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3 years ago

Find the measure of an interior and an exterior angle of a regular 46-gon

1 answer:

7 0

For any polygon, the formula of the interior angle is 180 - 360/n where n is the number of sides of the polygon. The exterior angle is the supplementary angle of the interior angle. Hence when n is equal to 46, then interior angle is equal to 172.17 degrees and the exterior is equal to 7.83 degrees.

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What is the fourth term in the binomial expansion (a+b)^6)

Dafna11 [192]

Answer:

$20a^3b^3$

Step-by-step explanation:

Binomial Series

$(a+b)^n=a^n+\dfrac{n!}{1!(n-1)!}a^{n-1}b+\dfrac{n!}{2!(n-2)!}a^{n-2}b^2+...+\dfrac{n!}{r!(n-r)!}a^{n-r}b^r+...+b^n$

Factorial is denoted by an exclamation mark "!" placed after the number. It means to multiply all whole numbers from the given number down to 1.

Example: 4! = 4 × 3 × 2 × 1

Therefore, the fourth term in the binomial expansion (a + b)⁶ is:

$\implies \dfrac{n!}{3!(n-3)!}a^{n-3}b^3$

$\implies \dfrac{6!}{3!(6-3)!}a^{6-3}b^3$

$\implies \dfrac{6!}{3!3!}a^{3}b^3$

$\implies \left(\dfrac{6 \times 5 \times 4 \times \diagup\!\!\!\!3 \times \diagup\!\!\!\!2 \times \diagup\!\!\!\!1}{3 \times 2 \times 1 \times \diagup\!\!\!\!3 \times \diagup\!\!\!\!2 \times \diagup\!\!\!\!1}\right)a^{3}b^3$

$\implies \left(\dfrac{120}{6}\right)a^{3}b^3$

$\implies 20a^3b^3$

7 0

2 years ago

a gymnasium is 88 feet long and 76 wide on a blueprint the gymnasium is 5.5 inches long what is the width of the gymnasium on th

attashe74 [19]

First we would need to find the portion of the gymnasium to the blueprint to do that please do this:

88/5.5 = 16

The length divided by the blueprint's length

Since we know that the gymnasium is 16 times the blueprint, to find the width divide 16 to 76:

76/16 = 4.75

The width divided by the 16 times

The width of the blueprint is 4.75 inches

6 0

3 years ago

Read 2 more answers

What’s the correct answer for this question?

weqwewe [10]

Answer:

Last answer choice

Step-by-step explanation:

The AAS congruence theorem uses two adjacent angles, followed by a side length on the side (not in between the angles.) Therefore, the first answer is ruled out (because it deals with angles and not sides), and the second answer is ruled out because it involves side lengths between angles. LP=MO may be true, but it does not compare the two triangles that we are interested in. However, the last answer choice is correct, because a midpoint divides a line exactly in half, meaning that both halves are the same length and therefore congruent. Therefore, the last answer choice is correct. Hope this helps!

7 0

3 years ago

Please help me with question 2. What is the degree measure of the angle measure? Please show steps!

marshall27 [118]

Answer:

because of a geometry theorem since the angles have the same arc length they have the same angle measure

20 degrees

3 0

3 years ago

What the answer now hurry up

maxonik [38]

Answer:

Below

Step-by-step explanation:

The equation of a circle is written as:

(x-a)^2 + (y-b)^2 = r^2

● ( a,b) are the coordinates of the center . Here (0,-2)

● r is the radius (here 12)

So the equation is:

x^2 + (y+2)^2 = 12^2

6 0

3 years ago