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ra1l [238]
3 years ago
15

An interior angel of a regular polygon has a measure of 120 degrees. What type of polygon is it

Mathematics
2 answers:
romanna [79]3 years ago
8 0

Answer: The figure is a regular hexagon.

Step-by-step explanation:

nirvana33 [79]3 years ago
7 0

Answer:hexagon

Step-by-step explanation:

Each interior angle=120

Each interior angle in a polygon=180(n-2)/n

120=180(n-2)/n

Cross multiply

120n=180(n-2)

120n=180n-360

Collect like terms

180n-120n=360

60n=360

Divide both sides by 60

60n/60=360/60

n=6

the polygon has 6 sides which means that it is an hexagon

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What is the coordinates of the center of an ellipse defined by the equation 16x^2 + 25y^2 + 160x - 200y + 400 = 0 ? Please give
pickupchik [31]

16x^2 + 25y^2 + 160x - 200y + 400 = 0     Rearrange and regroup.

(16x^2 + 160x) + (25y^2 - 200y ) = 0-400.     Group the xs together and the ys together.

16(X^2 + 10x) + 25(y^2-8y) = -400.     Factorising.

We are going to use completing the square method.

Coefficient of x in the first expression = 10.

Half of it = 1/2 * 10 = 5. (Note this value)

Square it = 5^2  = 25.     (Note this value)


Coefficient of y in the second expression = -8.

Half of it = 1/2 * -8 = -4. (Note this value)

Square it = (-4)^2  = 16. (Note this value)


We are going to carry out a manipulation of completing the square with the values

25 and 16.  By adding and substracting it.


16(X^2 + 10x) + 25(y^2-8y) = -400

16(X^2 + 10x + 25 -25) + 25(y^2-8y + 16 -16) = -400

Note that +25 - 25 = 0.    +16 -16 = 0. So the equation is not altered.

16(X^2 + 10x + 25) -16(25) + 25(y^2-8y + 16) -25(16) = -400


16(X^2 + 10x + 25) + 25(y^2-8y + 16)  = -400 +16(25) + 25(16)    Transferring the terms -16(25) and -25(16)

to other side of equation.  And 16*25 = 400


16(X^2 + 10x + 25) + 25(y^2-8y + 16)  = 25(16)


16(X^2 + 10x + 25) + 25(y^2-8y + 16)  = 400

We now complete the square by using the value when coefficient was halved.


16(x-5)^2 + 25(y-4)^2  = 400

Divide both sides of the equation by 400


(16(x-5)^2)/400 + (25(y-4)^2)/400  = 400/400              Note also that, 16*25 = 400.


((x-5)^2)/25 + ((y-4)^2)/16  = 1

((x-5)^2)/(5^2) + ((y-4)^2)/(4^2)  = 1


Comparing to the general format of an ellipse.

((x-h)^2)/(a^2) + ((y-k)^2)/(b^2)  = 1


Coordinates of the center = (h,k).

Comparing   with above   (x-5) = (x - h) , h = 5.

Comparing   with above   (y-k) = (y - k) , k = 4.

Therefore center = (h,k) = (5,4).

Sorry the answer came a little late.  Cheers.

3 0
3 years ago
Write the number in witch the digit 2 is one tenth the value of the digit 2 in 8.524.
spin [16.1K]
Well the 2 in 8.524 would be 0.02 or 2 hundredths. Here's my explanation, the 8 is the whole number because it's before the decimal point, the 5 is the tenth or 0.5 and as you go further the number gets smaller so after the 5 is the 2 and that would be 2 hundredths or 0.02. So basically it's like going from tens, to hundreds, to thousands but only going in reverse order.
4 0
3 years ago
Use the Law of Sines to find the missing angle of the triangle. Find m<b to the nearest tenth.
defon
1. By the Law of Sines, you have:

 SinA/a=SinB/b=SinC/c

  2. You don't need the fraction SinC/c, so you can eliminate it. Then:

 SinA/a=SinB/b

 A=40°
 a=19
 B=m∠b
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 3. When you substitute this values into SinA/a=SinB/b, you obtain:

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 SinB=13xSin(40°)/19
 m∠b=SinB^-1(13xSin(40°)/19)
 m∠b=26.1°

 Therefore, the answer is: 26.1 degrees.
6 0
2 years ago
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