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3 years ago

How is the formula for finding the sum of interior angle measures of polygons dervived

Mathematics

1 answer:

SSSSS [86.1K]3 years ago

8 0

Step-by-step explanation:

Draw lines from one vertex to the other vertices, splitting the polygon into triangles. If the polygon has n sides, there will be n−2 triangles. Each triangle's angles add up to 180°. So the sum of all the interior angles is:

S = (n−2) 180°

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A table represents the function f(x) = 2. What is true of the given function?

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F(x) = 2 is a linear function that is parallel to the x axis at y=2

It neither increase nor decrease. It's just parallel to x'ox

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4 years ago

Shannon’s rectangular countertop is 3 feet wide. It is 3 times as long as it is wide. Find the length and area of Shannon’s coun

kompoz [17]

Answer:

9 feet long

Step-by-step explanation:

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3 years ago

Mark invests $8,008 in a retirement account with a fixed annual interest rate of 2% compounded 6 times per year. What will the a

love history [14]

Given:

Principal value = $8,008

Rate of interest = 2% compounded 6 times per year.

Time = 16 years

To find:

The account balance after 16 years.

Solution:

The formula for amount is:

$A=P\left(1+\dfrac{r}{n}\right)^{nt}$

Where, P is principal, r is the rate of interest, n is the number of times interest compounded in an year and t is the number of years.

Putting $P=8,008, r=0.02,n=6,t=16$ in the above formula, we get

$A=8008\left(1+\dfrac{0.02}{6}\right)^{6(16)}$

$A=8008\left(\dfrac{6.02}{6}\right)^{96}$

$A=11022.1721148$

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3 years ago

A craftsman is making a dulcimer with the same dimensions as the one shown. The surface shown requires a special, more durable t

Bogdan [553]

Answer:

$\displaystyle A=\frac{3h^2}{2}+h$

Step-by-step explanation:

<u>Area of trapezoid</u>

Given a trapezoid shape whose parallel sides measure b1 and b2 and whose height (perpendicular to the base) is h, then the area of the trapezoid is given by

$\displaystyle A=\frac{b_1+b_2}{2}\cdot h$

The dulcimer has the following dimensions

$b_1=2h+1$

$b_2=h+1$

and height h

Thus

$\displaystyle A=\frac{2h+1+h+1}{2}\cdot h=\frac{3h+2}{2}\cdot h$

Operating

$\displaystyle A=\frac{3h^2+2h}{2}=\frac{3h^2}{2}+h$

$\boxed{A=\frac{3h^2}{2}+h}$

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3 years ago

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Gemiola [76]

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3 years ago