Answer:
-45
Step-by-step explanation:
Answer:
x = 8, and y = 12
Step-by-step explanation:
There are 2 variables, so you need 2 equations to form a system of equations in two variables.
The upper left triangle has all angle measures given: 100, 2x + y, 5x + y. We know that the sum of the measures of the angles of a triangle is 180.
First equation:
100 + 2x + y + 5x + y = 180
Simplify:
7x + 2y = 80 (First equation)
Now we see that the upper and lower sides are parallel, so alternate interior angles are congruent. The angles measuring 2x + y and 5x - y are alternate interior angles and are congruent.
Second equation:
2x + y = 5x - y
Simplify:
3x - 2y = 0 (Second equation)
Now we use the first equation and the second equation as a system of simultaneous equations to solve for x and y.
7x + 2y = 80
3x - 2y = 0
Solve the second equation for 2x.
3x = 2y
Now replace 2y in the first equation with 3x.
7x + 3x = 80
10x = 80
x = 8
Replace x with 8 in the second equation.
3(8) - 2x = 0
24 = 2x
x = 12
Answer: x = 8, and y = 12
The three slices are each approximately 1/9 pound in weight, and, since 2/9 is less than 1/4, he can eat 2 whole slices and be okay. If he wants to eat partial slices, then he could eat 2 1/4 slices, as each slice weighs 4/36 pounds, so 2 slices would equal 8/36 pounds, leaving 1/36 pound left over in his diet, which is a quarter of the third slice.
2.25
Volume of can, V = pi * r^2 * h
V = 3.14 * (3.5/2)^2 * 5
V = 3.14 * 1.75^2 * 5
V = 3.14 * 3.0625 * 5
V = 48.08125 inches^3
V = 48.08 inches^3
if the diameter of a circle is 15, its radius is half that or 7.5.
![\bf \textit{area of a circle}\\\\ A=\pi r^2~~ \begin{cases} r=radius\\[-0.5em] \hrulefill\\ r=7.5 \end{cases} A=\pi (7.5)^2\implies A=56.25\pi \implies \stackrel{\pi =3.14}{A=176.625}](https://tex.z-dn.net/?f=%5Cbf%20%5Ctextit%7Barea%20of%20a%20circle%7D%5C%5C%5C%5C%20A%3D%5Cpi%20r%5E2~~%20%5Cbegin%7Bcases%7D%20r%3Dradius%5C%5C%5B-0.5em%5D%20%5Chrulefill%5C%5C%20r%3D7.5%20%5Cend%7Bcases%7D%20A%3D%5Cpi%20%287.5%29%5E2%5Cimplies%20A%3D56.25%5Cpi%20%5Cimplies%20%5Cstackrel%7B%5Cpi%20%3D3.14%7D%7BA%3D176.625%7D%20)
