20 f(x)
х
g(x)
The tables given are for the linear functions
f(x) and
g(x). What is the input value for which f(x) = g(x) is true?
X
-2
3
-2
4
-1
3 3 3
-1
3
0
0
N
1
3
1
1
2.
3
2.
O
3
3
3
-1

the answer is b 1/10

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