Distance geometry problem : Mike lives in the white house at the top of the hill and Mike wants to go play video games with his friend who lives in the brown house. Mike usually take the route that passes by the haunted purple house, and it always freaks him out. To avoid this, Mike's mom tells him to take the straight path there but he is convinced it's a longer route than his route. Mike decides to look into it and see which route is actually faster, who's right? Mike or Mike’s mom?

360 different combinations

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

yes

step-by-step explanation:

so of course you want to start by plugging the 5 in which goes to 7(5)+3(5)=50 because 7*5=35 and 3*5=15 and then add them together, then plug in the 5 to the other equation as well 9(5)+5=50 because 9*5= 45 and then add 5 and so yes they are equivalent.