Answer:
Step-by-step explanation:
The formula for volume of a cylinder is
V = πr²h where r is the radius and h is the height.
We are given r = 5 and h = 2.5, plug those values in and simplify...
V = π(5²)(2.5)
V = π(25)(2.5)
V = 62.5π
Question 1:Multiply both sides of the proportion by 35.
You get.
7(x-1) = 4x+2
7x-7 = 4x+2
Now, add both sides by 7 and subtract both sides by 4x
3x = 9
Divide both sides by 3
x=3
Question 2:Multiply both the numerator and the denominator of
![\frac{x+1}{x+3}](https://tex.z-dn.net/?f=%5Cfrac%7Bx%2B1%7D%7Bx%2B3%7D)
by 3.
We want to multiply it by 3 so that the +1 and +3 become +3 and +9. +3 and +9 have a difference of 6, just like 15 and 21, which is what we want.
![\frac{3x+3}{3x+9} = \frac{15}{21}](https://tex.z-dn.net/?f=%20%5Cfrac%7B3x%2B3%7D%7B3x%2B9%7D%20%3D%20%5Cfrac%7B15%7D%7B21%7D%20)
Set the numerator equal to the numerator and the denominator equal to the denominator.
3x+3 = 15
3x+9 = 21
If you solve both of these, you get x=4 for both.
That's your answer.
Hope this helps! :)
The value of <u>a</u> is 2 and the value of <u>b</u> is 6.
<h3>Factoring</h3>
In math, factoring or factorization is used to write an algebraic expression in factors. There are some rules for factorization. One of them is a factor out a common term for example: x²-x= x(x-1), where x is a common term.
You should factor the given expression.
![2-\frac{x+3}{x+1}-\frac{x-5}{x-1}\\ \\ 2+\frac{-\left(x+3\right)\left(x-1\right)-\left(x-5\right)\left(x+1\right)}{\left(x+1\right)\left(x-1\right)}\\ \\ \mathrm{Apply\:the\:fraction\:rule}:\quad \:a+\frac{b}{c}=\frac{ac+b}{c}\\ \\ \frac{2\left(x+1\right)\left(x-1\right)-\left(x+3\right)\left(x-1\right)-\left(x-5\right)\left(x+1\right)}{\left(x+1\right)\left(x-1\right)}\\ \\ \frac{2x+6}{\left(x+1\right)\left(x-1\right)}=\frac{2x+6}{x^2-1}](https://tex.z-dn.net/?f=2-%5Cfrac%7Bx%2B3%7D%7Bx%2B1%7D-%5Cfrac%7Bx-5%7D%7Bx-1%7D%5C%5C%20%5C%5C%202%2B%5Cfrac%7B-%5Cleft%28x%2B3%5Cright%29%5Cleft%28x-1%5Cright%29-%5Cleft%28x-5%5Cright%29%5Cleft%28x%2B1%5Cright%29%7D%7B%5Cleft%28x%2B1%5Cright%29%5Cleft%28x-1%5Cright%29%7D%5C%5C%20%5C%5C%20%5Cmathrm%7BApply%5C%3Athe%5C%3Afraction%5C%3Arule%7D%3A%5Cquad%20%5C%3Aa%2B%5Cfrac%7Bb%7D%7Bc%7D%3D%5Cfrac%7Bac%2Bb%7D%7Bc%7D%5C%5C%20%5C%5C%20%5Cfrac%7B2%5Cleft%28x%2B1%5Cright%29%5Cleft%28x-1%5Cright%29-%5Cleft%28x%2B3%5Cright%29%5Cleft%28x-1%5Cright%29-%5Cleft%28x-5%5Cright%29%5Cleft%28x%2B1%5Cright%29%7D%7B%5Cleft%28x%2B1%5Cright%29%5Cleft%28x-1%5Cright%29%7D%5C%5C%20%5C%5C%20%5Cfrac%7B2x%2B6%7D%7B%5Cleft%28x%2B1%5Cright%29%5Cleft%28x-1%5Cright%29%7D%3D%5Cfrac%7B2x%2B6%7D%7Bx%5E2-1%7D)
Read more about the factoring here:
brainly.com/question/11579257
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7(2x+5)=4x-9-x
14x+35=3x-9
11x = -44
x = -4
7(2*-4+5)=4*-4-9--4
7(-3)=-21
-21=-21. so it checks out and x = -4