Baseball player Joe Wilson had some signed cards with him before he met his fans. He gave the first group of fans 1/2 of the cards. Then he gave the second group of fans 1/3 of the remaining cards. Finally, he gave the third group of fans 1/4 of cards that were left. After that, he still had 60 cards left. How many cards did he originally have with him?

Use the distributive property to factor the expression. 15x + 6 a) 2 5 b) − 2 5 c) 3(5x + 2) d) 5(3x + 6)

Acomposition of transformations maps δxyz to δx"y"z". the first transformation for this composition is , and the second transformation is a 90° rotation about point x'.

Asystem of linear equations with more equations than unknowns is sometimes called an overdetermined system. can such a system be consistent? illustrate your answer with a specific system of three equations in two unknowns. choose the correct answer below. a. yes, overdetermined systems can be consistent. for example, the system of equations below is consistent because it has the solution nothing. (type an ordered pair.) x 1 equals 2 comma x 2 equals 4 comma x 1 plus x 2 equals 6 b. no, overdetermined systems cannot be consistent because there are fewer free variables than equations. for example, the system of equations below has no solution. x 1 equals 2 comma x 2 equals 4 comma x 1 plus x 2 equals 12 c. yes, overdetermined systems can be consistent. for example, the system of equations below is consistent because it has the solution nothing. (type an ordered pair.) x 1 equals 2 comma x 2 equals 4 comma x 1 plus x 2 equals 8 d. no, overdetermined systems cannot be consistent because there are no free variables. for example, the system of equations below has no solution. x 1 equals 2 comma x 2 equals 4 comma x 1 plus x 2 equals 24