The shelf in a cabinet is set into a notch at a height of 12 inches. So that the shelf can be adjusted to different heights, the cabinetmaker cuts notches at one-inch intervals above and below the shelf. Write and solve an absolute-value equation for the maximum and minimum heights of a shelf set two notches above or below the 12-inch height.

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

Last month, a 770 g box of cereal was sold at a grocery store for $3.10. however, this month, the cereal manufacturer launched the same cereal in a 640 g box, which is being sold at $2.50. what is the percent change in the unit price?

Which value of m will create a system of parallel lines with no solution? y = mx - 6 8x - 4y = 12