The space between each rail on a deck is 3/4 of a foot. If the carpenter wants there to be 1/2 of a foot less space between each rail, what will the new spacing be?

Graph red beads cost $1 an ounce and gold beads cost $3 an ounce. juanita wants to purchase a 12-ounce mixture of red and gold beads that she can sell for $2 an ounce. the solution of the system shows the number of beads needed for juanita to break even. x + y = 12, x + 3y = 24 how many ounces of red beads will juanita buy to break even? how many ounces of gold beads will she buy?

Find the area of the region that is inside r=3cos(theta) and outside r=2-cos(theta). sketch the curves.

Given the median qr and trapezoid mnpo what is the value of x?