<em><u>Answer:</u></em>
<em><u>y = 5, 3; x = 171, 155</u></em>
<em><u>Step-by-step explanation:</u></em>
8y - 15 = y^2
y^2-8y+15=0
y^2-3y-5y+15=0
y(y-3)-5(y-3)=0
(y-5)(y-3)=0
y can be 5 or 3.
x = 180 - (8y - 15)
x = 180 - (8(3)-15)
x = 180 - 9
x = 171
OR
x = 180 - (8(5) - 15)
x = 180 - 25
x = 155
<span>1/2
This problem can be easily solved 2 ways, you can enumerate all 32 possibilities and count the number that have 0, 1, or 2 heads. Or you can calculate result directly. For no more than 2 heads, we want the sum of 0 heads, 1 head, and 2 heads. So
0 heads = (1/2)^5 = 1/32
1 head = (1/2)*(1/2)^5 * 5!/(1!4!) = 1/32 * 5 = 5/32
2 heads = (1/2)^2*(1/2)^5 * 5!/(2!3!) = 1/32 * 10 = 10/32
And finally:
1/32 + 5/32 + 10/32 = 16/32 = 1/2</span>
So based on the theorem about vertical angles are congruent it is safe to assume that:
6y - 27 = 105 degrees
and
12x + 15 = 75 degrees
And solve it out for x and y
6y - 27 = 105
6y = 132
y = 22
12x + 15 = 75
12x = 60
x = 5
You could plug the x and y values in to check if it makes sense