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ioda
3 years ago
15

Match each part of the expression with what it represents

Mathematics
1 answer:
Oduvanchick [21]3 years ago
8 0

The monomial x would be the length of the sports banner.

-We know this because we typically use a basic variable for the thing that does not change. In this case, the length of the sports banner remains the same.

The second degree term in the expression would be the increase in area of the culture banner to make the sports banner.

-We can tell this because when we increase the width of the banner by 12, the resulting polynomial is 12x larger than x^2 (which was the original area of the culture banner.

The binomial expression x + 12 would be the width of the sports banner.

-Since we are increasing the width of the culture banner from x, x + 12 would represent the new width of the sports banner.

The first degree term in the expression would be the area of the culture banner.

-Because side of the culture banner is the same before the increase, multiplying x by itself will give you an area of x^2. This is the first degree term.

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The area of the rectangular pen is 10,000 m² and the area of the circular pen is 12,738.95 m².

For the rectangular pen, we want the sides to be congruent.  To minimize perimeter and maximize area, the figure needs to be equilateral.

400/4 = 100 m for each side

This means that the area is 100(100) = 10,000 m².

If the pen is circular, this means the circumference is 400 m.  Circumference is given by the formula C=πd:

400 = 3.14d

Divide both sides by 3.14:
400/3.14 = 3.14d/3.14
127.389 = d

The radius is half of the diameter:
r = 127.389/2 = 63.6945

The area of the circle is given by A=πr²:

A=3.14(63.6945)² = 12738.9465 ≈ 12738.95 m²
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