Pablo and Kenneth are going make and sell some wooden figures to raise money for a charity. Pablo will carve them and Kenneth will paint them. It takes Pablo 2 hours to carve a small figure (S) and 3 hours to carve a large one (L). He plans to spend 24 hours carving. Kenneth will paint the figures and only has enough time to paint at most 10 of them. They want to raise as much money as possible.

Which two of the following equations model the constraints of this situation? (The constraints are the limits on what Pablo and Kenneth can make.)

Question 1 options:

3S+2L=24

S+L=24

2S+3L=10

2S+3L=24

S+L=10
Question 2 (10 points)
They plan to sell the small figures for $8 and the large figures for $10. How many of each figure should Pablo and Kenneth create to earn the most amount of money possible? For full credit, explain HOW you got your answer and WHY you think this is the best combination of figures.

dc=6 square root of 3 and ac is 12 square root 3

c and d

step-by-step explanation:

square root of 3/2 = 18/c

cross multiply to get 18*2=√3*c

36/√3 * √3/√3 = c

c= 36*√3/3

c=12√3

6/20

step-by-step explanation:

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!

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