A47-foot-long piece of pipe is to be cut into three pieces. the second piece is three times as long as the first piece, and the third piece is two feet more than five times the length of the first piece. what is the length of the longest piece?

a. 5 feet
b. 15 feet
c. 27 feet
d. 32 feet

Which graph corresponds to the function f(x) = x2 + 4x – 1?

1. an economy consists of three workers: larry, moe, and curly. each works 10 hours a day and can produce two services: mowing lawns and washing cars. in an hour, larry can either mow one lawn or wash one car; moe can either mow one lawn or wash two cars; and curly can either mow two lawns or wash one car. a. calculate how much of each service is produced under the following circumstances: a. all three spend all their time mowing lawns. b. all three spend all their time washing cars. c. all three spend half their time on each activity d. larry spends half of his time on each activity, while moe only washes cars and curly only mows lawns b. using your answers to part a, draw a production possibilities frontier and label points a, b, c, and d on your graph. explain why the production possibilities frontier has the shape it does. c. are any of the allocations calculated in part a inefficient? explain.

Which choice has the correct steps in graphing the solution set to the following inequality? -45_> 20x-5y