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3 years ago

Polygon Angle Sums - Part 2

Mathematics

1 answer:

Rashid [163]3 years ago

5 0

Answer:

x = 80°

Step-by-step explanation:

Find attached the complete question with diagram. Also find attached the diagram used for solving the question.

There area 3 angles in the diagram:

x + 8, 2x + 12, x + 20

Let the interior angles be labelled a, b, and c

a+ 2x+12 = 180° (sum of angles on a straight line)

a= 180-(2x+12) = 168 -2x in degrees

b+ x+20 = 180° (sum of angles on a straight line)

b = 180-(x+20) = 160 -x in degrees

c+ x+8 = 180° (sum of angles on a straight line)

c = 180-(x+8) = 172-x in degrees

a+b+c = 180° (sum of angles in triangle)

(168 -2x)° + (160 -x)° + (172-x)° = 180°

500 -4x = 180

500-180 = 4x

320 = 4x

x = 320/4

x = 80°

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4 of 4 Find the area of the shape below. Give your answer in terms of T. 4cm 32cm The diagram is not drawn to scale. 8cm

andrey2020 [161]

The answer is 176π cm².

Given shape is a combination of 3 semi-circles.

And we need to find the area of the colored region.

The diameter of the biggest semi-circle is 32 cm.

Let d₁, and r₁ denote the diameter and radius of the biggest semi-circle respectively.

⇒ d₁ = 32 cm and r₁ = 32/2 = 16

The diameter of the smallest semi-circle is 4cm.

Let d₂, and r₂ denote the diameter and radius of the smallest semi-circle.

⇒ d₂ = 4 cm and r₂ = 4/2 = 2

Let d₃, and r₃ denote the diameter and radius of the middle semi-circle.

From the diagram, the diameter of the middle semi-circle is,

d₃ = d₁ - (d₂ + 8) = 32 -(4 + 8) = 32 - 12 = 20

⇒ d₃ = 20 cm and r₂ = 20/2 = 10

The area of a semi-circle is given by the formula πr²/2, where r is the radius.

Let A₁ denote the area of the biggest semi-circle.

Then A₁ = π(r₁)²/2 = π × (16)² / 2 = 256π/2 = 128π cm²

Let A₂ denote the area of the smallest semi-circle.

Then A₂ = π(r₂)²/2 = π × (2)² / 2 = 4π/2 = 2π cm²

Let A₃ denote the area of the middle semi-circle.

Then A₃ = π(r₃)²/2 = π × (10)² / 2 = 100π/2 = 50π cm²

Therefore, the area of the colored region is A₁ + A₃ - A₂

= 128π + 50π - 2π

= 176π cm²

Learn more at:

brainly.com/question/19581549

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8 0

2 years ago

What is the range of this function

STatiana [176]

Yo sup??

Range refers to the permissible values of y

on observing the given set the possible values of y are

{2,3,4}

therefore your answer is option A

Hope this helps.

8 0

3 years ago

If a parabola with vertex (−2,1) also contains the point (1,6) which point must also be on the parabola?

zepelin [54]

Answer:

(-5,6)

Step-by-step explanation:

I graphed the points and found that (-5,6) would fall on the parabola.

The equation of the line is $y=\frac{5}{9}(x+2)^{2}+1$ , if you need it.

If this answer is correct, please make me Brainliest!

3 0

3 years ago

Can someone help me out on this please having trouble on both and show work please !!

inysia [295]

The difference of the expression is as follows:

(6y⁴ + 3y² - 7) - (12y⁴ - y² + 5) = - 6y⁴ + 4y² - 12

3(x - 5) - (2x + 4) = x - 19

<h3>How to find the difference of the expression?</h3>

The difference of the expression can be found when we combine the like terms.

Therefore,

(6y⁴ + 3y² - 7) - (12y⁴ - y² + 5)

6y⁴ + 3y² - 7 - 12y⁴ + y² - 5

6y⁴ - 12y⁴ + 3y² + y² - 7 - 5

- 6y⁴ + 4y² - 12

3(x - 5) - (2x + 4)

3x - 15 - 2x - 4

3x - 2x - 15 - 4

x - 19

learn more on expression here: brainly.com/question/14294918

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3 years ago

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HACTEHA [7]

I think its 4.7

Step-by-step explanation:

4 0

3 years ago