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2 years ago

Find the area of the regular octagon.

Mathematics

1 answer:

user100 [1]2 years ago

4 0

Answer:

236.59mm²

Step-by-step explanation:

The formula for the area of a regular polygon is 1/2ap, with <em>a</em> being the apothem and <em>p</em> being the perimeter.

To start, get the perimeter by multiplying 7 (one side of the polygon) by 8 to get 56.

Next, we have to find the apothem (the perpendicular segment from the center of the polygon to one of the sides).

First, create a right triangle on an of the polygon's sides, where the hypotenuse is equal to the radius of the polygon, one of the legs is the apothem, and the other leg is equivalent to half of the side.

Next, using the polygon angle formula (n-2(360)/n), we can get the base angle of the triangle, 1/2(135), or 67.5.

We can use this angle and some trigonometry to find the the apothem.

First, use SOHCAHTOA to figure out if you will use sine, cosine, or tangent (in this case, tangent).

Next, set up an equation using the tangent of 67.5 to find the apothem - tan67.5 = a/3.

And set the equation equal to <em>a</em> (a = 3.5tan67.5).

Now that you have the apothem, plug it into the area formula to get A = 1/2(56)(3.5tan67.5) and solve!

(28)(3.5tan67.5)

(28)(8.4497)

236.59mm²

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A bag contains 2 yellow balls, 3 green balls, 5 red balls and 6 black balls.

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The probability of either a yellow or a red ball being drawn if only one is drawn is 7/16.

<h3>What is probability?</h3>

The probability is the measure of the likelihood of an event to happen. It measures the certainty of the event. The formula for probability is given by; P(E) = Number of Favourable Outcomes/Number of total outcomes.

According to the given question.

Numnber of yellow balls = 2

Number of green balls = 3

Number of red balls = 5

Number of black balls = 6

So,

The total number of balls in a bag = 2+ 3+ 5 + 6 = 16

And,

The sum of yellow and red ball = 2 + 5 = 7

Therefore,

The probability of either a yellow or a red ball being drawn if only one ball is drawn

= $\frac{total\ number\ of \ red \ and \ yellow\ balls }{Total\ number\ of \ balls}$

$= \frac{7}{16}$

Hence, the probability of either a yellow or a red ball being drawn if only one is drawn is 7/16.

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2 years ago

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WILL MARK BRANLIEST IF GOTTEN RIGHT!!!

german

Answer:

they are alternate interior angles

Step-by-step explanation:

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3 years ago

Find all complex solutions of 3x^2+2x+5=0 . (If there is more than one solution, separate them with commas.)

barxatty [35]

Answer:

$\large\boxed{-\dfrac{1}{3}-\dfrac{\sqrt{14}}{3}i,\ -\dfrac{1}{3}+\dfrac{\sqrt{14}}{3}i}$

Step-by-step explanation:

Use

$ax^2+bx+c=0\\\\x=\dfrac{-b\pm\sqrt{b^2-4ac}}{2a}$

$3x^2+2x+5=0\\\\a=3,\ b=2,\ c=5\\\\b^2-4ac=2^2-4(3)(5)=4-60=-56\\\\\sqrt{b^2-4ac}=\sqrt{-56}=\sqrt{(4)(-14)}=\sqrt4\cdot\sqrt{-14}=2\sqrt{-14}$

Use

$i=\sqrt{-1}$

$\sqrt{-14}=\sqrt{(-1)(14)}=\sqrt{-1}\cdot\sqrt{14}=i\sqrt{14}$

Therefore:

$x=\dfrac{-2\pm 2i\sqrt{14}}{2(3)}=-\dfrac{2}{6}\pm\dfrac{2i\sqrt{14}}{6}=-\dfrac{1}{3}\pm \dfrac{\sqrt{14}}{3}i$

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4 years ago

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