Remember these two combinations: logab=loga+logb, log(a/b)=loga-logb
3logx=logx^3
(1/2)log(x+2)=log(x+2)^(1/2)
2log(z-4)=log(z-4)^2
so the given expression can be combined into log{[(x^3)(z-4)^2]/(x+2)^(1/2)}
well, putting the movie in fifths, she watched 3/5, the whole movie will be 5/5 = 1.
![\begin{array}{ccll} \stackrel{movie}{fraction}&hour\\ \cline{1-2} \frac{3}{5}&\frac{5}{8}\\[1em] \underset{whole}{1}&x \end{array}\implies \cfrac{~~ \frac{3}{5}~~}{1}=\cfrac{~~ \frac{5}{8}~~}{x}\implies \cfrac{3}{5}x=\cfrac{5}{8}\implies \cfrac{3x}{5}=\cfrac{5}{8} \\\\\\ 24x=25\implies x = \cfrac{25}{24}\implies x = 1\frac{1}{24}\qquad \textit{1 hour, 2 minutes and 30 seconds}](https://tex.z-dn.net/?f=%5Cbegin%7Barray%7D%7Bccll%7D%20%5Cstackrel%7Bmovie%7D%7Bfraction%7D%26hour%5C%5C%20%5Ccline%7B1-2%7D%20%5Cfrac%7B3%7D%7B5%7D%26%5Cfrac%7B5%7D%7B8%7D%5C%5C%5B1em%5D%20%5Cunderset%7Bwhole%7D%7B1%7D%26x%20%5Cend%7Barray%7D%5Cimplies%20%5Ccfrac%7B~~%20%5Cfrac%7B3%7D%7B5%7D~~%7D%7B1%7D%3D%5Ccfrac%7B~~%20%5Cfrac%7B5%7D%7B8%7D~~%7D%7Bx%7D%5Cimplies%20%5Ccfrac%7B3%7D%7B5%7Dx%3D%5Ccfrac%7B5%7D%7B8%7D%5Cimplies%20%5Ccfrac%7B3x%7D%7B5%7D%3D%5Ccfrac%7B5%7D%7B8%7D%20%5C%5C%5C%5C%5C%5C%2024x%3D25%5Cimplies%20x%20%3D%20%5Ccfrac%7B25%7D%7B24%7D%5Cimplies%20x%20%3D%201%5Cfrac%7B1%7D%7B24%7D%5Cqquad%20%5Ctextit%7B1%20hour%2C%202%20minutes%20and%2030%20seconds%7D)
Answer:
The length of side x is 
Step-by-step explanation:
Pythagorean Theorem:
In a right triangle, with sides a and b, and hypothenuse h, we have that:

In this question:
The vertical line on the sides means that both are equal, that is, measuring x, so
.
Hypothenuse is the square root of 12. So 





The length of side x is 
They won 6/11 games.
When you add the games they won, lost, and tied you see that they played a total of 11 games. It tells you that they won 6 games so you would put 6 as the numerator and 11 as the denominator and get 6/11.