M<APB + m<BPC = 90 complementary angles
m<FPB + m<BPC = 180 linear pair
m<APB = m<EPD vertical angles
m<FPD = m<APC right angles are congruent
m<EPC + m<EPF = 180 linear pair
m<BPC = m<EPD vertical angles
Answer:
m = -2
Step-by-step explanation:
<em>Distribute first.</em>
24 = -6(m+1) + 18
24 = -6m - 6 + 18
<em>Then you combine like terms.</em>
24= -6m + 12
<em>Then you still combine like terms. You subtract 12 from each side.</em>
24 = -6m + 12
-12 - 12
12= -6m
<em>Then divide by -6 to isolate the variable.</em>
12 = -6m
/-6 /-6
-2 = m
<em />
Define rates at which the individuals paint.
Bill: x = 1/8 signs/h
Bob: y = (2 signs)/(8 h) = 1/4 signs/h
Barry: z = (4/3 signs)/(8 h) = 1/6 signs/h
The job is to paint 2 signs, working together.
In the first 3 hours, the amount painted is
(x+y+z signs/h)*(3 h) = (1/8 + 1/4 + 1/6)*3 = 13/8 signs
Remaining: 2 - 13/8 = 3/8 signs
Barry quits.
In the next 1/2 hour (30 minutes), the amount painted is
(x + y signs/h)*(0.5 h) = (1/8 + 1/4)*0.5 = 3/16 signs
Remaining: 3/8 - 3/16 = 3/16 signs
Now Bob quits.
The time for Bill to finish the job is
(3/16 signs)/(1/8 signs/h) = 3/2 h
Answer: Bill finishes the job in 1.5 hours (or 1 hour, 30 minutes)
