In each diagram, line p is parallel to line f, and line t intersects lines p and f. Based on these diagrams, which statement is true? F The value of x should be 75, because the angles shown in the diagrams are congruent. G The value of x should be 105, because the measures of the angles shown in the diagrams add up to 180°. H The value of x should be 140, because the measures of the angles shown in the diagrams should add up to 360° and 360−(110 + 110) = 140. J The value of x should be 70, because the measures of the angles shown in the diagrams are both 70°.

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 function in vertex form is equivalent to f(x) = x2 + 6x + 3? f(x) = (x + 3)2 + 3 f(x) = (x + 3)2 − 6 f(x) = (x + 6)2 + 3 f(x) = (x + 6)2 − 6

What is the angle measure, or angle of depression, between this bird and the bird watcher?