Question

PLEASE HELP ASAP !! (Picture included)

Answer 1

This is the question that's gonna put me over the top and make me a Brainly Genius. Of course working for free doing middle school math homework doesn't really sound like a genius, but I'm doing it anyway.

This one is the Pythagorean Theorem of course:

$(x+3)^2 + (x+4)^2 = (x+10)^2$

$x^2 + 6x + 9 + x^2 + 8x + 16 = x^2 + 20 x + 100$

$x^2 - 6x - 75 = 0$

The Shakespeare Quadratic Formula (2b or -2b) is a little shortcut for the quadratic formula when the middle term is even.

$x^2-2bx+c \textrm{ has zeros } x=b\pm \sqrt{b^2-c}$

So we get

$x = 3 \pm \sqrt{3^2 -(-75)} = 3 \pm \sqrt{84} = 3 \pm 2 \sqrt{21}$

The minus root is less than -6 giving negative sides, so we reject it and conclude

$x = 3 + 2 \sqrt{21}$

Choice C

When I hit Add I officially become a Genius. Maybe I should retire.