A 50 foot ladder is set against the side of a house so that it reaches up 48 feet. If Mila grabs the ladder at its base and pulls it 6 feet farther from the house, how far up the side of the house will the ladder reach now? (The answer is not 42 ft.) Round to the nearest tenth of a foot.

~31.3

first use the pythagorean theorem. a^2+(40)^2=50^2.

simply. a+1600=2500. subtract 1600 from both sides. a^2=900.

square root both sides to get a= 30

then find how far the top of the ladder is from the ground once in its new position.

a^2+(39)^2=50^2.

simplify. a^2+1512=2500. subtract 1512 from both sides to get a^2=979.

square root both sides to get a=31.288975. round to the nearest tenth to get a=31.3

hello from mrbilldoesmath!

answer:

25x^2 + 90x + 84

discussion:

mn(x) = m(n(x)) = m( 5x + 9) =

(5x + 9)^2 + 3 =>

25x^2 + 90x + 9^2 + 3 =

25x^2 + 90x + 84                 (as 9^2 = 9*9 = 81)

which is the second choice

regards,  

mrb

p.s.   i'll be on vacation from friday, dec 22 to jan 2, 2019. have a great new year!