The cost that a carpet cleaning company charges is directly proportional to the number for rooms cleaned. The cost is 32$ for each room. How many rooms can a hotel pay to clean for 500$ write and solve an equation

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

In each diagram, line p is parallel to line f, and line t intersects lines p and f. based on the diagram, what is the value of x? ( provide explanation)

Look at this system of equations. -3x + 3y = 12 y = x + 4 the solution set of this system is best explained by which of these statements? a) the graphs of the equations are the same line because the equations have the same slope and the same y-intercept. the system has infinitely many solutions. b) the graphs of the equations are parallel lines because they have the same slope but different y-intercepts. the system has no solution. c) the graphs of the equations are lines that intersect at one point because the equations have the same slope but different y-intercepts. the system has exactly one solution. d) the graphs of the equations are lines that intersect at one point because the equations have the same slope and the same y-intercept. the system has exactly one solution.