Two variables are proportionally related with a constant of proportionality . Which of the following points must lie on the graph of this relationship? A) (k, 0)

B) (k, 1)

C) (0,k )

D) (1,k )

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

Suppose that the price p (in dollars) and the weekly sales x (in thousands of units) of a certain commodity satisfy the demand equation 4p cubedplusx squaredequals38 comma 400. determine the rate at which sales are changing at a time when xequals80, pequals20, and the price is falling at the rate of $.20 per week.

Complex numbers multiply √-4 * √-25 and show all intermediate steps. alternative notation is sqrt(-4) * sqrt(-25).