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krok68 [10]
3 years ago
6

Peter has a set of polygonal tiles, where all the polygons are regular and have the same side length. He find that two pentagons

and a decagon can fit together perfectly. Peter also find that a triangle, an octagon, and an n-gon also fit together perfectly. Find n. (Remember that all the tiles are regular polygons.)
Mathematics
1 answer:
maxonik [38]3 years ago
4 0

Answer:

24 sides

Step-by-step explanation:

Angle at a point = 360°

To find the number of degrees in each interior angle of a regular polygon, we make use of

180(n - 2)/n

There are 8 sides in a regular octagon,

Each interior of a regular octagon= 180(8-2)/8

= 6 * 180/8

= ¾ * 180

= 135°

The interior angle of a regular triangle (equilateral triangle) is 60°

The interior angle of the regular n-gon is given by

360° - 135 - 60°

= 165°

Since the interior angle is 165°

Then

180(n - 2)/n = 165 for the regular n-gon

Solving for n

Multiply both sides by n

180(n - 2) = 165n ------ Open the bracket

180n - 360 = 165n ----- Collect Like Terms

180n - 165n = 360

15n = 360 ----- Divide both sides by 15

n = 360/15

n = 24

Thus, the number of sides of the regular n-gon is 24

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pychu [463]

Answer:

3 cases

Step-by-step explanation:

45 - 27 = 18

18 ÷ 5 = 3

Tax is probably like $1 so It would add up to 18.

8 0
3 years ago
Please help me due tomorrow
Tom [10]

<u>Given </u><u>:</u><u>-</u>

  • The slope of the line through points (3,y) and (4,10) is 7 .

<u>To </u><u>Find</u><u> </u><u>:</u><u>-</u>

  • The value of y .

<u>Solution</u><u> </u><u>:</u><u>-</u>

As we know that the slope of the line is difference of ordinate divided by the difference of absicca as ,

\longrightarrow m = y -10 / 3 - 4

\longrightarrow 7 (-1) = y -10

\longrightarrow -7 = y -10

\longrightarrow y = 10 -7

\longrightarrow y = 3

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5 0
2 years ago
What is the difference? startfraction 2 x 5 over x squared minus 3 x endfraction minus startfraction 3 x 5 over x cubed minus 9
weeeeeb [17]

The difference of the expression \frac{2x^5}{x^2 - 3x} - \frac{3x^5}{x^3 - 9x} is \frac{2x^5(x + 3) - 3x^5}{x(x - 3)(x + 3)}

<h3>How to determine the difference?</h3>

The expression is given as:

\frac{2x^5}{x^2 - 3x} - \frac{3x^5}{x^3 - 9x}

Factor the denominators of the expressions:

\frac{2x^5}{x(x - 3)} - \frac{3x^5}{x(x^2 - 9)}

Apply the difference of two squares to x² - 9

\frac{2x^5}{x(x - 3)} - \frac{3x^5}{x(x - 3)(x + 3)}

Take LCM

\frac{2x^5(x + 3) - 3x^5}{x(x - 3)(x + 3)}

Hence, the difference of the expression \frac{2x^5}{x^2 - 3x} - \frac{3x^5}{x^3 - 9x} is \frac{2x^5(x + 3) - 3x^5}{x(x - 3)(x + 3)}

Read more about expressions at:

brainly.com/question/723406

#SPJ4

6 0
2 years ago
Solve for y. <br> 6y-1.5x=8
schepotkina [342]
I'm pretty sure y=1.3=0.25x
8 0
3 years ago
What is 15% of ____ is 27
serious [3.7K]

Answer:

it's 180

15% of 180 is 27

hope it helps :)

3 0
3 years ago
Read 2 more answers
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