1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
earnstyle [38]
3 years ago
14

A company is manufacturing a gear in the shape of a regular polygon. The measure of each angle of the gear is 162º. How many sid

es does the gear have??
Mathematics
2 answers:
Marta_Voda [28]3 years ago
8 0
Triangle has 180° total
square has 360° total
pentagon has 540° total
hexagon has 720° total
so they increase by 180° for every side to the polygon starting at 3 sides instead of 1 so if n is how many sides in the polygon then
(n-2)×180=degrees TOTAL inside the polygon
(n-2)×180/n=degrees for EACH angle in the polygon

(n-2)×180/n=162
multiply both sides by n
(n-2)×180=162n
divide both sides by 180
n-2=162n/180
n-2=0.9n
subtract 0.9n and add 2 to both sides to get n alone
0.1n=2
n=20 sides
Icosagon is the term for a 20 sided polygon
BabaBlast [244]3 years ago
7 0

Answer:

Gear have 20 sides .

Step-by-step explanation:

Given : A company is manufacturing a gear in the shape of a regular polygon. The measure of each angle of the gear is 162º.

To find : How many sides does the gear have.

Solution : We have given that  each angle of polygon = 162 degree.

By the property of polygon :

Each angle of polygon = \frac{(n-2)180}{n}.

Where, n is number of sides polygon .

Plugging the values,

162 ° =  \frac{(n-2)180}{n}.

On simplify right side , we can write it as:

162  °  = \frac{180n}{n} -\frac{360}{n}.

162  °  =  180 -\frac{360}{n}.

On subtracting by 180 both side.

162 -180 = -\frac{360}{n}.

-18°  = - \frac{360}{n}.

On multiplying by n both side

-18° × n = -360°

On dividing by - 18 by both side

n = \frac{360}{18}.

n = 20 .

Therefore , gear have 20 sides .

You might be interested in
given the recursive formula for a geometric sequence find the common ratio the 8th term and the explicit formula.did I set these
lesya [120]

Answer:


Step-by-step explanation:

1)Since we know that recursive formula of the geometric sequence is

a_{n}=a_{n-1}*r

so comparing it with the given recursive formula a_{n}=a_{n-1}*-4

we get common ratio =-4

8th term= a_{1}*(r)^{n-1}=-2*(-4)^{7} =32768.

Explicit Formula =-2*(-4)^{n-1}

2) Comparing the given recursive formula a_{n}=a_{n-1}*-2

with standard recursive formula a_{n}=a_{n-1}*r

we get common ratio =-2

8th term= a_{1}*(r)^{n-1}=-4*(-2)^{7} =512.

Explicit Formula =-4*(-2)^{n-1}

3)Comparing the given recursive formula a_{n}=a_{n-1}*3

with standard recursive formula a_{n}=a_{n-1}*r

we get common ratio =3

8th term= a_{1}*(r)^{n-1}=-1*(3)^{7} =-2187.

Explicit Formula =-1*(3)^{n-1}

4)Comparing the given recursive formula a_{n}=a_{n-1}*-4

with standard recursive formula a_{n}=a_{n-1}*r

we get common ratio =-4

8th term= a_{1}*(r)^{n-1}=3*(-4)^{7} =-49152.

Explicit Formula =3*(-4)^{n-1}

5)Comparing the given recursive formula a_{n}=a_{n-1}*-4

with standard recursive formula a_{n}=a_{n-1}*r

we get common ratio =-4

8th term= a_{1}*(r)^{n-1}=-4*(-4)^{7} =65536.

Explicit Formula =-4*(-4)^{n-1}

6)Comparing the given recursive formula a_{n}=a_{n-1}*-2

with standard recursive formula a_{n}=a_{n-1}*r

we get common ratio =-2

8th term= a_{1}*(r)^{n-1}=3*(-2)^{7} =-384.

Explicit Formula =3*(-2)^{n-1}

7)Comparing the given recursive formula a_{n}=a_{n-1}*-5

with standard recursive formula a_{n}=a_{n-1}*r

we get common ratio =-5

8th term= a_{1}*(r)^{n-1}=4*(-5)^{7} =-312500.

Explicit Formula =4*(-5)^{n-1}

8)Comparing the given recursive formula a_{n}=a_{n-1}*-5

with standard recursive formula a_{n}=a_{n-1}*r

we get common ratio =-5

8th term= a_{1}*(r)^{n-1}=2*(-5)^{7} =-156250.

Explicit Formula =2*(-5)^{n-1}

6 0
3 years ago
Find the shaded area of each figure, round your answer to one decimal place if necessary
Annette [7]
<h2>area of shaded portion = 49.5 yd²</h2><h2>____________________</h2>

<u>Step-by-step explanation:</u>

radius of circle = 5 yd ------ ( <em>g</em><em>i</em><em>v</em><em>e</em><em>n</em><em> </em><em>)</em>

height of triangle = 16 yd --- ( <em>g</em><em>i</em><em>v</em><em>e</em><em>n</em><em> </em><em>)</em>

base of triangle = 16 yd ----- ( <em>g</em><em>i</em><em>v</em><em>e</em><em>n</em><em> </em><em>)</em>

area of triangle = 1/2 × base × height

= 1/2 × 16 × 16

= 128 yd²

area of circle = π × radius²

= 3.14 × 5 × 5 --- ( π = 3.14 )

= 78.5 yd²

<h2>---------------------------------------</h2>

area of shaded portion = area of triangle - area of circle

area of shaded portion= 128 yd²-78.5 yd²

area of shaded portion = 49.5 yd²

<h2>--------------------------------------</h2><h2>PLEASE FOLLOW ME</h2>
8 0
2 years ago
Draw any two convex pentagons. For each of them measure the sum of its interior angles using a protractor. Explain the result of
m_a_m_a [10]
Shouldn;t it be 540?
4 0
3 years ago
Read 2 more answers
What is the best estimate for the product of 289 and 7
Nat2105 [25]
290 * 7 = 1400 + 630 = 2,030
2030 - 7 = 2,023
4 0
3 years ago
Read 2 more answers
Solve and model 7/10-3/10
sergij07 [2.7K]
Hello,

\frac{7}{10} -  \frac{3}{10} = 2/5 

Solution.

<span>\frac{7}{10} - \frac{3}{10}= The denominators are the same so you subtract the numerator. Your answer should be </span>\frac{4}{10}  simplified your answer is \frac{2}{5}.

Have A Good Day!
7 0
3 years ago
Other questions:
  • 9.12cm<br> 10.36cm<br> 11.34cm<br> 12.61cm
    7·1 answer
  • Yin has 3 blue shirts. 10% of her shirts are blue. Liang has 1.5 times as many shirts as Yin has. How many shirts does Liang hav
    12·1 answer
  • 130 rounded to the nearest hundred
    7·2 answers
  • Solve by the elimination method
    14·1 answer
  • 1. A drink and a box of popcorn together cost 90p. Two drinks and a box of popcorn together cost £1.45. What does a box of popco
    11·1 answer
  • The most points you will EVER GETTTTTT i would do more points but brainly doesn't let me
    7·2 answers
  • Adsila's recipe for peach frozen yogurt says to mix 3 cups blended peaches for every 2 cups vanilla yogurt. Which of these froze
    11·1 answer
  • A 5-pound bag of sugar costs $9.25. What is the unit price of the sugar?
    9·2 answers
  • Someone please help me with this, I will really appreciate it!! Please.
    5·1 answer
  • Can y’all help me on question 6?!
    14·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!