Use the Pythagorean Theorem to solve for x. *
2 answers:
The other person provided a great answer but i do it a little different....
All i did was use the formula A^2=C^2-B^2. I Plugged in the numbers to the formula and got A^2=10^2-6^2. Next, I found what 10^2 equals by doing 10*10 which equals 100. Then, i found out what 6^2 equals by doing 6*6 which equals 36. Next, what i did was subtracted 100 from 36 and got 64. Finally i found the square root of the number 64 which equal 8 since 8x8=64.
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Start with the answer format we want, and work your way toward forming a single fraction like so
Compare that last expression to (2x+1)/(x+2). Notice how the ax and 2x match up, so a = 2 must be the case.
Then we have 2a+b as the remaining portion in the numerator. Plugging in a = 2 leads to 2a+b = 2*2+b = 4+b. Set this equal to the +1 found in (2x+1)/(x+2) to have the terms match.
So, 4+b = 1 leads to b = -3
Therefore, a = 2 and b = -3
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An alternative route:
I added and subtracted 4 in the third step so that I could form 2x+4, which then factors to 2(x+2). That way I could cancel out a pair of (x+2) terms toward the very end.
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Other alternative methods involve synthetic division or polynomial long division. They are slightly separate but related concepts.