Figure PQRS is rotated by 180 degrees about the origin in the counterclockwise direction to obtain figure P′Q′R′S′: A coordinate grid is labeled from negative 5 to 0 to 5 on both x and y axes at increments of 1. Figure PQRS has P at ordered pair negative 4, negative 2, Q at negative 2, negative 3, R at negative 3, negative 4, S at negative 4, negative 4. Figure P prime Q prime R prime S prime has P prime at ordered pair 4, 2, Q prime at 2, 3, R prime at 3, 4, S prime at 4, 4. Which statement best compares the lengths of the sides of the two figures? Length of PQ = Length of P′Q′ Length of PQ = Length of R′S′ Length of RS = Length of P′Q′ Length of RS = Length of Q′R′

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

Given the expression (7 ? 4i) ? (2 + 6i), perform the indicated operation and write the answer in the form a + bi.

The graph shows the amount of money noah earned based on the number of lawns he cut. which list shows the dependent quantities in the graph?