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3 years ago

If an exterior angle of a regular polygon is 21.2Â°, how many sides does the polygon have?

Mathematics

1 answer:

sesenic [268]3 years ago

3 0

360 divided by x = 21.2 recurring
So rearrange that to get x = 360 divided by 21.2
Which rounds up to 17

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A rectangle has width that is 6 meters less than the length. The area of the rectangle is 280 square meters. Find the dimensions

salantis [7]

Dimensions are length 20 meter and width 14 meter

Solution:

Let "a" be the length of rectangle

Let "b" be the width of rectangle

Given that,

A rectangle has width that is 6 meters less than the length

Width = length - 6

b = a - 6

The area of the rectangle is 280 square meters

The area of the rectangle is given by formula:

$Area = length \times width$

Substituting the values we get,

$Area = a \times (a-6)\\\\280 = a^2-6a\\\\a^2-6a -280=0$

Solve the above equation by quadratic formula

$\mathrm{For\:a\:quadratic\:equation\:of\:the\:form\:}ax^2+bx+c=0\mathrm{\:the\:solutions\:are\:}\\\\\quad x_{1,\:2}=\frac{-b\pm \sqrt{b^2-4ac}}{2a}$

$\mathrm{For\:}\quad a=1,\:b=-6,\:c=-280:\quad a_{1,\:2}=\frac{-\left(-6\right)\pm \sqrt{\left(-6\right)^2-4\cdot \:1\left(-280\right)}}{2\cdot \:1}$

$a =\frac{6 \pm \sqrt{36+1120}}{2}\\\\a = \frac{6 \pm \sqrt{1156}}{2}\\\\a = \frac{6 \pm 34}{2}\\\\Thus\ we\ have\ two\ solutions\\\\a = \frac{6+34}{2} \text{ or } a = \frac{6-34}{2}\\\\a = 20 \text{ or } a = -14$

Since, length cannot be negative, ignore a = -14

Thus solution of length is a = 20

Therefore,

width = length - 6

width = 20 - 6 = 14

Thus dimensions are length 20 meter and width 14 meter

6 0

3 years ago

Which of the following is a valid exclusion for the algebraic fraction 8ab^2x/4a^2b - 8ab^2

avanturin [10]

The valid exclusion of the algebraic fraction is (c) a =0, b =0, a =2b

<h3>How to determine the valid exclusion?</h3>

The expression is given as:

8ab^2x/4a^2b - 8ab^2

Set the denominator to 0

4a^2b - 8ab^2 = 0

Divide through by 4ab

a - 2b = 0

Add 2b to both sides

a = 2b

Hence, the valid exclusion of the algebraic fraction is (c) a =0, b =0, a =2b

Read more about algebraic fraction at:

brainly.com/question/4344214

#SPJ1

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