Two joggers run 8 miles north and then 5 miles west. what is the shortest distance, to the nearest tenth of a mile, they must travel to return to their starting point? (do pythagorean theorem)

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

Which best describes a central bank's primary goals? limiting inflation and reducing unemployment reducing unemployment and maintaining cash flow controlling stagflation and reducing unemployment managing credit and ensuring the money supply's liquidity

Add: (6x^2-5x+3) + (3x^3+7x-8) a. 9x^2+12x-5 b. 9x^2+2x+11 c. 9x^2+2x-5 d. 9x^2-2x+5