Answer:
x = -11
Step-by-step explanation:
Convert fraction into negative exponential form: ![(36^-^1)^x^-^4=(216^-^1)^x^+^1\\](https://tex.z-dn.net/?f=%2836%5E-%5E1%29%5Ex%5E-%5E4%3D%28216%5E-%5E1%29%5Ex%5E%2B%5E1%5C%5C)
Simplify using exponent power rule: ![(a^n)^m=a^n^m:36^-^x^+^4=216^-^x^-^1](https://tex.z-dn.net/?f=%28a%5En%29%5Em%3Da%5En%5Em%3A36%5E-%5Ex%5E%2B%5E4%3D216%5E-%5Ex%5E-%5E1)
Convert both sides of the equation into terms with same base:![(6^2)^-^x^+^4=(6^3)^-^x^-^1](https://tex.z-dn.net/?f=%286%5E2%29%5E-%5Ex%5E%2B%5E4%3D%286%5E3%29%5E-%5Ex%5E-%5E1)
Simplify using exponent power rule:
![(a^n)^m=a^n^m:6^-^2^x^+^8=6^-^3^x^-^3](https://tex.z-dn.net/?f=%28a%5En%29%5Em%3Da%5En%5Em%3A6%5E-%5E2%5Ex%5E%2B%5E8%3D6%5E-%5E3%5Ex%5E-%5E3)
Based on the given conditions, corresponding exponents are equal:
![-2x=8=-3x-3](https://tex.z-dn.net/?f=-2x%3D8%3D-3x-3)
Rearrange unknown terms to the left side of the equation:
![-2x+3x=-3-8](https://tex.z-dn.net/?f=-2x%2B3x%3D-3-8)
Combine like terms: ![x=-3-8](https://tex.z-dn.net/?f=x%3D-3-8)
Calculate the sum or difference: ![x = -11](https://tex.z-dn.net/?f=x%20%3D%20-11)
Thurs, x = -11
[RevyBreeze]
Answer:
![\displaystyle k = -\frac{1}{8}](https://tex.z-dn.net/?f=%5Cdisplaystyle%20k%20%3D%20-%5Cfrac%7B1%7D%7B8%7D)
Step-by-step explanation:
We are given the equation:
![\displaystyle y = kx^3](https://tex.z-dn.net/?f=%5Cdisplaystyle%20y%20%3D%20kx%5E3)
And we want to determine the value of <em>k</em> such that the graph passes through the point (-2, 1).
Hence, when <em>x</em> = -2, <em>y</em> = 1. Substitute:
![\displaystyle (1) = k(-2)^3](https://tex.z-dn.net/?f=%5Cdisplaystyle%20%281%29%20%3D%20k%28-2%29%5E3)
Simplify:
![\displaystyle 1 = -8k](https://tex.z-dn.net/?f=%5Cdisplaystyle%201%20%3D%20-8k)
Hence:
![\displaystyle k = -\frac{1}{8}](https://tex.z-dn.net/?f=%5Cdisplaystyle%20k%20%3D%20-%5Cfrac%7B1%7D%7B8%7D)
Answer:
SORRY I ONLY NOW THE ANSWER FOR THE SECOND QUESTION SRY!!
18-Jul-2019 · So, the price of a full tank is 11.9*3.04=36.176. ... tank of gas if one gallon costs $3.04 and the tank holds 11.9 gallons
Step-by-step explanation:
HOPE IT HELPS XD :)