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
ziro4ka [17]
2 years ago
12

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

Mathematics
1 answer:
Nataliya [291]2 years ago
3 0

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 <u>13 sides.</u>

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 <u>7 sides.</u>

(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 <u>Square.</u>

<u>(c)</u>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 <u>sum of the exterior angle of a polygon is 360 degrees.</u>

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 <u>does not change either in a regular or irregular polygon.</u>

You might be interested in
2|3x - 2|= 14 how would you solve this absolute value equation?
Feliz [49]

Answer: 2. |3x-2|= 14

|3x-2|=2.7/2

|3x-2|=7

x∈ {3,-5/3

Step-by-step explanation: \frac{5}{3}

6 0
2 years ago
Read 2 more answers
Giải hộ toi bài tập nó khá khó
deff fn [24]

Answer:

hhhhhhhhhhhhhhhhhhhh

5 0
2 years ago
Given the function f(x)= 14x^2 + 5x - 1 answer the question if you could change the 14 to any other number, but the rest has to
polet [3.4K]
This is a polynomial of degree 2, and remember that complex roots always come in pairs; therefore, in a second degree polynomial you can only have 0 real roots and 2 complex roots, or 2 real roots and 0 complex roots. There is no way you can have 1 real root and 1 complex root because, as stated before, complex (non-real) roots always come in pairs; so the only way of having 1 real root is dumping the polynomial of degree 2 (14 x^{2}) by changing the 14 to 0. That way we'll left with f(x)=5x-1 which only has one real root:
0=5x-1
5x=1
x= \frac{1}{5}

7 0
3 years ago
Read 2 more answers
Which function's graph is shown below?
STALIN [3.7K]

Answer:

A. y = cos x

Step-by-step explanation:

The function that we see graphed has the point (0,1), this means whichever trig function f(x) it represents f(0) = 1.

Now, only the cosine function has the property that cos(0) = 1, thus choice A is the correct answer.

5 0
2 years ago
Read 2 more answers
Describe the sampling distribution of p(hat). Assume the size of the population is 30,000.n=800, p=0.6a) Determine the mean of t
Leno4ka [110]

Answer:

Standard deviation of the binomial distribution

                               = \sqrt{n p q} = \sqrt{192}  = 13.856

Step-by-step explanation:

<u><em>Explanation:-</em></u>

Given size 'n' = 800

The population proportion 'p'=0.6

Let 'X' be the random variable of the binomial distribution

a)  mean of the binomial distribution  = n p = 800 ×0.6

                                                             μ  = 480

b)  variance of the binomial distribution

                                                                      = n p q

                                                                      =  800 X 0.6 ×0.4

                                                                 σ²  = 192

Standard deviation of the binomial distribution

                                                             σ    = \sqrt{n p q} = \sqrt{192}  = 13.856

6 0
2 years ago
Other questions:
  • WILL GIVE A BRAINLIEST IF UR 100% CORRECT PLEASE HELP!!!
    9·1 answer
  • Decide whether the triangles can be proven congruent by the given postulate or theorem. If not, state what information is needed
    13·1 answer
  • One gallon of paint is equivalent to 3.78 liters.Michael wants to determine how many centiliters this is.Which answer choice is
    5·1 answer
  • How many downloads did song 1 have at minute 3?
    6·2 answers
  • This is due by today, someone help me please!
    12·1 answer
  • Lynn is tracking the progress of her plats growth.today the plant is 7cm.The plant grows 2cm per day find an equation that repre
    5·1 answer
  • I still don’t understand please help. I put the most I could but I still don’t know :(
    8·1 answer
  • Which equation has the solution x = -4? 2(x - 4) = 16 3x + 6 - 2x = -2 (1/4)x + 4 = 3 (x + 6)3 = -6​
    15·1 answer
  • Classify as a rational or irrational: -8.2
    9·2 answers
  • Write an equation of the line with the given slope, m and y intercept (0,b) m=-6, b =-1/2 plss
    15·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!