Find the intercepts for both planes.
Plane 1, <em>x</em> + <em>y</em> + 2<em>z</em> = 2:



Plane 2, 4<em>x</em> + 4<em>y</em> + <em>z</em> = 8:



Both planes share the same <em>x</em>- and <em>y</em>-intercepts, but the second plane's <em>z</em>-intercept is higher, so Plane 2 acts as the roof of the bounded region.
Meanwhile, in the (<em>x</em>, <em>y</em>)-plane where <em>z</em> = 0, we see the bounded region projects down to the triangle in the first quadrant with legs <em>x</em> = 0, <em>y</em> = 0, and <em>x</em> + <em>y</em> = 2, or <em>y</em> = 2 - <em>x</em>.
So the volume of the region is



There are eight books total and he only grabbed two so the probability would be 2 out of 16 or 2:16
Answer:
The center is (-10,10) and the radius is 4sqrt(3)
Step-by-step explanation:
(x + 10)^2 + (y - 10)^2 = 48
We can write the equation of a circle as
(x -h)^2 + (y - k)^2 = r^2 where (h,k) is the center and r is the radius
(x- -10)^2 + (y - 10)^2 = (sqrt(16*3) )^2
(x- -10)^2 + (y - 10)^2 = (4sqrt(3)) ^2
The center is (-10,10) and the radius is 4sqrt(3)
X = [-(-8) +/- sqrt((-8)^2 -4*41)] / 2
x = ( 8 + sqrt (-100) / 2 and (8 - sqrt(-100) / 2
4 +or- 5i
For every 7 votes for candidate a, there are 4 votes for candidate c