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put this solution on YOUR website!1.an angle measure 14 degress less than three times its compliment. find the measure of the angle and it compliment.
Let the angle be "x"; then the complement is (90-x).
EQUATION:
x = 3(90-x)-14
x = 270-3x-14
4x = 256
x = 64
90-x = 26
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2. the length of a rectangle is 4ft longer than twice its width. find the dumension of a rectangle if its perimeter is 58 ft.
l = 2w + 4
2l + 2w = 58
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Rearrange:
l - 2w = 4
l + w = 29
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Subtract the 1st equation from the 2nd to get:
3w = 25
w = 25/3 ft(width)
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Substitute to find "l":
l + (25/3) = 29
l = (87/3)-(25(3)
l = 62/3 ft (length)
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2. one angle of a triangle measure 9 degress more than the second angle. the third angle is seven times larger than the second angle. find the measures of each angle of the triangle.
1st angle = x degrees
2nd angle = x-9 degrees
3rd angle = 7(x-9) = 7x-63 degrees
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EQUATION:
x + x-9 + 7x-63 = 180
9x -72 = 180
x - 8 = 20
x = 28 degrees (1st angle)
x-9 = 19 degrees (2nd angle)
7(x-9) = 133 degrees (3rd angle)
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4. the width of a rectangle is 3 feet shorter than its length. the perimeter is 76 decreased by the width. find the dimensions of the rectangle.
w = l -3
2l + 2w = 76 - w
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Rearrange:
2l - 2w = 63
2l+3w = 76
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Subtract 1st from 2nd to solve for "w":
5w = 13
w = 13/5 ft (width)
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Substitute into l - w = 3 to solve for "l":
l - (13/5) = (15/5)
l = 28/5 ft (length)
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Cheers,
Stan H
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