If cash prizes are to be avoided, then . . .
-- The first prize has to be a car.
-- The second prize can be a motorbike or a trip ... 2 possibilities.
For each of those . . .
-- The third prize has to be a TV.
Since there's no choice with the first or third prizes,
I only see two different ways to avoid a cash prize.
X^2+10x+25= 24+25
(x+5)^2= 49
x+5= +-7 (plus or minus 7)
x= -7-5
x=-12
x=7-5
x=2
Final answer: x={-12, 2}
The answer is ....................
X=5
Y=3
Uhh, answer choices?
In any case, since
is inscribed in a semicircle, it is a right triangle (due to the inscribed angle theorem). Thus, by the Pythagorean theorem,
Now, the circumradius of a right triangle (the radius of the circle passing through all three of its vertices) is simply half its hypotenuse, so ![OJ=OK=OL=\frac{\sqrt{157}}{2}\approx \boxed{6.265}.](https://tex.z-dn.net/?f=OJ%3DOK%3DOL%3D%5Cfrac%7B%5Csqrt%7B157%7D%7D%7B2%7D%5Capprox%20%5Cboxed%7B6.265%7D.)