Carpet costs $21.95 per square yard and the padding to put under it costs $2.55 per square yard. Felix plans to install padding and carpet in the region shown in the figure. What is the total cost of the carpet and padding needed to exactly cover the room?

$1679.175 or $1679.18

Step-by-step explanation:

split the carpet into rectangles to make it easier to look at

one rectangle is 2 yards in height and 9 yards in width (5 yards plus 4 yards)

area of a rectangle = (w)(h), so 9 x 2 = 18 yards in area.

second triangle is 4 yards in width, and 3 yards in height.

area of a rectangle = (w)(h), so 4 x 3 = 12 yards in area.

Total area = 30 yards

30(21.95)(2.55) = $1679.175 or $1679.18

(0,-3) see attached graph

step-by-step explanation:

a. to solve the system, graph the two equations.

x = y+3 becomes y=x-3 has m=1/1 and b=-3. start at (0,-3) on the y-axis and plot a point. then move up 1 unit and 1 unit to the right. plot a point and connect.

y=-4x+3 has m =-4/1 and b=-3. start at (0,-3) on the y-axis and plot a point. then move down four units and to the right 1 unit. plot a point and connect.

the solution is the point (x,y) where the two lines intersect. by the graph below it is (0,-3).

b. to solve by substitution, substitute y = -4x-3 into x= y+3

x= (-4x-3) +3

x=-4x

5x=0

x=0

now substitute x = 0 back in to find y.

y= -4(0)-3

y=0-3

y=-3

solution is (0,-3)

c. use elimination by adding the equations together.

x-y=3

4x+y=-3

5x=0

x=0

then substitute into one equation to find y.

y=-4(0)-3

y=-3

answer: '

the distance between points l and m

step-by-step explanation: