Answer: Well if you were going to think of a circle you can divide it into 4 equal sizes in one of the is equal to two pentagons and a half. If you add all is equal to a loop full of pentagons [which makes 10 pentagons]. Because the ring is made out of regular pentagons, we can work out that each of the interior angles of each pentagon is 108* degrees. By extending the lines that two pentagons share, assuming they will all meet in the middle, it will create a triangle. As we know each angle of a [regular] pentagon is 108* degrees, we know the two base angles of the triangle would equal to 72** which leaves the top angle to be 36 degrees. As [the sum of] angles at a point is 360 degrees, and 36 is divisible by 360, it will make a complete ring. Also, as 360 ÷ 36 = 10, we know that the ring will be made out of 10 pentagons. as formula to calculate the the size of a interior angle of a polygon is (n×180−360)÷n (for n being the number of sides that the polygon has). because the triangle is made by extending the lines, and angles on a line is 180 degrees, 180−108 (an interior angle of a pentagon) =72.
Answer:
Manuel owes more to Calvin(75 cents) as compared to Lester(50 cents).
Step-by-step explanation:
We are given the following information in the question:
Manuel borrowed 50 cents from Lester and 75 cents from Calvin. Manuel claims that he owes lee to Calvin.
Manuel's claim is wrong.
This could be understood by comparing:
The negative sign here states that this amount is owed to someone, we do not own this money.
Thus, Manuel owes more to Calvin(75 cents) as compared to Lester(50 cents).
The sum of the interior angles with n number of sides is solved through the equation,
S = 180 x (n - 2)
For 37 - gon,
S = 180 x (37 - 2) = 6300
Thus, the sum of the interior angles of a 37-gon is 6300°.
Answer:
190 children and 150 adults
Step-by-step explanation:
1. 1.25x + 2y = 537.5
2. x + y = 340
Here, x represents the children and y represents the adults.
Again, the first equation represent the cost of tickets, while the second represents the number of people.
From the above equation, we can solve for x and y
From equation 2,
x + y = 340
x = 340 - y
Substitute for x in equation 1
1.25x + 2y = 537.5
Then,
1.25(340 - y) + 2y = 537.5
Expand the bracket
425 - 1.25y + 2y = 537.5
Collect like terms
-1.25y + 2y = 537.5 - 425
0.75y = 112.5
y = 150.
To get the value of x, substitute for y in equation 2
x + y = 340
x + 150 = 340
x = 340 - 150
x = 190
Therefore,
There were 190 children and 150 adults at the pool that day