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3 years ago

Show any calculations, including 180 degrees, go step by step pls.

Mathematics

1 answer:

ICE Princess25 [194]3 years ago

5 0

Answer:

120°, 120°, 60°, 60°

Step-by-step explanation:

m∠1 = 180° - 60° = 120°

m∠1 = m ∠2 (alternate interior)

m∠3 = 60° (vertical to given angle)

m∠4 = m∠3 (alternate exterior)

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The figures below are made out of circles, semicircles, quarter circles, and a square. Find the area and the perimeter of each f

WITCHER [35]

Answer:

Part 1) $A=36(\pi-2)\ cm^2$

Part 2) $P=6(\pi+2\sqrt{2})\ cm$

Step-by-step explanation:

The picture of the question in the attached figure

Part 1) Find the area

we know that

The area of the shape is equal to the area of a quarter of circle minus the area of an isosceles right triangle

$A=\frac{1}{4}\pi r^{2}-\frac{1}{2}(b)(h)$

we have that the base and the height of triangle is equal to the radius of the circle

$r=12\ cm\\b=12\ cm\\h=12\ cm$

substitute

$A=\frac{1}{4}\pi (12)^{2}-\frac{1}{2}(12)(12)\\A=(36\pi-72)\ cm^2$

simplify

Factor 36

$A=36(\pi-2)\ cm^2$

Part 2) Find the perimeter

The perimeter of the figure is equal to the circumference of a quarter of circle plus the hypotenuse of the right triangle

The circumference of a quarter of circle is equal to

$C=\frac{1}{4}(2\pi r)=\frac{1}{2}\pi r$

substitute the given values

$C=\frac{1}{2}\pi (12)\\C=6\pi\ cm$

Applying the Pythagorean Theorem

The hypotenuse of right triangle is equal to

$AC=\sqrt{12^2+12^2}\\AC=\sqrt{288}\ cm$

simplify

$AC=12\sqrt{2}\ cm$

Find the perimeter

$P=(6\pi+12\sqrt{2})\ cm$

simplify

Factor 6

$P=6(\pi+2\sqrt{2})\ cm$

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3 years ago

Miss hit travel 21120 ft how many miles did she travel

Sunny_sXe [5.5K]

4 miles because there are 5280 ft in one mile so if you were to multiply that by 4 you would get 21120 ft

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If there are 100 students in a Masters Degree program at OU, and there`s a 5% failure rate, how many students are left after 12

Leviafan [203]

5% fail
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Show any calculations, including 180 degrees, go step by step pls.​

Show any calculations, including 180 degrees, go step by step pls.