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2 years ago

Find the measures of the interior

Mathematics

1 answer:

Ainat [17]2 years ago

6 0

Answer:

Angle 1 = 108°

Angle 2 = 72°

Angle 3 = 120°

Angle 4 = 96°

Angle 5 = 144°

Step-by-step explanation:

We need to find the measures of the interior angles in a pentagon if the measure of each consecutive angle is in the ratio 9:6:10:8:12.

Let x be the common ratio

So, we can write:

Angle 1 = 9x

Angle 2 = 6x

Angle 3 = 10x

Angle 4 = 8x

Angle 5 = 12x

We know that the <em>sum of all angles of pentagon = 540</em>

So, adding all angles and equal them to 540, we can find value of x

$9x+6x+10x+8x+12x=540\\45x=540\\x=\frac{540}{45}\\x=12$

So, we get the value of x: x=12

Now, calculating the angles by putting x=12:

Angle 1 = 9x = 9(12) = 108°

Angle 2 = 6x = 6(12) = 72°

Angle 3 = 10x = 10(12) = 120°

Angle 4 = 8x = 8(12) = 96°

Angle 5 = 12x= 12(12) = 144°

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Hatshy [7]

Answer:

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Step-by-step explanation:

The volume of a square pyramid is given by $V=\frac{1}{3}\cdot s^2\cdot h$

Since pyramids A and B are similar, their corresponding side lengths are proportion. Since the base edge of B is half that of A's, each dimension of B will be half of A. Since the formula for volume requires the multiplication of three dimensions, the volume of pyramid A will be $2^3=8$ times larger than the volume of pyramid B.

Thus, the volume of pyramid A is equal to $16\cdot 8=\boxed{128\:\mathrm{in^3}}$ . You can also find the dimensions of pyramid A and use the formula.

The surface area consists of the sum of all areas of the 2D shapes that make the figure. Since all dimensions of pyramid A are twice the dimensions of pyramid B, the ratio of the surface area of pyramid A to pyramid B is $2^2:1=\boxed{4:1}$

The surface area of a square pyramid can be found by adding the areas of the three triangles and one square that make it up. As one long messy formula, that becomes $2s\sqrt{\left(\frac{s}{2}\right)^2+h^2}+s^2$ for a square pyramid with base edge $s$ and height $h$ .

Plugging in values, we get the following:

$A_a\approx \boxed{179.4\:\mathrm{cm^2}},\\A_b\approx \boxed{44.8\:\mathrm{cm^2}}$

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2 years ago

Danny wants to improve his technique for punting the football, so he devises an experiment to help. He goes to the field with 5

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Answer should be (A)

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3 years ago

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3 years ago

A spherical boulder is 20 feet in diameter and weight almost 8 tons.Find its volume.Use 3.14 for T round to the nearest whole nu

olya-2409 [2.1K]

Answer:

4187 ft³

Step-by-step explanation:

$\frac{4}{3}$ πr³

π = 3.14

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2 years ago

The sum measures of angle X and angle Y is 90. If the angle X is 30 less than twice the measure of angle Y, what is the measure

krek1111 [17]

Answer:

C. 50

Step-by-step explanation:

x+y=90

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3 years ago