Questions:
A clothing manufacturer uses the model a = √(f + 4) - √(36 - f) to estimate the amount of fabric to order from a mill. In the formula, a is the number of apparel items (in hundreds) and f is the number of units of fabric needed. If 400 apparel items will be manufactured , how many units of fabric should be ordered?
Answer:
32 units of fabrics
Step-by-step explanation:
Given
![a = \sqrt{f + 4} - \sqrt{36 - f}](https://tex.z-dn.net/?f=a%20%3D%20%5Csqrt%7Bf%20%2B%204%7D%20-%20%5Csqrt%7B36%20-%20f%7D)
Required
Find f when a = 4
Substitute 4 for a
![4 = \sqrt{f + 4} - \sqrt{36 - f}](https://tex.z-dn.net/?f=4%20%3D%20%5Csqrt%7Bf%20%2B%204%7D%20-%20%5Csqrt%7B36%20-%20f%7D)
Rewrite as:
![\sqrt{36 - f} + 4 = \sqrt{f + 4}](https://tex.z-dn.net/?f=%5Csqrt%7B36%20-%20f%7D%20%2B%204%20%3D%20%5Csqrt%7Bf%20%2B%204%7D)
Square both sides
![(\sqrt{36 - f} + 4)^2 = (\sqrt{f + 4})^2](https://tex.z-dn.net/?f=%28%5Csqrt%7B36%20-%20f%7D%20%2B%204%29%5E2%20%3D%20%28%5Csqrt%7Bf%20%2B%204%7D%29%5E2)
![(\sqrt{36 - f} + 4)^2 = f + 4](https://tex.z-dn.net/?f=%28%5Csqrt%7B36%20-%20f%7D%20%2B%204%29%5E2%20%3D%20f%20%2B%204)
![36 - f + 8\sqrt{36 - f} + 16 = f + 4](https://tex.z-dn.net/?f=36%20-%20f%20%2B%208%5Csqrt%7B36%20-%20f%7D%20%2B%2016%20%3D%20f%20%2B%204)
Collect Like Terms
![8\sqrt{36 - f}= f +f+ 4 - 36 -16](https://tex.z-dn.net/?f=8%5Csqrt%7B36%20-%20f%7D%3D%20f%20%2Bf%2B%204%20-%2036%20-16)
![8\sqrt{36 - f}= 2f -48](https://tex.z-dn.net/?f=8%5Csqrt%7B36%20-%20f%7D%3D%202f%20-48)
Divide through by 2
![4\sqrt{36 - f}= f -24](https://tex.z-dn.net/?f=4%5Csqrt%7B36%20-%20f%7D%3D%20f%20-24)
Square both sides
![16(36-f) = (f - 24)^2](https://tex.z-dn.net/?f=16%2836-f%29%20%3D%20%28f%20-%2024%29%5E2)
![16(36-f) = f^2 - 48f + 576](https://tex.z-dn.net/?f=16%2836-f%29%20%3D%20f%5E2%20-%2048f%20%2B%20576)
![576-16f = f^2 - 48f + 576](https://tex.z-dn.net/?f=576-16f%20%3D%20f%5E2%20-%2048f%20%2B%20576)
![-16f = f^2 - 48f](https://tex.z-dn.net/?f=-16f%20%3D%20f%5E2%20-%2048f)
Collect like terms
![f^2 - 48f + 16f = 0](https://tex.z-dn.net/?f=f%5E2%20-%2048f%20%2B%2016f%20%3D%200)
![f^2 -32f = 0](https://tex.z-dn.net/?f=f%5E2%20-32f%20%3D%200)
Factorize
![f(f - 32) = 0](https://tex.z-dn.net/?f=f%28f%20-%2032%29%20%3D%200)
or ![f = 32](https://tex.z-dn.net/?f=f%20%3D%2032)
f can not be 0 because some units must be ordered.
So, f = 32
The answer is to the expression is -18
Answer:
a
Step-by-step explanation:
the ratio of boys to girls is 15:9 or 15/9 or 1.67 or 5/3.
plz mark brainliest
26% of 65 is 0.26*65 = 16.90
Carly made 17 of her 65 foul shots.