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makvit [3.9K]
3 years ago
11

A square has an area of 49 square inches. Explain how to find the perimeter of the square.

Mathematics
1 answer:
dexar [7]3 years ago
3 0
It is a square, so you know the sides are equal. You also know that 49 is a squared number. so you do 49 square rooted and you get 7. the perimeter is adding all the side lengths. So you take 7 and multiply it by 4 since a square has 4 sides. and u have your perimeter. 28!<span />
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Which polynomial function has a leading coefficient of 1 and roots (7 i) and (5 – i) with multiplicity 1? f(x) = (x 7)(x – i)(x
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It looks like you might have intended to say the roots are 7 + i and 5 - i, judging by the extra space between 7 and i.

The simplest polynomial with these characteristics would be

f(x) = (x - (7 + i)) (x - (5 - i))

but seeing as each of the options appears to be a quartic polynomial, I suspect f(x) is also supposed to have only real coefficients. In that case, we need to pair up any complex root with its conjugate to "complete" f(x). We end up with

f(x) = (x - (7 + i)) (x - (7 - i)) (x - (5 - i)) (x - (5 + i))

which appears to most closely resemble the third option. Upon expanding, we see f(x) does indeed have real coefficients:

f(x) = (x^2 - (7^2 - i^2)) (x^2 - (5^2 - i^2)) = (x^2 - 8) (x^2 - 6) = x^4 - 14x^2 + 48

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Step-by-step explanation:

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