All categories

2 years ago

O is the center of the regular decagon below. Find its perimeter. Round to the

Mathematics

1 answer:

dangina [55]2 years ago

7 0

The perimeter of the regular decagon is 110.5

<h3>what is a Decagon?</h3>

A Decagon is a polygon with 10 sides and 10 angles.
A Polygon can be regular or irregular. When the polygon is regular, we say that the sides of the polygon are equal.

Analysis:

The sum of the interior angles of a polygon is given by : (n - 2 ) x 180

number of sides of a decagon (n) = 10

(10-2) x 180 = 1440°

So each interior angle is 1440/10 = 144°

in the diagram, if we draw a line from o to bisect the angle, we form a right angle triangle with 72°. Also the 17 line divides the side of the polygon into two since it is a line drawn from the center of the decagon.

To find the base of the triangle, we use trigonometric ratios

tan 72 = 17/base

base = 17/tan72

base = 17/3.0776

base = 5.523

to find the side of the decagon, we multiply by 2

side of decagon = 2 x 5.523 = 11.046

perimeter of decagon = 10 x side of decagon

perimeter of decagon = 110.5

in Conclusion, the perimeter of the regular decagon is : 110.5

Learn more about polygon : brainly.com/question/1592456

#SPJ1

You might be interested in

Working alone at its constant rate, pump X pumped out ¼ of the water in a tank in 2 hours. Then pumps Y and Z started working an

madam [21]

Answer:

The correct option is B) 12.

Step-by-step explanation:

Consider the provided information.

Working alone at its constant rate, pump X pumped out ¼ of the water in a tank in 2 hours.

As we know: $rate =\dfrac{ work}{time}$ ,

The rate of pump X is $\frac{\frac{1}{4}}{2} = \frac{1}{8}$

$\frac{1}{4}$ of the water is pumped out of the tank, that means only $\frac{3}{4}$ is left to be pumped out.

All 3 pumps pumped out the remaining $\frac{3}{4}$ of the water out in 3 hours.

The combined rate of all three pumps is: $\frac{\frac{3}{4}}{3} = \frac{1}{4}$

Pump Y, working alone at its constant rate, would have taken 18 hours to pump out the rest of the water.

The rate of pump Y = $\frac{\frac{3}{4}}{18} = \frac{1}{24}$

Let z is the time taken by pump Z, then the rate of pump Z is $\frac{1}{z}$ .

Therefore,

$\dfrac{1}{8}+\dfrac{1}{24}+\dfrac{1}{z}=\dfrac{1}{4}$

Multiplying both sides by 24 z.

$3z + z + 24 = 6z\\24 = 2z\\12 = z$

Hence, the correct option is B) 12.

5 0

3 years ago

Shannon is putting a fence around her garden, except where there is a gate that is 3 feet wide. One foot of the fence costs $43.

Anon25 [30]

x = the number of feet of fence

y = the total cost of the fence and gate

43x + 128 = y

[fence costs $43 per feet(x) plus the cost of the gate(128) equals the total cost of the fence and gate(y)]

7 0

4 years ago

PLEASE HELP!!! The amount of polonium-210 remaining, P(t), after t days in a sample can be modeled by the exponential function P

exis [7]

Answer:

$P(t)=100(0.994)^t$

Step-by-step explanation:

A calculator shows the value of $e^{-.006} \approx 0.994$ meaning that each day, about 99.4% of the sample remains.

The formula $P(t)=100e^{-0.006t} = 100(e^{-0.006})^t=100(0.994)^t$

Evaluate this at <em>t</em> = 16 to get 91 grams remain.

3 0

3 years ago

Estimate show how you estimated 412 divided by 97

nataly862011 [7]

<span>the division of 412 divided by 97 can be estimated as:

412 can be estimated as: 400
97 can be estimated to 100

so, now on dividing 400/100 we get, the answer as 4.

To verify the estimation: when 412 is divided by 97, the answer is 4.24 which can be nearly written as 4 only.

Thus, our estimation was correct.</span>

8 0

4 years ago

Write these numbers in order of size. start with the smallest number: 1/2, 2/3, 2/5, 3/4

qaws [65]

First make the fractions into decimals so it's easier to compare them.

1/2 ⇒ 0.5
2/3 ⇒ 0.66
2/5 ⇒ 0.4
3/4 ⇒ 0.75

Now it's easy to order the numbers from least to greatest.

First order the decimals.

0.4, 0.5, 0.66, 0.75

Now order them with their corresponding fractions.

2/5, 1/2, 2/3, 3/4 is your answer.

3 0

4 years ago

Read 2 more answers