The answer is 10.<span>Think of the outlier as in the dot that's off-topic out of the entire graph. </span>
Answer:
![PQ = x + 13](https://tex.z-dn.net/?f=PQ%20%3D%20x%20%2B%2013)
The dimension of the garden is 52.5ft by 43.5ft
Step-by-step explanation:
Given
The shape above
Required
Determine PQ
Determine dimension of the garden
Calculating Length PQ
Represent the length of the inner rectangle as L
Represent the width of the inner rectangle as W
![W = x](https://tex.z-dn.net/?f=W%20%3D%20x)
![L = x + 9](https://tex.z-dn.net/?f=L%20%3D%20x%20%2B%209)
The distance between the inner rectangle and the outer triangle is 4ft
This implies that;
![PQ = L + 4](https://tex.z-dn.net/?f=PQ%20%3D%20L%20%2B%204)
Substitute
for ![L](https://tex.z-dn.net/?f=L)
![PQ = x + 9 + 4](https://tex.z-dn.net/?f=PQ%20%3D%20x%20%2B%209%20%2B%204)
![PQ = x + 13](https://tex.z-dn.net/?f=PQ%20%3D%20x%20%2B%2013)
Also;
![QR = W + 4](https://tex.z-dn.net/?f=QR%20%3D%20W%20%2B%204)
Substitute
for ![W](https://tex.z-dn.net/?f=W)
![QR = x + 4](https://tex.z-dn.net/?f=QR%20%3D%20x%20%2B%204)
Calculating The Dimension of The Garden
First, we need to determine the Area of the inner rectangle
![Area_1 = L * W](https://tex.z-dn.net/?f=Area_1%20%3D%20L%20%2A%20W)
Recall that
and ![L = x + 9](https://tex.z-dn.net/?f=L%20%3D%20x%20%2B%209)
So;
![Area_1 = x * (x + 9)](https://tex.z-dn.net/?f=Area_1%20%3D%20x%20%2A%20%28x%20%2B%209%29)
For the bigger rectangle
![Area_2 = PQ * QR](https://tex.z-dn.net/?f=Area_2%20%3D%20PQ%20%2A%20QR)
Recall that
and ![QR = x + 4](https://tex.z-dn.net/?f=QR%20%3D%20x%20%2B%204)
So;
![Area_2 = (x + 13)(x + 4)](https://tex.z-dn.net/?f=Area_2%20%3D%20%28x%20%2B%2013%29%28x%20%2B%204%29)
Given that the Area of the walkway is ![400ft^2](https://tex.z-dn.net/?f=400ft%5E2)
This implies that
![Area_2 = Area_1 + 400](https://tex.z-dn.net/?f=Area_2%20%3D%20Area_1%20%2B%20400)
Substitute
and ![Area_2 = (x + 13)(x + 4)](https://tex.z-dn.net/?f=Area_2%20%3D%20%28x%20%2B%2013%29%28x%20%2B%204%29)
![(x + 13)(x + 4) = x * (x + 9) + 400](https://tex.z-dn.net/?f=%28x%20%2B%2013%29%28x%20%2B%204%29%20%3D%20x%20%2A%20%28x%20%2B%209%29%20%2B%20%20400)
Open All Brackets
![x^2 + 13x + 4x + 52 = x^2 + 9x + 400](https://tex.z-dn.net/?f=x%5E2%20%2B%2013x%20%2B%204x%20%2B%2052%20%3D%20x%5E2%20%2B%209x%20%2B%20%20400)
![x^2 + 17x + 52 = x^2 + 9x + 400](https://tex.z-dn.net/?f=x%5E2%20%2B%2017x%20%2B%2052%20%3D%20x%5E2%20%2B%209x%20%2B%20%20400)
Collect Like Terms
![x^2 - x^2 + 17x - 9x = 400- 52](https://tex.z-dn.net/?f=x%5E2%20-%20x%5E2%20%2B%2017x%20-%209x%20%3D%20%20400-%2052)
![8x = 348](https://tex.z-dn.net/?f=8x%20%3D%20348)
Divide both sides by 8
![\frac{8x}{8} = \frac{348}{8}](https://tex.z-dn.net/?f=%5Cfrac%7B8x%7D%7B8%7D%20%3D%20%5Cfrac%7B348%7D%7B8%7D)
![x = \frac{348}{8}](https://tex.z-dn.net/?f=x%20%3D%20%5Cfrac%7B348%7D%7B8%7D)
![x =43.5](https://tex.z-dn.net/?f=x%20%3D43.5)
Since the dimensions of the garden is
and ![L = x + 9](https://tex.z-dn.net/?f=L%20%3D%20x%20%2B%209)
<em>Substitute 43.5 for x in both cases</em>
![L = 43.5 + 9 = 52.5](https://tex.z-dn.net/?f=L%20%3D%2043.5%20%2B%209%20%3D%2052.5)
![W = 43.5](https://tex.z-dn.net/?f=W%20%3D%2043.5)
<em>Hence, the dimension of the garden is 52.5ft by 43.5ft</em>
Answer:
6/1 = 24/4
Step-by-step explanation:
3 times is basically multiply by 3 cube is 3 multiplied by a number
Ex:3 cube would be 3x3x3
Answer: The answer should be 35
Step-by-step explanation: If you take 140 divide it by 4 it should be the answer