The polynomial p(x) = x5 − 9x4 + 13x3 + 57x2 − 86x − 120 has a total of zeroes. it can have a maximum of positive real roots and a maximum of negative real roots.

Astudent received the following grades last semester. find the student's semester grade point average. an a is algebra (3 credits), a b in history ( 3 credits), a in sociology ( 3 credits) a d in english ( 3credits) and a c in seminar ( 2credits). an a is worth 4 points, a b is worth 3 points a c is worth 2 points and a d is worth 1 point.

In the diagram, the ratio of ab to ae is (1/2) . what is the ratio of the length of to the length of ?

Afurniture manufacturer produces chairs and sofas. each chair requires 10 yards of fabric, and each sofa requires 20 yards of fabric. the manufacturer has 300 yards of fabric available. to fulfill orders, the number of sofas must be at least twice the number of chairs. let x be the number of chairs and y the number of sofas. which inequalities are described in the problem? check all of the boxes that apply