The smallest exterior angle of a polygon is 40degrees the largest exterior angle is 80 degrees a) what is the smallest possible number of sides b) what is the largest possible number of sides

Answers

Answer 1

Answer:

a) The smallest possible number of sides of the polygon is a regular polygon with 5 sides

b) The largest possible number of sides of the polygon is a regular polygon with 9 sides

Step-by-step explanation:

a) The smallest exterior angle of the polygon = 40°

The largest exterior angle of the polygon = 80°

Therefore, we have the interior angles are;

The smallest interior angle of the polygon = 180° - 40° = 140°

The largest interior angle of the polygon = 180° - 80° = 100°

Therefore, we have

The interior angles of a regular polygon are given by the following formula;

[tex]Interior \ angle =\dfrac{(n-2) \times 180 ^{\circ}}{n}[/tex]

For an interior angle of 100°, we have;

[tex]100^{\circ} =\dfrac{(n-2) \times 180 ^{\circ}}{n}[/tex]

100/180 × n = n - 2

2 = n - 100/180 × n = 4/9·n

2 = 4/9·n

n = 18/4 = 4.5

Therefore, given that a square has an interior angle of 90° we have the smallest possible number of sides polygon = 5 sides

b) For 140°, we have;

[tex]140^{\circ} =\dfrac{(n-2) \times 180 ^{\circ}}{n}[/tex]

140/180 × n = n - 2

2 = n - 140/180 × n = 2/9·n

2 = 2/9·n

n = 18/2 = 9

n = 9 sides

Therefore, the largest possible number of sides = 9 Sides.


Related Questions

1
If x = 4 and y = -2, the value of
2
1 xy² is

Answers

Answer:

16

Step-by-step explanation:

PEMDAS

An ostrich is being chased by a cheetah,
The ostrich is running at 44 feet per
second and the cheetah at 110 feet per
second. If the two started at the same
place and the ostrich got a 60-second
head start, how many seconds will it be
before the cheetah catches it?

Answers

Answer:

  40 seconds

Step-by-step explanation:

  (ostrich speed * seconds) + head start = (cheetah speed * seconds)

                                        44x + (44 * 60) = 110x

                                             44x + 2640 = 110x

                                                       2640 = 66x

                                                              x = 40

No. of seconds before cheetah catches ostrich = 40 seconds

What is speed?

Speed tells us how slow or fast an object moves. It describes the distance travelled divided by the time taken to cover the distance.

Speed is directly Proportional to Distance and Inversely proportional to Time.

Speed = Distance/Time

Given,

Speed of ostrich = 44 feet per second

Speed of cheetah = 110 feet per second

Starting point is same

Ostrich got 60 second head start

Distance travelled by ostrich in 60 second = 44 × 60 = 2640 feet

let  S  be the number of seconds that it will take the cheetah to catch the ostrich

Distance covered by cheetah = 110S

Distance that  the ostrich will cover before being caught  is  2640 + 44S

According to the question

110S  = 2640 + 44S  

110S - 44S =2650

66S  =  2640  

S = 2640/66

S = 40 seconds.

Hence, It will be 40 seconds before cheetah catches the ostrich.

Learn more about speed here:

https://brainly.com/question/7359669

#SPJ2

Rachel got 18 out of 30 correct on her science test. What percent did she get on her test?

Answers

Answer:

60% or D

Step-by-step explanation:

Divide 100 by 30

3.333333. . .

Multiply 18 by 3.333333. . .

The answer is 60%

Hope this helped :)

(50 points) Use the spinner below. Show your work, making sure to simplify your answers. (Note: The smallest section of the circle is 1/16 of the circle.)

16. What is P(red, yellow, blue)?

17. What is P(orange, yellow)?

18. P(green, blue, purple)?

19. P(pink)?

20. P(red, orange, yellow, green, blue, purple)?

Thank you!!

Answers

Answer:

I have the same questions and I got them right

Step-by-step explanation:

16. What is P(red, yellow, blue)?

P(red, yellow, blue)=  6/16= 3/8.

4/16+ 1/16+ 1/16= 6/16= 3/8

17. What is P(orange, yellow)?

P(orange, yellow)= 1/8

1/16+1/16= 2/16= 1/8

18. P(green, blue, purple)?

P(green, blue, purple)= 5/8

7/16+1/16+2/16= 10/16= 5/8.

19. P(pink)?

P(pink)=0

There is no pink color.

20. P(red, orange, yellow, green, blue, purple)?

P(red, orange, yellow, green, blue, purple)= 16/16= 1.

4/16+ 1/16+ 1/16+ 7/16+1/16+2/16 =16/16= 1.

Hope it helps!!!

plzzzzzz helpppppp plzzz

Answers

Answer:

D. 6

Step-by-step explanation:

Answer:

B, 6

I think! hope it helped

can a system of linear equation have exactly 2 solutions ? why or why not?

Answers

Answer:

Under normal circumstances a system of two linear equations can have 0, 1 or infinitely many solutions.

Step-by-step explanation:

Help ASAP plz
Jacob bought 5 boxes of pencils for his drawing class. Each box contains 12 pencils. Which point on the graph shows the number of pencils he bought?

Answers

Answer:

it would be (5,60)

Step-by-step explanation:

he bought 5 boxes

each box has 12 pencils

5*12=60

Find the modulus of the complex number 6-2i

Answers

Answer:

The modulus of the complex number 6-2i is:

[tex]|z|\:=2\sqrt{10}[/tex]

Step-by-step explanation:

Given the number

[tex]6-2i[/tex]

We know that

[tex]z = x + iy[/tex]

where x and y are real and [tex]\sqrt{-1}=i[/tex]

The modulus or absolute value of z is:

[tex]|z|\:=\sqrt{x^2+y^2}[/tex]

Therefore, the modulus of [tex]6-2i[/tex]  will be:

[tex]z=6-2i[/tex]

[tex]z=6+(-2)i[/tex]

[tex]|z|\:=\sqrt{x^2+y^2}[/tex]

[tex]|z|\:=\sqrt{6^2+\left(-2\right)^2}[/tex]

    [tex]=\sqrt{6^2+2^2}[/tex]

    [tex]=\sqrt{36+4}[/tex]

    [tex]=\sqrt{40}[/tex]

    [tex]=\sqrt{2^2}\sqrt{2\cdot \:5}[/tex]

    [tex]=2\sqrt{2\cdot \:5}[/tex]

   [tex]=2\sqrt{10}[/tex]

Therefore, the modulus of the complex number 6-2i is:

[tex]|z|\:=2\sqrt{10}[/tex]

Donny joined a club that costs $40 per month. Is the cost over time a proportional or non-proportional relationship?

Answers

Answer:

The cost over time is a proportional relationship

Step-by-step explanation:

Proportional relationships are relationships between two variables where their ratios are equivalent. Another way to think about them is that, in a proportional relationship, one variable is always a constant value times the other. That constant is know as the "constant of proportionality"

ratio// please help!!

Answers

Answer:

The loose sweets

Step-by-step explanation:

100 divided by 0.89 = 112

120 divided by 1.49 = 80

Answer:

Step-by-step explanation:

1.49 ÷ 120 = 0.0124 GBP per gram

0.89 ÷ 100 = 0.0089 GBP per gram < 0.01 (The price of loose sweets is better value)

Mr. Moretti is making welcome bags to give to the 18 students in his homeroom on the first day of school he puts m mechanical pencils in each bag he puts twice as many regular pencils in each bag

Answers

Answer:

The total number of pencils is 6

Step-by-step explanation:

According to the given scenario, the computation of the total number of pencils is as follows:

There are 18 students

And let us assume there is m mechanical pencils that put in each bag

also he put twice of the regular pencil

So if he put the 3 mechanical pencil

So, the total number of pencils is

= 3 × 2

= 6

As it twice of the regular pencil

hence, the  total number of pencils is 6

Solve the system by elimination

Answers

Answer:

x= -2 y= -5

Step-by-step explanation:

Eliminate y by subtract = 3x-6x-2y+2y=6 ; x=-2

plug-in x = -2

-6-2y = 4 y = -5

Answer:

(- 2, - 5)

Step-by-step explanation:

[tex]\left \{ {{3x-2y=4} \atop {6x-2y=-2}} \right.[/tex]

(2) - (1)

(6x - 3x) + [- 2y - (- 2y)]= - 2 - 4

3x = - 6 ⇒ x = - 2

3( - 2) - 2y = 4 ⇔ - 6 - 2y = 4 ⇒ y = - 5

(- 2, - 5)

Need help will mark brainliest

Answers

Answer:

I am grade 5 and I don't know about what it is at all. but please make me as the brainliest

Help please I really need it thanks

Answers

Answer:

the last triangle

Step-by-step explanation:

the pythagorean theroem only works for right triangles. a right triangle is a triangle that has a 90 degree angle it the last one is the only one. so its d

pls mark branilest

Marcus buys a pair that cost $35.99 plus 5.5% tax. Tai buys a pair of shoes that cost $ 39.99 plus 9% tax. Tai uses a coupon off her purchase. What is the difference in the total cost to the nearest cent that Marcus and Tai pay for their shoes?

Answers

Answer:

The difference is $5.62

Step-by-step explanation:

The total cost Marcus will pay is

35.99 + 5.5% of 35.99

= 35.99 + 0.055(35.99) = 35.99 + 1.97945 = 37.96945

The total cost Tai will pay is;

39.99 + 9% of 39.99

= 39.99 + 0.09(39.99) = 43.5891

The difference between the total costs will be;

43.5891 - 37.96945 = 5.61965

To the nearest cent, this is 5.62

Henry took a total of 9 quizzes over the course of 3 weeks. How many weeks of school will Henry have to attend this quarter before he will have taken a total of 15 quizzes? Assume the
relationship is directly proportional

Answers

Answer:

5 weeks if it stays the rate of 3 quizzes a week

brainliest if correct please

Step-by-step explanation:

True or false: a translation produces congruent figures?

A.) true
B.) false

Answers

The correct answer is A so it’s true
The answer is A.) true hope this helps

A blueprint for a house has a scale of 1:30. A wall in the blueprint is 3 in. What is the length of the actual wall?
30
60
90
120

Answers

Answer:

C.90

Step-by-step explanation:

1 inch = 30

30 * 3 = 90

please help... please need help!!!

Answers

Answer:

2 gallons maybe?

Step-by-step explanation:

Mary is writing invitations for her birthday party. She plans to invite 16 friends. So far, Mary has written 12 invitations. Which of the following show the amount of invitations Mary has written? Select two that apply.

25/100
25%
75/100
75%

WILL RECIEVE A LOT IF YOU HELP ME

Answers

Answer:

The answer is 75% and 75/100

can u peoples help me

Answers

I think it goes in the one line of symmetry

Will mark Brainliest

what is the range of the function

Answers

The range of the function is [-6, 4], as those are the lowest and highest y values, respectively.

Solve for a
C = ab/
a + b

Answers

A = cb / c + b PLESAE GIB BARNILEST

Suppose there are two blocks of solid iron. One block is a cube, three inches on a side. The other block is a cube three miles on a side. Obviously, the large cube is many, many times greater volume than the small cube, and many, many times heavier. Is the large cube more dense than the small cube, or less dense?

Answers

Answer:

The density is the same because both cubes are composed of the same element Iron(Fe).

Answer:

I believe the large cube would be denser.

Step-by-step explanation:

HEEEEEELP MEEEEEEEEEE PLZZZZZZZZZZZZZZZ WITH NUMBER 4

Answers

Answer:

4 2/3 cups of water

Step-by-step explanation:

The original recipe has 3 1/2 cups of potatoes and 3 1/4 cups of water.

4.

If you put 5 cups of potatoes, you can find the amount of water you need using a proportion.

3 1/2 cups of potatoes is to 3 1/4 cups of water as 5 cups of of potatoes is to x cups of water.

(3 1/2) / (3 1/4) = 5/x

(7/2) / (13/4) = 5/x

7/2 * x = 13/4 * 5

2/7 * 7/2 * x = 2/7 * 13/4 * 5

x = 130/28

x = 65/14

x = 4 9/14

4 9/14 as a decimal is 4.64 which is close to 4.6666...

Answer: 4 2/3 cups of water

Solve for C p=b+c/5 I need help

Answers

Answer:

Step-by-step explanation:

p =  b + c/5                     Subtract b from both sides

p - b = c/5                       Put brackets around the left side

(p - b) = c/5                     Multiply by 5

5(p - b) = c

A kitchen sink faucet streams 0.5 gallon of water in 10 seconds. A bathroom sink faucet streams 0.75 gallon of water in 18 seconds. Which faucet will fill a


3-gallon container faster?

Answers

Answer:

the kitchen sink faucet will fill the container faster than the bathroom faucet.

Step-by-step explanation:

I found the unit rate for both faucets in order to be able to compare them.

Kitchen faucet:

.5 gallons in 10 seconds   = 1 gallon in 20 seconds  (0.5 x 2= 1 gal, 10 sec x 2=20 seconds)

.75 gallons in 18 seconds  = 1 gallon in 24 seconds  (0.75 = 3/4     3/4 x 4/3=1 gallon, 18 x 4/3 = 24 seconds)

Terrence took a total of 16 pages of notes during 8 hours of class. In all, how many hours will
Terrence have to spend in class before he will have a total of 18 pages of notes in his
notebook? Assume the relationship is directly proportional.

Answers

16 pages/8 hrs

2 pages/ he

18/2=9

18 pages/9 hrs

9 hours is your answer.

five less than three times a number is 1. What is the number?

Answers

Answer: 3 times a number can be written as 3x.

Five less than 3x means you must subtract 5 from 3x.

the word "is" means equals,

so 3x-5=10

Step-by-step explanation:

since it is given that 3 times a number less than five is 1

since it is given that 3 times a number less than five is 1 getting equation:- 3x-5=1

since it is given that 3 times a number less than five is 1 getting equation:- 3x-5=1 x=6/3

since it is given that 3 times a number less than five is 1 getting equation:- 3x-5=1 x=6/3 x=2

How many solutions does the nonlinear system of equations graphed below
have?

Answers

The system has two because each solution is the point where two lines are crossing each other.
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