Response:
Detailed explanation:
Line PU acts as a transversal intersecting parallel lines QR and ST
The angles PRQ and UST sum to 180 degrees
- 15(x+2) = 180 - 135
- 15x + 30 = 45
- 15x = 15
- x = 1
1. Angle DEF
2. Definition of congruent angles
3. Measure of angle GHI
Calculate the rates at which each individual paints.
Bill: x = 1/8 signs/hour
Bob: y = (2 signs)/(8 hours) = 1/4 signs/hour
Barry: z = (4/3 signs)/(8 hours) = 1/6 signs/hour
They need to paint a total of 2 signs cooperatively.
During the first 3 hours, the amount completed is
(x+y+z signs/hour)*(3 hours) = (1/8 + 1/4 + 1/6)*3 = 13/8 signs
Left: 2 - 13/8 = 3/8 signs
Barry leaves the job.
In the following half hour (30 minutes), the total painted is
(x + y signs/hour)*(0.5 hours) = (1/8 + 1/4)*0.5 = 3/16 signs
Left: 3/8 - 3/16 = 3/16 signs
Bob then quits.
The time it takes for Bill to finish the job is
(3/16 signs)/(1/8 signs/hour) = 3/2 hours
Answer: Bill completes the job in 1.5 hours (or 1 hour and 30 minutes).
Let L represent the yards in a roll of lace ribbon and S represent the yards in a roll of satin ribbon. We can formulate two equations: 3L + 2S = 120 yards (Equation 1) and 2L + 4S = 160 yards (Equation 2). If we multiply Equation 1 by 2 and subtract Equation 2, we have: 6L + 4S = 240 yards (Equation 1) and 2L + 4S = 160 yards (Equation 2). Thus, 4L equals 80 yards, leading to L equating to 20 yards. For Equation 1, substituting gives 3(20 yards) + 2S = 120 yards, leading to 2S equal to 60 yards, so S equals 30 yards. Therefore, a roll of lace ribbon contains 20 yards, while a roll of satin ribbon has 30 yards.
