If RQ and SP are congruent, then 2x+3=4x-7.
3=2x-7
10=2x
x=5
Answer:
Step-by-step explanation:
f(x) = y = 3x/(8 + x) (I am assuming that the 8 + x is the denominator. Please use parentheses in the future if you forgot this. If there are no parentheses, then my solution will not work for you.)
Exchange x and y; that is, replace x by y and y by x simultaneously:
x = 3y/(8 + y).
Then use algebra to solve for y in terms of x:
(8 + y)x = 3y (multiply both sides by the denominator to clear the fraction)
8x + xy = 3y (distribute)
xy − 3y = −8x (rearrange terms with all y's on the left side of the equation)
y(x − 3) = −8x (factor out y as a common factor)
y = −8x/(x − 3) (divide by x − 3)
Finally, replace y by f-1(x):
f-1(x) = −8x/(x − 3).
This is the inverse of f(x). It can be checked by finding f(f-1(x)) and f-1(f(x)), and verifying that both equal x after simplifying.
Answer:
It would take him 6 minutes to walk 720 feet.
Step-by-step explanation:
720 / 2 = 360 (seconds)
360 seconds = 6 minutes
If 2 sodas and 4 hamburgers are $12.00 and 4 sodas and 2 hamburgers are $9.00 how much is a single hamburger?
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2s + 4h = 12, (1) 4s + 2h = 9. (2) Multiply (1) by 2. You will get 4s + 8h = 24, (1') 4s + 2h = 9. (2') Distract (2') from (1'). You will get 8h - 2h = 24 - 9, or 6h = 15 ---> h =  =  = 2.5. Thus one hamburger price is $2.50. Then from (1) s =  = 1. Answer. One hamburger price is $2.50 and 1 soda costs $1.00.
There is even more elegant way to solve the problem.
Simply add all hamburgers and all sodas. 6 hamburgers and 6 sodas. $12 + $9 = $21.
Hence, 1 hamburger + 1 soda =  = $3.50.
Having this, everybody can solve to the end in this way, actually, without equations and using the mental math only.
Question: A man measures the angle of elevation to the top of a mountain to be 12 degrees. He drives 7 miles closer and finds the angle of elevation to be 37 degrees. How high is the mountain?
