Let's call the number x. Twice the number means 2x, and half the number means x/2. We Multiply the whole thing by x, and that thing in total equals x.
Putting this into equation form...
x(2x+x/2)=x
2x^2+x^2/2=x
5x^2/2=x
5x^2=2x
5x=2
x=2/5
Therefore, our mystery number is 2/5.
You are very welcome!
:P
Set it so that \(x^2-3x+7=3x-2\) .
Now bring over to the left side: \(x^2-6x+9=0\)
We can find out that \(x=3\).
Now plug it in to \(y=3x-2 => y=3(3)-2 => y=7\)
Therefore, the y-coordinate is 7.
We don't have dimensions of an isosceles trapezoid here...
For non-trig...
This was a hard one for me, too.
Derived from AoPS.
This is the answer to #3.
Thank you! It was a little long, but sometimes problems have to be :D
Oh, sorry. I'll do it next time.
Is there another way to do it without trig? Either way, thanks :D
