(0,-9);slope=4 (3,-8):slope=-3
(-4,-7);slope=1
(4,9);slope=5
(-6,-8);slope= 5/6
(7,-8); slope= -2

I need each of the problems answered with and explanation.

answer: ouch. thats difficult

step-by-step explanation:

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