(Teaser) The total number of sides in two regular polygons is 13, and total number of diagonals is 25. How many sides are in each polygon?

T he two polygons have 8 sides and 5 sides.  

Step-by-step explanation:

A purely algebraic solution seems as if it would be very messy. Use trial and error, along with the formula for the number of diagonals in a n-sided polygon.

number of diagonals in a polygon with n sides: n(n-3)/2

10 sides and 3 sides: 10(7)/2 + 3(0)/2 = 35+0 = 35 nope

9 sides and 4 sides: 9(6)/2 + 4(1)/2 = 27+2 = 29 nope

8 sides and 5 sides: 8(5)/2 + 5(2)/2 = 20+5 = 25 yep!

20%

step-by-step explanation:

the final amount you will pay is $68.04.

the tip is determined by the pre-tax amount, so we calculate the tip based on the original bill, not after we've added sales tax.

to find the tip:

we can divide 54.00 by 100 to get 1% of 54. then we multiply that by 18.

54 / 100 = .54

.54 x 18 = 9.72

tip = 9.72$

to find the tax:

we can divide 54.00 by 100 to get 1% of 54. then we can multiply that by 8 to get 8%.

54 / 100 = .54

.54 x 8 = 4.32

tax= 4.32

now we can add the tip and tax to the bill to get our total.

54 + 9.72 + 4.32 = 68.04

total: $68.04

step-by-step explanation: