Answer:
416 the answer is that I hope it is Right
Answer:
3.160
Step-by-step explanation:
You can solve for x using logarithm.
Rewrite in logarithm form
![log_{6}4=2x\\\\x=\frac{log_64}{2}\\x=\frac{\frac{log4}{log6}}{2}\\x=\frac{log4}{log6} * \frac{1}{2}\\x=\frac{log4}{log6 * 2}\\x\approx0.386852807\\36^{6(0.386852807)-2} \approx3.160](https://tex.z-dn.net/?f=log_%7B6%7D4%3D2x%5C%5C%5C%5Cx%3D%5Cfrac%7Blog_64%7D%7B2%7D%5C%5Cx%3D%5Cfrac%7B%5Cfrac%7Blog4%7D%7Blog6%7D%7D%7B2%7D%5C%5Cx%3D%5Cfrac%7Blog4%7D%7Blog6%7D%20%2A%20%5Cfrac%7B1%7D%7B2%7D%5C%5Cx%3D%5Cfrac%7Blog4%7D%7Blog6%20%2A%202%7D%5C%5Cx%5Capprox0.386852807%5C%5C36%5E%7B6%280.386852807%29-2%7D%20%5Capprox3.160)
Given:
A = charges 9.95 per month for the first 10 hours and 1.69 per hour for all those over 10 hours.
B = charges a flat fee of 19.95
A = 9.95 + 1.69(x-10) where x is the total number of hours used.
B = 19.95
A = B
9.95 + 1.69(x - 10) = 19.95
1.69x - 16.9 = 19.95 - 9.95
1.69x = 10 + 16.9
1.69x = 26.9
x = 26.9/1.69
x = 15.92 hours
If usage does not go over 10 hours, it is cheaper to use A.
<em />If usage is between 15-16 hours, A or B is acceptable. They cost almost the same.
If usage is beyond 16 hours, it is cheaper to use B.
Alright, lets get started.
![-\frac{2}{3} (2x-\frac{1}{2} )\leq \frac{1}{5}x -1](https://tex.z-dn.net/?f=-%5Cfrac%7B2%7D%7B3%7D%20%282x-%5Cfrac%7B1%7D%7B2%7D%20%29%5Cleq%20%5Cfrac%7B1%7D%7B5%7Dx%20-1)
Distributing
into parenthesis
![-\frac{4x}{3}+ \frac{2}{6} \leq \frac{x}{5} -1](https://tex.z-dn.net/?f=-%5Cfrac%7B4x%7D%7B3%7D%2B%20%5Cfrac%7B2%7D%7B6%7D%20%5Cleq%20%5Cfrac%7Bx%7D%7B5%7D%20-1)
![-\frac{4x}{3}+ \frac{1}{3} \leq \frac{x}{5} -1](https://tex.z-dn.net/?f=-%5Cfrac%7B4x%7D%7B3%7D%2B%20%5Cfrac%7B1%7D%7B3%7D%20%5Cleq%20%5Cfrac%7Bx%7D%7B5%7D%20-1)
Subtracting
from both sides
![-\frac{4x}{3}+ \frac{1}{3}- \frac{1}{3}\leq\frac{x}{5}-1- \frac{1}{3}](https://tex.z-dn.net/?f=-%5Cfrac%7B4x%7D%7B3%7D%2B%20%5Cfrac%7B1%7D%7B3%7D-%20%5Cfrac%7B1%7D%7B3%7D%5Cleq%5Cfrac%7Bx%7D%7B5%7D-1-%20%5Cfrac%7B1%7D%7B3%7D)
![-\frac{4x}{3} \leq \frac{x}{5}- \frac{4}{3}](https://tex.z-dn.net/?f=-%5Cfrac%7B4x%7D%7B3%7D%20%5Cleq%20%5Cfrac%7Bx%7D%7B5%7D-%20%5Cfrac%7B4%7D%7B3%7D)
Adding
in both sides
![-\frac{4x}{3}+ \frac{4}{3} \leq \frac{x}{5} -\frac{4}{3}+ \frac{4}{3}](https://tex.z-dn.net/?f=-%5Cfrac%7B4x%7D%7B3%7D%2B%20%5Cfrac%7B4%7D%7B3%7D%20%5Cleq%20%5Cfrac%7Bx%7D%7B5%7D%20-%5Cfrac%7B4%7D%7B3%7D%2B%20%5Cfrac%7B4%7D%7B3%7D)
![-\frac{4x}{3} +\frac{4}{3} \leq \frac{x}{5}](https://tex.z-dn.net/?f=-%5Cfrac%7B4x%7D%7B3%7D%20%2B%5Cfrac%7B4%7D%7B3%7D%20%5Cleq%20%5Cfrac%7Bx%7D%7B5%7D)
Adding
in both sides
![-\frac{4x}{3} +\frac{4}{3} +\frac{4x}{3} \leq \frac{x}{5} +\frac{4x}{3}](https://tex.z-dn.net/?f=-%5Cfrac%7B4x%7D%7B3%7D%20%2B%5Cfrac%7B4%7D%7B3%7D%20%2B%5Cfrac%7B4x%7D%7B3%7D%20%5Cleq%20%5Cfrac%7Bx%7D%7B5%7D%20%2B%5Cfrac%7B4x%7D%7B3%7D)
![\frac{4}{3} \leq \frac{x}{5} +\frac{4x}{3}](https://tex.z-dn.net/?f=%5Cfrac%7B4%7D%7B3%7D%20%5Cleq%20%5Cfrac%7Bx%7D%7B5%7D%20%2B%5Cfrac%7B4x%7D%7B3%7D)
Making common denominator, adding fractions
![\frac{4}{3} \leq \frac{23x}{15}](https://tex.z-dn.net/?f=%5Cfrac%7B4%7D%7B3%7D%20%5Cleq%20%5Cfrac%7B23x%7D%7B15%7D)
It means
![23x\geq \frac{4*15}{3}](https://tex.z-dn.net/?f=23x%5Cgeq%20%5Cfrac%7B4%2A15%7D%7B3%7D)
![23x\geq 20](https://tex.z-dn.net/?f=23x%5Cgeq%2020)
Dividing 23 in both sides
![x\geq \frac{20}{23}](https://tex.z-dn.net/?f=x%5Cgeq%20%5Cfrac%7B20%7D%7B23%7D)
In interval notation
[
,∞)
This is the answer
Hope it will help :)
Answer:
![x^3y^5](https://tex.z-dn.net/?f=x%5E3y%5E5)
Step-by-step explanation:
![\frac{(x^3y^2)^2(xy^2)}{x^4y} = \frac{(x^6y^4)(xy^2)}{x^4y}=\frac{x^7y^6}{x^4y} =x^3y^5](https://tex.z-dn.net/?f=%5Cfrac%7B%28x%5E3y%5E2%29%5E2%28xy%5E2%29%7D%7Bx%5E4y%7D%20%3D%20%5Cfrac%7B%28x%5E6y%5E4%29%28xy%5E2%29%7D%7Bx%5E4y%7D%3D%5Cfrac%7Bx%5E7y%5E6%7D%7Bx%5E4y%7D%20%3Dx%5E3y%5E5)
Here , the general rules followed are :-
i) ![x^m * x^n =x^m^+^n](https://tex.z-dn.net/?f=x%5Em%20%2A%20x%5En%20%3Dx%5Em%5E%2B%5En)
ii) ![(x^my^n)^z = (x^m^z)(y^n^z)](https://tex.z-dn.net/?f=%28x%5Emy%5En%29%5Ez%20%3D%20%28x%5Em%5Ez%29%28y%5En%5Ez%29)
iii) ![\frac{x^my^n} {x^ay^b} = (x^m^-^a)(y^n^-^b)](https://tex.z-dn.net/?f=%5Cfrac%7Bx%5Emy%5En%7D%20%7Bx%5Eay%5Eb%7D%20%3D%20%28x%5Em%5E-%5Ea%29%28y%5En%5E-%5Eb%29)