Answer:
The factorized expression is
![1 + x](https://tex.z-dn.net/?f=1%20%2B%20x)
Step-by-step explanation:
The first step to solve this problem is knowing that:
![(f(x))^{-1} = \frac{1}{f(x)}](https://tex.z-dn.net/?f=%28f%28x%29%29%5E%7B-1%7D%20%3D%20%5Cfrac%7B1%7D%7Bf%28x%29%7D)
So
![(xe^{-x})^{-1} + e^{x}](https://tex.z-dn.net/?f=%28xe%5E%7B-x%7D%29%5E%7B-1%7D%20%2B%20e%5E%7Bx%7D)
![\frac{1}{xe^{-x}} + e^{x}](https://tex.z-dn.net/?f=%5Cfrac%7B1%7D%7Bxe%5E%7B-x%7D%7D%20%2B%20e%5E%7Bx%7D)
![xe^{-x}(\frac{1}{xe^{-x}} + e^{x})](https://tex.z-dn.net/?f=xe%5E%7B-x%7D%28%5Cfrac%7B1%7D%7Bxe%5E%7B-x%7D%7D%20%2B%20e%5E%7Bx%7D%29)
![1 + x](https://tex.z-dn.net/?f=1%20%2B%20x)
The factorized expression is
![1 + x](https://tex.z-dn.net/?f=1%20%2B%20x)
Number 20 should be A.) An increase of the variety of goods available.
Number 21 should be E.) Manufacturing.
Left side:
1-sin²(x) = cos²(x)
1-sin²(x) / cos(x) = cos²(x) / cos(x) = <em>cos(x)</em>
Right side:
sin(2x) = 2 sin(x) cos(x)
sin(2x) / 2 sin(x) = 2 sin(x) cos(x) / 2 sin(x) = <em>cos x </em>
Answer:
2A/b = h
4 inches = h
Step-by-step explanation:
A = 1/2bh in terms of h
Multiply each side by 2
2A = bh
Divide by b
2A/b = h
Let A = 18 and b = 9
2*18/9 = h
4 = h
Answer:
Approximately ![238\ gallons](https://tex.z-dn.net/?f=238%5C%20gallons)
Step-by-step explanation:
we know that
The volume of a cylinder (barrel) is equal to
![V=\pi r^{2}h](https://tex.z-dn.net/?f=V%3D%5Cpi%20r%5E%7B2%7Dh)
in this problem we have
![h=4.5\ ft](https://tex.z-dn.net/?f=h%3D4.5%5C%20ft)
-----> the radius is half the diameter
substitute
![V=(3.14)(1.5^{2})(4.5)=31.7925\ ft^{3}](https://tex.z-dn.net/?f=V%3D%283.14%29%281.5%5E%7B2%7D%29%284.5%29%3D31.7925%5C%20ft%5E%7B3%7D)
Convert to gallons
![31.7925\ ft^{3}*7.5=238.44\ gallons](https://tex.z-dn.net/?f=31.7925%5C%20ft%5E%7B3%7D%2A7.5%3D238.44%5C%20gallons)