Answer:
the ratio is 3:1
Step-by-step explanation:
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
I don't think there is a way of working this out. I reckon you're supposed to guess it. The answer is
<span>
</span>f(x) = x<span>³</span>
Answer:
<h3>
-58, -57, -56</h3>
Step-by-step explanation:
x - the first of consecutive integers
x+1 - the second of consecutive integers
x+2 - the third of consecutive integers
x+x+2 - sum of the first and third integers
3(x+x+2) - three times the sum of the first and third integers
3(x+x+2) = -342
÷3 ÷3
2x + 2 = -114
-2 -2
2x = -116
÷2 ÷2
x = -58
x+1 = -58 + 1 = -57
x+2 = -58 + 2 = -56
