You buy 5 balloons and 3 banners for $14. Your friend buys 1 balloon and

8-35. Use your knowledge of polygons to answer the questions below, if possible.

Nataliya [291]

Answer:

(a)I. 13 Sides II. 7 Sides

(b) 4 Sides, Square

(c)x=52 degrees

(d)x=107 degrees

(e)1620 degrees

Step-by-step explanation:

(a)The Sum of the Interior angle of polygon with n sides is derived using the formula: (n-2)180.

I. If the Interior angle is $1980^0$

Then:

$(n-2)180^0=1980^0\\$Divide both sides by 180^0 $ to isolate n$\\n-2=11\\$Add 2 to both sides of the equation\\n-2+2=11+2\\n=13$

The polygon has 13 sides.

II. If the Interior angle is $900^0$

Then:

$(n-2)180^0=900^0\\$Divide both sides by 180^0 $ to isolate n$\\n-2=5\\$Add 2 to both sides of the equation\\n-2+2=5+2\\n=7$

The polygon has 7 sides.

(b)The sum of the exterior angle of a polygon is 360 degrees,

Each exterior angle of a n-sided regular polygon is: $\frac{360^0}{n}$

If the exterior angle of a regular polygon is 90°

Then:

$90\°=\frac{360^0}{n}\\ 90n=360\\n=4$

The regular polygon has 4 sides and it is called a Square.

(c)The Sum of the Interior angle of polygon with n sides is derived using the formula: (n-2)180.

Each Interior angle of a regular n-sided polygon is: $\frac{(n-2)180^0}{n}$

For a pentagon, n=5

Then:

$\frac{(5-2)180^0}{5}=2x+4\\108=2x+4\\108-4=2x\\104=2x\\x=52^0$

(d)The sum of the exterior angle of a polygon is 360 degrees.

If four of the exterior angles of a pentagon are 57, 74, 56, and 66.

Let the fifth angle=x

Then:

$57+74+56+66+x=360^0\\253+x=360\\x=107^0$

(e)The Sum of the Interior angle of polygon with n sides is derived using the formula: (n-2)180.

In an 11-gon., n=11

Therefore, the sum of the interior angle=(11-2)180= $1620^0$

The sum of the interior angle does not change either in a regular or irregular polygon.

3 0

3 years ago

1) Expand and simplify the following: a)3(x squared plus 3x cubed - 2)

Musya8 [376]

Answer:

3x³ + x² - 2

Step-by-step explanation:

a) 3(x squared plus 3x cubed - 2)

x squared = x²

3x cubed = 3x³

3(x squared plus 3x cubed - 2)

= 3(x² + 3x³ - 2)

= 3x² + 9x³ - 6

Rearrange according to power

= 9x³ + 3x² - 6

When the expression is divided by 3, it is equivalent to

3x³ + x² - 2

5 0

3 years ago

What’s a complex conjugate in math

goldenfox [79]

Answer:

Step-by-step explanation:

In mathematics, the complex conjugate of a complex number is the number with an equal real part and an imaginary part equal in magnitude but opposite in sign. For example, the complex conjugate of 3 + 4i is 3 − 4i. In polar form, the conjugate of is.

3 0

3 years ago

Pleaseeeee neeeddd helppp asappp

Rufina [12.5K]

ANSWER:

Segment TS is a Chord

If AR = 14 , then QS = 14 ×2 = 28

∆ATS is an Isosceles Triangle

HOPE THIS HELP YOU , FOR ANY QUESTION PLEASE ASK ME

7 0

2 years ago

Simplify: 7^6 ÷ 7^2 A.) 7^3 B.) 7^4 C.) 7^8 D.) 7^12

juin [17]

7^6/7^2
(7*7*7*7*7*7)/(7*7)
the answer is b. 7^4

6 0

3 years ago

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