Answer:
19.488
Step-by-step explanation:
8.12 x 2.4 = 19.488
Answer:
А.The system has two solutions, but only one is viable because the other results in a negative width.
Step-by-step explanation:
Given
Let:
length of play area A
width of play area A
length of play area B
width of play area B
Area of A
Area of B
From the question, we have the following:
![L_A = 1 + 4W_A](https://tex.z-dn.net/?f=L_A%20%3D%201%20%2B%204W_A)
![W_B = 2 + W_A](https://tex.z-dn.net/?f=W_B%20%3D%202%20%2B%20W_A)
![L_B = 2 + 3W_B](https://tex.z-dn.net/?f=L_B%20%3D%202%20%2B%203W_B)
![x = y](https://tex.z-dn.net/?f=x%20%3D%20y)
The area of A is:
![x = L_A * W_A](https://tex.z-dn.net/?f=x%20%3D%20L_A%20%2A%20W_A)
This gives:
![x = (1 + 4W_A) * W_A](https://tex.z-dn.net/?f=x%20%3D%20%281%20%2B%204W_A%29%20%2A%20W_A)
Open bracket
![x = W_A + 4W_A^2](https://tex.z-dn.net/?f=x%20%3D%20W_A%20%2B%204W_A%5E2)
The area of B is:
![y = L_B * W_B](https://tex.z-dn.net/?f=y%20%3D%20L_B%20%2A%20W_B)
![y = (2 + 3W_B) * ( 2 + W_A)](https://tex.z-dn.net/?f=y%20%3D%20%282%20%2B%203W_B%29%20%2A%20%28%202%20%2B%20W_A%29)
Substitute: ![W_B = 2 + W_A](https://tex.z-dn.net/?f=W_B%20%3D%202%20%2B%20W_A)
![y = (2 + 3(2 + W_A)) * ( 2 + W_A)](https://tex.z-dn.net/?f=y%20%3D%20%282%20%2B%203%282%20%2B%20W_A%29%29%20%2A%20%28%202%20%2B%20W_A%29)
Open brackets
![y = (2 + 6 + 3W_A) * ( 2 + W_A)](https://tex.z-dn.net/?f=y%20%3D%20%282%20%2B%206%20%2B%203W_A%29%20%2A%20%28%202%20%2B%20W_A%29)
![y = (8 + 3W_A) * ( 2 + W_A)](https://tex.z-dn.net/?f=y%20%3D%20%288%20%2B%203W_A%29%20%2A%20%28%202%20%2B%20W_A%29)
Expand
![y = 16 + 8W_A + 6W_A + 3W_A^2](https://tex.z-dn.net/?f=y%20%3D%2016%20%2B%208W_A%20%2B%206W_A%20%2B%203W_A%5E2)
![y = 16 + 14W_A + 3W_A^2](https://tex.z-dn.net/?f=y%20%3D%2016%20%2B%2014W_A%20%2B%203W_A%5E2)
We have that:
![x = y](https://tex.z-dn.net/?f=x%20%3D%20y)
This gives:
![W_A + 4W_A^2 = 16 + 14W_A + 3W_A^2](https://tex.z-dn.net/?f=W_A%20%2B%204W_A%5E2%20%3D%2016%20%2B%2014W_A%20%2B%203W_A%5E2)
Collect like terms
![4W_A^2 - 3W_A^2 + W_A -14W_A - 16 =0](https://tex.z-dn.net/?f=4W_A%5E2%20-%203W_A%5E2%20%2B%20W_A%20%20-14W_A%20%20-%2016%20%3D0)
![W_A^2 -13W_A - 16 =0](https://tex.z-dn.net/?f=W_A%5E2%20%20-13W_A%20%20-%2016%20%3D0)
Using quadratic calculator, we have:
or
--- approximated
But the width can not be negative; So:
![W = 1.19](https://tex.z-dn.net/?f=W%20%3D%201.19)
The answer is the second choice. Hope that was helpful
Answer:
-2
Step-by-step explanation:
Start with the vertex form of the equation of a parabola: y - k = a(x - h)^2
Here h = -2, k = -3, x = -1, y = -5. Find a:
-5 - [-3] = a(-1 - [-2])^2, or
-5 + 3 = a(1)^2, or
-2 = a
The unknown coefficient is -2.