In the largest triangle, the missing side has length
√((11 + 5)² - <em>x</em> ²) = √(256 - <em>x</em> ²)
But it's also the hypotenuse of the triangle with side lengths 11 and <em>y</em>, so that its length can also be written as
√(11² + <em>y</em> ²) = √(121 + <em>y</em> ²)
so that
√(256 - <em>x</em> ²) = √(121 + <em>y</em> ²)
or, by taking the squares of both sides,
256 - <em>x</em> ² = 121 + <em>y</em> ²
<em>y</em> ² = 135 - <em>x</em> ²
In the smallest triangle, you have
5² + <em>y</em> ² = <em>x</em> ² ==> <em>x</em> ² = 25 + <em>y</em> ²
Substitute this into the previous equation and solve for <em>y</em> :
<em>y</em> ² = 135 - (25 + <em>y</em> ²)
<em>y</em> ² = 110 - <em>y</em> ²
2<em>y</em> ² = 110
<em>y</em> ² = 55
<em>y</em> = √55
Answer:
11x-8
Step-by-step explanation:
First distribute the 3 and 2. (Only in the parenthesis!):
3(x-2)+2(4x-1)
3x-6+8x-2
Combine like terms:
3x+8x=11x
-6-2=-8
So the answer is:
11x-8
Well, the solid line is y≥x/2-1 whereas the dotted line has the equation
y<4x+1. The solution to this system of inequalities comes out to
being (.8<span>,3.2)</span>