Louis is filling two tanks of water in his home. Tank A currently contains 27 gallons and has a hose filling it at a rate of 3 gallons per minute. The other tank, Tank B, has 38 gallons and is being filled at a rate of 2 gallons
per minute.
. Write a system of equations that can be used to determine when the tanks will have an equal amount of
water after being filled for the same amount of time.
• How many minutes will it take for the tanks to have an equal amount of water? Show your work.

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

it's undefined because anything multiplied by 0 is 0. that said, 7 days is 168 hours

the diagram shows you   triangle def with de=4, df=9 and de≠df≠ef.

the sum of the lengths of two triangles' sides are always greater than the length of the third side:

substitute sides lengths:

then 5< ef< 13 (option 3 is true).

def is a scalene triangle with all sides of different lengths (option 5 is true, option 2 is false).

answer: correct choices are 1, 3 and 5