%3D%20x%5E2%20-x%5E2%2B%20y%5E2%20-y%5E2)
![6x - 8y + 25 =0](https://tex.z-dn.net/?f=6x%20-%208y%20%2B%2025%20%3D0)
Recall that ![y = 3x + 1](https://tex.z-dn.net/?f=y%20%3D%203x%20%2B%201)
![6x - 8(3x + 1) + 25 = 0](https://tex.z-dn.net/?f=6x%20-%208%283x%20%2B%201%29%20%2B%2025%20%3D%200)
![6x - 24x - 8 + 25 = 0](https://tex.z-dn.net/?f=6x%20-%2024x%20-%208%20%2B%2025%20%3D%200)
![-18x+ 17 = 0](https://tex.z-dn.net/?f=-18x%2B%2017%20%3D%200)
![-18x=- 17](https://tex.z-dn.net/?f=-18x%3D-%2017)
Solve for x
![x = \frac{-17}{-18}](https://tex.z-dn.net/?f=x%20%3D%20%5Cfrac%7B-17%7D%7B-18%7D)
![x = \frac{17}{18}](https://tex.z-dn.net/?f=x%20%3D%20%5Cfrac%7B17%7D%7B18%7D)
Substitute
for x in ![y = 3x + 1](https://tex.z-dn.net/?f=y%20%3D%203x%20%2B%201)
![y = 3 * \frac{17}{18} + 1](https://tex.z-dn.net/?f=y%20%3D%203%20%2A%20%5Cfrac%7B17%7D%7B18%7D%20%2B%201)
![y = \frac{17}{6} + 1](https://tex.z-dn.net/?f=y%20%3D%20%5Cfrac%7B17%7D%7B6%7D%20%2B%201)
![y = \frac{17 + 6}{6}](https://tex.z-dn.net/?f=y%20%3D%20%5Cfrac%7B17%20%2B%206%7D%7B6%7D)
![y = \frac{23}{6}](https://tex.z-dn.net/?f=y%20%3D%20%5Cfrac%7B23%7D%7B6%7D)
Answer:
72%
Step-by-step explanation:
36*100=3600
3600/50=72