Answer:
The length is 15 yards
Step-by-step explanation:
Given
Represent the width with W and length with L: So
![Area = 135yd^2](https://tex.z-dn.net/?f=Area%20%3D%20135yd%5E2)
![L=3W - 12](https://tex.z-dn.net/?f=L%3D3W%20-%2012)
Required
Determine the length of the rectangle:
Area is calculated as thus:
![Area = L * W](https://tex.z-dn.net/?f=Area%20%3D%20L%20%2A%20W)
Substitute 3W - 12 for L and 135 for Area
![135= (3W - 12) * W](https://tex.z-dn.net/?f=135%3D%20%283W%20-%2012%29%20%2A%20W)
![135= 3W^2 - 12W](https://tex.z-dn.net/?f=135%3D%203W%5E2%20-%2012W)
Reorder:
![3W^2 - 12W - 135= 0](https://tex.z-dn.net/?f=3W%5E2%20-%2012W%20-%20135%3D%200)
Divide through by 3
![W^2 - 4W - 45 = 0](https://tex.z-dn.net/?f=W%5E2%20-%204W%20-%2045%20%3D%200)
Expand:
![W^2 - 9W + 5W - 45 = 0](https://tex.z-dn.net/?f=W%5E2%20%20-%209W%20%2B%205W%20-%2045%20%3D%200)
![W(W - 9) + 5(W - 9) = 0](https://tex.z-dn.net/?f=W%28W%20%20-%209%29%20%2B%205%28W%20-%209%29%20%3D%200)
![(W + 5)(W-9) = 0](https://tex.z-dn.net/?f=%28W%20%2B%205%29%28W-9%29%20%3D%200)
or ![W - 9 = 0](https://tex.z-dn.net/?f=W%20-%209%20%3D%200)
or ![W = 9](https://tex.z-dn.net/?f=W%20%3D%209)
But width can't be negative
So:
![W = 9](https://tex.z-dn.net/?f=W%20%3D%209)
Recall that: ![L=3W - 12](https://tex.z-dn.net/?f=L%3D3W%20-%2012)
![L = 3 * 9 - 12](https://tex.z-dn.net/?f=L%20%3D%203%20%2A%209%20-%2012)
![L = 15](https://tex.z-dn.net/?f=L%20%3D%2015)
<em>Hence, the length 15 yards</em>
4(y - 7) = 2y - 38
4y - 28 = 2y - 38
4y - 2y = -38 + 28
2y = -10
y = -5
slope intercept form is: y = mx + b
m = slope
b = y-intercept
In the equation y = 1/4x + 8
m = 1/4 = slope
b = 8 = y-intercept
Answer:
5.3 or 28
Step-by-step explanation:
+
=![8^{2}](https://tex.z-dn.net/?f=8%5E%7B2%7D)
36+
=64
64-36=28
![\sqrt{28\\}](https://tex.z-dn.net/?f=%5Csqrt%7B28%5C%5C%7D)
=5.29 or 5.3