#1**+1 **

1) for this to be a right triangle, the other side would have to be 12, a 5/12/13 triangle.

so 5*12*1/2 for area is 30

2) the diagonals of a polygon are n(n-3)/2 this means (n-3)/2 = 10 so n = 23

3) the volume of the first block is 140 and cost $40

40/140 money per cm^3 is the cost

the volume of the second figure is 12*42*45 or 22680

22680 times 40/140 is $6480

4) the perimiter is 98 and two of the sides are equal.

thus we have two true equations.

if the sides that are equal, called x, and the base is called, y

then 2x+y = 98 and 35^2 + (y/2)^2 = x^2

using substitution, y=98-2x we get 35^2 + [(98-2x)/2]^2 = x^2

solving for x we get, x = 37

if x = 37 then the base is 98- 2(37) = 24

now area of triangle formula (24 * 35)/2 = 420

my bad, i'll fix #3

Guest Jun 29, 2018

edited by
Guest
Jun 30, 2018

edited by Guest Jun 30, 2018

edited by Guest Jun 30, 2018

#2**0 **

3) You reversed the cost!!

It should be: $40/140 x 22, 680 =**$6,480 - Cost of the larger block.**

Guest Jun 29, 2018

#5**+2 **

Here's 3

The total volume of the first prism is ( 4 * 7 * 5) = 140 cm^3

So....the price per cubic centimeter is 4000 cents/140 cm^3 ≈ 28.6 cents / cm^3

And the volume of the second prism is (12 * 42 * 45) = 22680 cm^3

So...the price of the second prism (block) is just

22680 cm^3 * 28.6 cents / cm^3 = 648648 cents ≈ $6486.48

CPhill
Jun 29, 2018

#6**+2 **

The formula to find the number of diagnols in a polygon is \(\frac{n(n-3)}{2}\).

Since we have 10n for the number of diagnols, we get: \(\frac{n(n-3)}{2}=10n\).

Taking 2 to the other side, we get: \(n(n-3)=20n\).

Dividing n on both sides, we get: \(n-3=20\)

This means that \(\boxed{n=23}\).

tertre
Jun 29, 2018