Answer:
2.4 miles in total
Step-by-step explanation:
"this answer needs to be atleast 20 characters long"
Answer:
where is the problem?
Step-by-step explanation:
Answer:
![\frac{(x+5)(x+2)}{x(x-3)(x+3)}](https://tex.z-dn.net/?f=%5Cfrac%7B%28x%2B5%29%28x%2B2%29%7D%7Bx%28x-3%29%28x%2B3%29%7D)
Step-by-step explanation:
The given expression is
![\frac{2x+5}{x^{2} -3x} -\frac{3x+5}{x^{3} -9x} -\frac{x+1}{x^{2}-9}](https://tex.z-dn.net/?f=%5Cfrac%7B2x%2B5%7D%7Bx%5E%7B2%7D%20-3x%7D%20-%5Cfrac%7B3x%2B5%7D%7Bx%5E%7B3%7D%20-9x%7D%20-%5Cfrac%7Bx%2B1%7D%7Bx%5E%7B2%7D-9%7D)
First, we need to factor each denominator
![\frac{2x+5}{x(x-3)} -\frac{3x+5}{x(x+3)(x-3)} -\frac{x+1}{(x-3)(x+3)}](https://tex.z-dn.net/?f=%5Cfrac%7B2x%2B5%7D%7Bx%28x-3%29%7D%20-%5Cfrac%7B3x%2B5%7D%7Bx%28x%2B3%29%28x-3%29%7D%20-%5Cfrac%7Bx%2B1%7D%7B%28x-3%29%28x%2B3%29%7D)
So, the least common factor (LCF) is
, because they are the factors that repeats.
Now, we diviide the LCF by each denominator, to then multiply it by each numerator.
![\frac{(x+3)(2x+5)-3x-5-x(x+1)}{x(x-3)(x+3)} =\frac{2x^{2}+5x+6x+15-3x-5-x^{2}-x }{x(x-3)(x+3)}\\\frac{x^{2}+7x+10}{x(x-3)(x+3)}](https://tex.z-dn.net/?f=%5Cfrac%7B%28x%2B3%29%282x%2B5%29-3x-5-x%28x%2B1%29%7D%7Bx%28x-3%29%28x%2B3%29%7D%20%3D%5Cfrac%7B2x%5E%7B2%7D%2B5x%2B6x%2B15-3x-5-x%5E%7B2%7D-x%20%7D%7Bx%28x-3%29%28x%2B3%29%7D%5C%5C%5Cfrac%7Bx%5E%7B2%7D%2B7x%2B10%7D%7Bx%28x-3%29%28x%2B3%29%7D)
Then, we factor the numerator, to do so, we need to find two numbers which product is 10 and which sum is 7.
![\frac{(x+5)(x+2)}{x(x-3)(x+3)}](https://tex.z-dn.net/?f=%5Cfrac%7B%28x%2B5%29%28x%2B2%29%7D%7Bx%28x-3%29%28x%2B3%29%7D)
Therefore, the expression is equivalent to
![\frac{(x+5)(x+2)}{x(x-3)(x+3)}](https://tex.z-dn.net/?f=%5Cfrac%7B%28x%2B5%29%28x%2B2%29%7D%7Bx%28x-3%29%28x%2B3%29%7D)
Answer:
Katie is 6 years old and Thomas is 3 years old
Step-by-step explanation:
Given that we should let K and T be the current ages of two siblings, Katie and Thomas.
If Katie is currently twice the age of Thomas then,
K = 2T
and in 6 years, Katie will be 4 times Thomas's current age then
K + 6 = 4T
Solving both equations simultaneously by substituting the value of K given in the first equation into the second
2T + 6 = 4T
Collect like terms
6 = 4T - 2T
6 = 2T
Divide both sides by 2
T = 3
Recall that K = 2T
K = 2 * 3
= 6
Hence Katie is 6 years old while Thomas is 3 years old
297:5.5
divide 5.5 by both sides which
5.5 divided by 5.5 is 1 and 297 divided by 5.5 is 54
1:54
the unit rate:
54 minutes per word or 54/1