catmg

x + 15 + x - 15 + x + 30 = 180

3x + 30 = 180

3x = 150

x = 50

=^._.^=

90 + 3x + 4x - 1 = 180

89 + 7x = 180

7x = 91

x = 13

=^._.^=

There are 2 cases. 

Penelope and Quentin are not officers. 

20*19*18 ways to choose from the other 20 people. 

Penelope and Quentin are officers. 

3*2*20 ways to choose another person from the other 20 and give assign them spots. 

20*19*18+3*2*20

=^._.^=

Draw this out and create a right triangle. 

With the right triangle, you should be able to figure out the other 2 angle measurements. 

Then, use the law of sines to find the height from the ground. :))

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a^3 + b^3 = 42

(a+b)(a^2 - ab + b^2) = 42

a^2 - ab + b^2 = 6

(a+b)^2 - 3ab = 6

49 - 3ab = 6

ab = 43/3

a^2 - ab + b^2 = 6

a^2 - 43/3 + b^2 = 6

a^2 + b^2 = 20 1/3

=^._.^=

We can use power of a point to find XY. 

8^2 = 4 * xy

xy = 16

Now we have a right triangle with legs 20 and 8. 

sqrt(20^2 + 8^2) = sqrt(464) = 4sqrt(29)

=^._.^=

Oh no, sometimes things glitch. :((

Try reposting the question?

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President = 10 options

Secretary = 9 options (can't be the person who was chosen for president)

Treasurer = 8 options (can't be president or secretary)

Morale officer = 7 options (can't be president, treasurer, or secretary)

Dog catcher = 6 options (can't be president secretary, treasurer, or morale officer)

10*9*8*7*6

=^._.^=

20 is even. 

10 is even. 

5 is odd.

16 is even. 

8 is even. 

4 is even. 

2 is even. 

1 is odd. 

4 is even... and it starts to repeat. 

Can you take it from here?

=^._.^=

x_0 = 160/2

x_0 = 80 

=^._.^=