Answer:
x ≈ 18.7
Step-by-step explanation:
This is a big equation, so let's break it down a bit.
![\frac{3}{2} \sqrt[4]{(2(x-6) ^3 )} +4=16](https://tex.z-dn.net/?f=%5Cfrac%7B3%7D%7B2%7D%20%5Csqrt%5B4%5D%7B%282%28x-6%29%20%5E3%20%29%7D%20%2B4%3D16)
Let's start by isolating the radical which is x.
So subtract 4 from both sides :
![\frac{3}{2} \sqrt[4]{(2(x-6) ^3)}](https://tex.z-dn.net/?f=%5Cfrac%7B3%7D%7B2%7D%20%5Csqrt%5B4%5D%7B%282%28x-6%29%20%5E3%29%7D)
![=12](https://tex.z-dn.net/?f=%3D12)
Now multiply both sides by 2 to get rid of the fraction :
![3\sqrt[4]{(2(x-6)^3)} = 24](https://tex.z-dn.net/?f=3%5Csqrt%5B4%5D%7B%282%28x-6%29%5E3%29%7D%20%3D%2024)
Now divide both sides by 3 to get rid of the number out of the poly root :
![\sqrt[4]{2(x-6) ^3}](https://tex.z-dn.net/?f=%5Csqrt%5B4%5D%7B2%28x-6%29%20%5E3%7D)
![=8](https://tex.z-dn.net/?f=%3D8)
Now take both sides of the equation to the power of 4 :
![2x^3 - 36x^2+216x-432=4096](https://tex.z-dn.net/?f=2x%5E3%20-%2036x%5E2%2B216x-432%3D4096)
And lastly, solve :
which is rounded up to
≈ ![18.7](https://tex.z-dn.net/?f=18.7)
Answer:
![D.\ y = \frac{5}{2} - 4](https://tex.z-dn.net/?f=D.%5C%20y%20%3D%20%5Cfrac%7B5%7D%7B2%7D%20-%204)
Step-by-step explanation:
Given
![5x - 2y = 18](https://tex.z-dn.net/?f=5x%20-%202y%20%3D%2018)
Required
Determine parallel line
First, we need to convert the equation to slope intercept form
![5x - 2y = 18](https://tex.z-dn.net/?f=5x%20-%202y%20%3D%2018)
![- 2y = 18 - 5x](https://tex.z-dn.net/?f=-%202y%20%3D%2018%20-%205x)
Make y the subject:
![y = \frac{18}{-2} - \frac{5x}{-2}](https://tex.z-dn.net/?f=y%20%3D%20%5Cfrac%7B18%7D%7B-2%7D%20-%20%5Cfrac%7B5x%7D%7B-2%7D)
![y = -9 + \frac{5}{2}x](https://tex.z-dn.net/?f=y%20%3D%20-9%20%2B%20%5Cfrac%7B5%7D%7B2%7Dx)
![y = \frac{5}{2}x - 9](https://tex.z-dn.net/?f=y%20%3D%20%5Cfrac%7B5%7D%7B2%7Dx%20-%209)
The general form of an equation is:
![y=mx + b](https://tex.z-dn.net/?f=y%3Dmx%20%2B%20b)
Where
![m = slope](https://tex.z-dn.net/?f=m%20%3D%20slope)
By comparison:
![m = \frac{5}{2}](https://tex.z-dn.net/?f=m%20%3D%20%5Cfrac%7B5%7D%7B2%7D)
From the condition of parallel equation.
A parallel equation will have an equal slope of ![\frac{5}{2}](https://tex.z-dn.net/?f=%5Cfrac%7B5%7D%7B2%7D)
From the list of given options, option D has a slope of ![\frac{5}{2}](https://tex.z-dn.net/?f=%5Cfrac%7B5%7D%7B2%7D)
Triangular number sequnce