Answer:
perimeter of the figure =32 units
area of the figure=56 units²
Absolute value of any number is always positive because it represent distance and distance will always positive.
To place chimney at least 30 feet , the distance along the width of the roof (x) will be x = 17.5 feet or x = 2.5 feet.
Since, The height of the roof is described by the function f(x)=−4/3|x−10| + 40
Since, minimum height is 30 feet.
So , substitute f(x)=30 in above expression.
30=−4/3|x−10| + 40
4/3|x−10| = 10
|x−10|=30/4
|x−10| = 7.5
Taking positive case,
x−10 = 7.5
x = 17.5 feet
Taking negative case,
x−10 = - 7.5
x = 10 - 7.5
x = 2.5 feet
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Use Pythagorean theorem.
[tex]|ON|^2+|MN|^2=|OM|^2\\\\x^2+x^2=8^2\\\\2x^2=64\ \ \ \ |divide\ both\ sides\ by\ 2\\\\x^2=32\to x=\sqrt{32}\\\\x=\sqrt{16\cdot2}\\\\x=\sqrt{16}\cdot\sqrt2\\\\\boxed{x=4\sqrt2}
Answer: |MN| = 4√2.
7/8 can be converted to .875 because 1/8 is .125 and .125*7=.875. Add -12 to it so the answer is -12.875
