First find the greatest common factor which is 3.
now write the GCF first, and then in parentheses, divide each term by the GCF;
3(108/3 + (-3x^2/3)
3(36 - x^2)
3(6^2 - x^2)
use the difference of squares;
3(6 + x)(6 - x)
hope this helped!
Answer:
With this ratio in 12 h the amount of people that will watch the movie is 1,440.
Step-by-step explanation:
In order to compute how many people will see the movie in 12 hours we need to find the ratio per hour of people watching the movie. We were given the information that 360 people watched the movie in 3 h, to convert this value to people per hour we can divide the amount of people that watched the movie on that time by the total amount of time that passed. We have:
ratio = 360/3 = 120 people/h
We now multiply the ratio of people watching the movie by the length of time that we want to know, that is 12h. So we have:
amount of people = time*ratio = 12*120 = 1440
Given:
The height of the given trapezoid = 6 in
The area of the trapezoid = 72 in²
Also given, one base of the trapezoid is 6 inches longer than the other base
To find the lengths of the bases.
Formula
The area of the trapezoid is
![A=\frac{1}{2} (b_{1} +b_{2} )h](https://tex.z-dn.net/?f=A%3D%5Cfrac%7B1%7D%7B2%7D%20%28b_%7B1%7D%20%2Bb_%7B2%7D%20%29h)
where, h be the height of the trapezoid
be the shorter base
be the longer base
As per the given problem,
![b_{2}=b_{1} +6](https://tex.z-dn.net/?f=b_%7B2%7D%3Db_%7B1%7D%20%20%2B6)
Now,
Putting, A=72,
and h=6 we get,
![\frac{1}{2} (b_{1} +b_{1}+6)(6) = 72](https://tex.z-dn.net/?f=%5Cfrac%7B1%7D%7B2%7D%20%28b_%7B1%7D%20%2Bb_%7B1%7D%2B6%29%286%29%20%3D%2072)
or, ![b_{1}+b_{1}+6 = \frac{(72)(2)}{6}](https://tex.z-dn.net/?f=b_%7B1%7D%2Bb_%7B1%7D%2B6%20%3D%20%5Cfrac%7B%2872%29%282%29%7D%7B6%7D)
or, ![2b_{1}+6 = 24](https://tex.z-dn.net/?f=2b_%7B1%7D%2B6%20%3D%2024)
or, ![2b_{1}=24-6](https://tex.z-dn.net/?f=2b_%7B1%7D%3D24-6)
or, ![b_{1}= \frac{18}{2}](https://tex.z-dn.net/?f=b_%7B1%7D%3D%20%5Cfrac%7B18%7D%7B2%7D)
or, ![b_{1}=9](https://tex.z-dn.net/?f=b_%7B1%7D%3D9)
So,
The shorter base is 9 in and the other base is = (6+9) = 15 in
Hence,
One base is 9 inches for one of the bases and 15 inches for the other base.