How many counterexamples do you need to prove a conjecture to be false

one , i guess

because the conjecture is only true if it satisfies all the cases.

we have three similar triangles, because each has a right angle and shares an angle.   let's write the angles in order: opposite to short leg, long leg, hypotenuse.

cab similar to bad similar to cbd

or as ratios,

ca: ab: cb = ba: ad: bd = cb: bd: cd

we also know

ac = ad + cd

(ad+cd): ab: cb = ba: ad: bd = cb: bd: cd

(ad+cd)/cb=cb/cd

we have cb=6, ad=5 and seek x=cd.

we reject the negative root and conclude x=4

answer: 4

if you are looking for the unit rate then the answer would be 9 because unit rate is distance divided by time.

step-by-step explanation: