All categories

3 years ago

A regular octagon is inscribed in a circle with a radius of 5 feet. What is the area of the octagon

Mathematics

2 answers:

Naddik [55]3 years ago

6 0

Answer:

70.58 ft²

Step-by-step explanation:

One pie-shaped sub-area of this octagon has two sides of length 5 ft and a central angle of 360°/8, or 45°. We need to find the area of one such sub-area and then multiply the result by 8 to find the total area of the octagon.

Picture this pie-shape, this isosceles triangle with two sides of length 5 ft and central angle 45°. Half of that angle is 22.5°. Half of the base of this triangle is 5 sin 22.5°, or 1.91; the full base length is twice that, or 3.82. the height of the triangle is 5 cos 22.5°, or 4.62.

The formula for the area of a triangle is

A = (1/2)(base)(height), which in this case is:

A = (1/2)(3.82 ft)(4.62 ft) = 8.82 ft²

and so the area of the whole octagon is 8(8.82 ft²), or 70.58 ft²

rusak2 [61]3 years ago

3 0

Answer:

D) 70.7

Step-by-step explanation:

I got it right

You might be interested in

A pair of dice is rolled. What is the conditional probability that the sum of numbersthat came up on the top of the dice is nine

netineya [11]

Answer:

a. 1/18 or one in eighteen

b. 1/4 or one in four

c. 1/4 or one in four

5 0

4 years ago

4a - 5b + 6ab - 8b – 3a =

andreyandreev [35.5K]

Write the thing spaced out:

4a -5b +6ab -8b -3a
The signs (+,-) are assigned to the numbers it is in front of.

We minus the "like" terms:
4a - 3a = 1a
-5b - 8b = -13b
+6ab = +6ab

Put them all together:
1a - 13b + 6ab

The answer for, "4a - 5b + 6ab - 8b - 3a" = "1a - 13b + 6ab"

7 0

4 years ago

Convert -11°20'49" to decimal degree form. Round your answer to three decimal places.

Veseljchak [2.6K]

Answer:

56.339 Degrees :3

heart if it helped

7 0

3 years ago

Which shows one way to determine the factors of 4x3 + x2 – 8x – 2 by grouping?

Korvikt [17]

Remember that to factoring by grouping, we should split the expression into tow pairs that have something in common. The idea is that after factoring each pair, we get a binomial common factor. Is worth pointing out that you can pair factors in more than one way.

Let's check how to determine the factors of our expression by grouping:

Step 1. Look for common multiples between the terms.

Notice that 4 and 8 are multiples of 2, 8 is a multiple of 4, and all of them are multiples of 1, so we are going to try more than one pairing combination.

Step 2. Look for common factors between the variables.

Usually, we want to pair variables with higher exponents so when we factor each pair, we end up with another common factor in binomial form.

Step 3. Factor each pair; if you end with another binomial common factor, you nailed it. If not, try again.

Les't apply our steps to our expression $4x^3+x^2-8x-2$

Applying step 1, we are pairing $4x^3$ and $-8x$ . Remember to pair the remaining factors as well.

$(4x^3-8x)+(x^2-2)$

The common factor in the first pair is $4x$ , so lets factor that out

$4x(x^2-2)+(x^2-2)$

Look! we have the binomial common factor $(x^2-2)$ . Unfortunately, $4x(x^2-2)+(x^2-2)$ is not in our given choices, so let's try again:

This time we are going to group the higher variables (step 2) $4x^3$ and $x^2$

$4x^3+x^2-8x-2$

$(4x^3+x^2)+(-8x-2)$

The common factor in the first pair is $x^2$ , and the common factor in the second one is -2, so let's factor out both of them:

$(4x^3+x^2)+(-8x-2)$

$x^2(4x+1)-2(4x+1)$

This time, we got option A.

We can conclude that the correct answer is: A) x2(4x + 1) – 2(4x + 1)

3 0

3 years ago

Joe is borrowing $15,000 in a savings account that earns 6% simple interest. How much interest will he owe after 5 years?

Gennadij [26K]

Answer:

$4,500

Step-by-step explanation:

You would divide $15,000 by 10 to get 10% then to get 30%, which is how much it is after 5 years, you would multiply by 3 to $4500 which is the answer

4 0

3 years ago