What conjecture can you make about the number of dots in the nth pattern?
A
n(n-1)
С
2
2
n(n+1)
(n - 1)(n + 1
B.
D
2
2
n2
2

8

step-by-step explanation:

just put √(2) * √(32) into a calculator. that will make the answer be 8.

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