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3 years ago

(a^4+4b^4)divided by (a^2-2ab+2b^2)

1 answer:

6 0

Simplify the following:
(a^4 + 4 b^4)/(a^2 - 2 a b + 2 b^2)
A common factor of a^4 + 4 b^4 and a^2 - 2 a b + 2 b^2 is a^2 - 2 a b + 2 b^2, so (a^4 + 4 b^4)/(a^2 - 2 a b + 2 b^2) = ((a^2 + 2 a b + 2 b^2) (a^2 - 2 a b + 2 b^2))/(a^2 - 2 a b + 2 b^2):((a^2 + 2 a b + 2 b^2) (a^2 - 2 a b + 2 b^2))/(a^2 - 2 a b + 2 b^2)
((a^2 + 2 a b + 2 b^2) (a^2 - 2 a b + 2 b^2))/(a^2 - 2 a b + 2 b^2) = (a^2 - 2 a b + 2 b^2)/(a^2 - 2 a b + 2 b^2)×(a^2 + 2 a b + 2 b^2) = a^2 + 2 a b + 2 b^2:
Answer: a^2 + 2 a b + 2 b^2

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What is the percent of decrease from 110 to 77

Charra [1.4K]

If you want to easily find the solution you can use your calculator.
Just divide 77 by 110 and see the result.
77/110 = 0.7 = 7/10 = 70/100 = 70%
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Explanation
110*x=77
x=77/110, but the answer is not a percent
So 77/110 = ?/100 => ?=77*100/110=70 => 70%
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Answer:

First we get the slope of line with points (2,3) & (1,5):

m=%28y%5B2%5D-y%5B1%5D%29%2F%28x%5B2%5D-x%5B1%5D%29

m=%285-3%29%2F%281-2%29=2%2F%28-1%29

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Knowing the slop, we can get the intercept in point (1,1):

y=mx%2Bb, SLOPE- INTERCEPT

1=-2%281%29%2Bb

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so, the eqn of the line: highlight%28y=-2x%2B3%29

The line with points (2,3) & (1,5): same slope because parallel, we'll check

VIA POINT SLOPE FORM:

m=%28y%5B2%5D-y%5B1%5D%29%2F%28x%5B2%5D-x%5B1%5D%29

m=%285-3%29%2F%281-2%29=2%2F-1 ----> m=-2, same right?

For the intercept thru pints (2,3):

Via SLOPE INTERCEPT FORM, we pick points (2,3)

3=-2%282%29%2Bb

b=3%2B4=7 ----> y intercept. The same value if you pick points (1,5).

Eqn of line: y=-2x%2B7 (Green line) parallel to y=-2x%2B3 (Red line)

See the graph,

--- see red line, it passes at point (1,1). Also green line passes points (2,3) & (1,5)

Step-by-step explanation:

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Step-by-step explanation:

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