Answer:
wrong
Step-by-step explanation:
the student added 4x with 3 instead of multiplying
Answer:
units
Step-by-step explanation:
Given
Shape: Kite WXYZ
W (-3, 3), X (2, 3),
Y (4, -4), Z (-3, -2)
Required
Determine perimeter of the kite
First, we need to determine lengths of sides WX, XY, YZ and ZW 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)
For WX:
![(x_1, y_1)\ (x_2,y_2) = (-3, 3),\ (2, 3)](https://tex.z-dn.net/?f=%28x_1%2C%20y_1%29%5C%20%28x_2%2Cy_2%29%20%3D%20%28-3%2C%203%29%2C%5C%20%282%2C%203%29)
![WX = \sqrt{(-3 - 2)^2 + (3 - 3)^2}](https://tex.z-dn.net/?f=WX%20%3D%20%5Csqrt%7B%28-3%20-%202%29%5E2%20%2B%20%283%20-%203%29%5E2%7D)
![WX = \sqrt{(-5)^2 + (0)^2}](https://tex.z-dn.net/?f=WX%20%3D%20%5Csqrt%7B%28-5%29%5E2%20%2B%20%280%29%5E2%7D)
![WX = \sqrt{25}](https://tex.z-dn.net/?f=WX%20%3D%20%5Csqrt%7B25%7D)
![WX = 5](https://tex.z-dn.net/?f=WX%20%3D%205)
For XY:
![(x_1, y_1)\ (x_2,y_2) = (2, 3)\ (4,-4)](https://tex.z-dn.net/?f=%28x_1%2C%20y_1%29%5C%20%28x_2%2Cy_2%29%20%3D%20%282%2C%203%29%5C%20%284%2C-4%29)
![XY = \sqrt{(2 - 4)^2 + (3 - (-4))^2}](https://tex.z-dn.net/?f=XY%20%3D%20%5Csqrt%7B%282%20-%204%29%5E2%20%2B%20%283%20-%20%28-4%29%29%5E2%7D)
![XY = \sqrt{-2^2 + (3 +4)^2}](https://tex.z-dn.net/?f=XY%20%3D%20%5Csqrt%7B-2%5E2%20%2B%20%283%20%2B4%29%5E2%7D)
![XY = \sqrt{-2^2 + 7^2}](https://tex.z-dn.net/?f=XY%20%3D%20%5Csqrt%7B-2%5E2%20%2B%207%5E2%7D)
![XY = \sqrt{4 + 49}](https://tex.z-dn.net/?f=XY%20%3D%20%5Csqrt%7B4%20%2B%2049%7D)
![XY = \sqrt{53}](https://tex.z-dn.net/?f=XY%20%3D%20%5Csqrt%7B53%7D)
For YZ:
![(x_1, y_1)\ (x_2,y_2) = (4,-4)\ (-3, -2)](https://tex.z-dn.net/?f=%28x_1%2C%20y_1%29%5C%20%28x_2%2Cy_2%29%20%3D%20%284%2C-4%29%5C%20%28-3%2C%20-2%29)
![YZ = \sqrt{(4 - (-3))^2 + (-4 - (-2))^2}](https://tex.z-dn.net/?f=YZ%20%3D%20%5Csqrt%7B%284%20-%20%28-3%29%29%5E2%20%2B%20%28-4%20-%20%28-2%29%29%5E2%7D)
![YZ = \sqrt{(4 +3)^2 + (-4 +2)^2}](https://tex.z-dn.net/?f=YZ%20%3D%20%5Csqrt%7B%284%20%2B3%29%5E2%20%2B%20%28-4%20%2B2%29%5E2%7D)
![YZ = \sqrt{7^2 + (-2)^2}](https://tex.z-dn.net/?f=YZ%20%3D%20%5Csqrt%7B7%5E2%20%2B%20%28-2%29%5E2%7D)
![YZ = \sqrt{49 + 4}](https://tex.z-dn.net/?f=YZ%20%3D%20%5Csqrt%7B49%20%2B%204%7D)
![YZ = \sqrt{53}](https://tex.z-dn.net/?f=YZ%20%3D%20%5Csqrt%7B53%7D)
For ZW:
![(x_1, y_1)\ (x_2,y_2) = (-3, -2)\ (-3, 3)](https://tex.z-dn.net/?f=%28x_1%2C%20y_1%29%5C%20%28x_2%2Cy_2%29%20%3D%20%28-3%2C%20-2%29%5C%20%28-3%2C%203%29)
![ZW = \sqrt{(-3 - (-3))^2 + (-2 - 3)^2}](https://tex.z-dn.net/?f=ZW%20%3D%20%5Csqrt%7B%28-3%20-%20%28-3%29%29%5E2%20%2B%20%28-2%20-%203%29%5E2%7D)
![ZW = \sqrt{(-3 +3)^2 + (-2 - 3)^2}](https://tex.z-dn.net/?f=ZW%20%3D%20%5Csqrt%7B%28-3%20%2B3%29%5E2%20%2B%20%28-2%20-%203%29%5E2%7D)
![ZW = \sqrt{0^2 + (-5)^2}](https://tex.z-dn.net/?f=ZW%20%3D%20%5Csqrt%7B0%5E2%20%2B%20%28-5%29%5E2%7D)
![ZW = \sqrt{0 + 25}](https://tex.z-dn.net/?f=ZW%20%3D%20%5Csqrt%7B0%20%2B%2025%7D)
![ZW = \sqrt{25}](https://tex.z-dn.net/?f=ZW%20%3D%20%5Csqrt%7B25%7D)
![ZW = 5](https://tex.z-dn.net/?f=ZW%20%3D%205)
The Perimeter (P) is as follows:
![P = WX + XY + YZ + ZW](https://tex.z-dn.net/?f=P%20%3D%20WX%20%2B%20XY%20%2B%20YZ%20%2B%20ZW)
![P = 5 + \sqrt{53} + \sqrt{53} + 5](https://tex.z-dn.net/?f=P%20%3D%205%20%2B%20%5Csqrt%7B53%7D%20%2B%20%5Csqrt%7B53%7D%20%2B%205)
![P = 5 + 5 + \sqrt{53} + \sqrt{53}](https://tex.z-dn.net/?f=P%20%3D%205%20%2B%205%20%2B%20%5Csqrt%7B53%7D%20%2B%20%5Csqrt%7B53%7D)
units
Answer:
The athlete will run 200 kilometers.
A atleta percorrerá 200 quilômetros no total.
Step-by-step explanation:
She will run x kilometers.
She has already run 5/8 of the distance(5/8 of x), and still needs to run 75 kilometers.
So
![\frac{5x}{8} + 75 = x](https://tex.z-dn.net/?f=%5Cfrac%7B5x%7D%7B8%7D%20%2B%2075%20%3D%20x)
![x - \frac{5x}{8} = 75](https://tex.z-dn.net/?f=x%20-%20%5Cfrac%7B5x%7D%7B8%7D%20%3D%2075)
![\frac{8x - 5x}{8} = 75](https://tex.z-dn.net/?f=%5Cfrac%7B8x%20-%205x%7D%7B8%7D%20%3D%2075)
![3x = 8*75](https://tex.z-dn.net/?f=3x%20%3D%208%2A75)
![x = \frac{8*75}{3}](https://tex.z-dn.net/?f=x%20%3D%20%5Cfrac%7B8%2A75%7D%7B3%7D)
![x = 200](https://tex.z-dn.net/?f=x%20%3D%20200)
The athlete will run 200 kilometers.
A atleta percorrerá 200 quilômetros no total.
Recall that one whole is 1, or in this case since the denominator is 4, then 4/4 is 1 whole, so the whole lawn is 4/4.