Janet is designing a frame for a client. she wants to prove to her client that m∠1 = m∠3 in her sketch. what is the missing justification in the proof? segment cd intersects segment ab, creating angles 1, 2, 3, and 4. statement justification segment cd intersects segment ab given ∠1 + ∠ 2 = 180° ∠ 2 + ∠3 = 180° ∠1 + ∠ 2 = ∠ 2 + ∠3 transitive property ∠1 = ∠3 subtraction property definition of supplementary angles intersecting lines postulate same-side interior angles theorem vertical angles theorem

The square pyramid has a volume of 441 cubic inches. what is the value of x? 1/7x is the height x is the base

Two cars which are 40 miles apart start moving simultaneously in the same direction with constant speeds. if the speed of the car which is behind is 56 mph and the speed of the other car is 48 mph, how many hours will it take for the car which is behind to catch up the car ahead of it?

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.