Steps:
216 mm3 is the volume.
Given the volume, you can take the cube root of the volume to find the side.
The cube root of 216 is 6.
Answer: 6
To graph the new shape, you must move each vertex down 3 units. This causes Q to become (1, 0), L to become (5, -2), and Q to become (1, 0). These values can be found by simply counting down by three for each point.
Answer:
[-5, 4) ∪ (4, ∞)
Step-by-step explanation:
Given functions:
![f(x)=\dfrac{1}{x-3}](https://tex.z-dn.net/?f=f%28x%29%3D%5Cdfrac%7B1%7D%7Bx-3%7D)
![g(x)=\sqrt{x+5}](https://tex.z-dn.net/?f=g%28x%29%3D%5Csqrt%7Bx%2B5%7D)
Composite function:
![\begin{aligned}(f\:o\:g)(x)&=f[g(x)]\\ & =\dfrac{1}{\sqrt{x+5}-3} \end{aligned}](https://tex.z-dn.net/?f=%5Cbegin%7Baligned%7D%28f%5C%3Ao%5C%3Ag%29%28x%29%26%3Df%5Bg%28x%29%5D%5C%5C%20%26%20%3D%5Cdfrac%7B1%7D%7B%5Csqrt%7Bx%2B5%7D-3%7D%20%5Cend%7Baligned%7D)
Domain: input values (x-values)
For
to be defined:
![x+5\geq 0 \implies x\geq -5](https://tex.z-dn.net/?f=x%2B5%5Cgeq%200%20%5Cimplies%20x%5Cgeq%20-5)
![\sqrt{x+5}\neq 3 \implies x\neq 4](https://tex.z-dn.net/?f=%5Csqrt%7Bx%2B5%7D%5Cneq%203%20%5Cimplies%20x%5Cneq%204)
Therefore,
and ![x > 4](https://tex.z-dn.net/?f=x%20%3E%204)
⇒ [-5, 4) ∪ (4, ∞)
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