The demand function for a certain make of replacement cartridges for a water purifier is given by the equation p=−0.01x2−0.1x+21 where p is the unit price in dollars and xis the quantity demanded each week, measured in units of a thousand. determine the consumers' surplus if the market price is set at $9/cartridge. (round your answer to two decimal places.)

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

In right ∆abc shown below, the midpoint of hypotenuse ac is located at d and segment bd is drawn.if ab = 12 and bc = 16, then explain why bd = 10. hint: consider what you know about the diagonals of a rectangle.

Identify the initial amount a and the growth factor b in the exponential function. a(x)=680*4.3^x