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
opposites are also called additive inverse and have the sum of zero.
So we know if there are 5 groups/dozens of Monarch butterflies, there are 2 groups/dozens of Queen butterflies. In other words, there are 5 Monarch butterflies for every 2 Queen butterflies.
Then we can turn that into an equation.
From the last equation we wrote we can see that the total number of butterflies in the farm is
.
When we compare the Queen butterflies to total butterflies, we get
The ratio of Queen butterflies to total butterflies is 2:7.
Answer:
The Answer is x=6 2/3
Step-by-step explanation:
The Area of a triangle is A= 1/2 bh, so we should think of the triangle as half of a square/rectangle. This means the total area of the theoritical Square is 400 sq ft. We then figure out this equation:
12 * 5x = 400
400/12 = 5x
80/12 = x which is equal to 6 2/3.
Hope this helps!
