Abackyard is 40.5 feet long and 25 feet wide. in order to install a pool, the yard needs to be reduced by a scale of 1/3. what is the area of the reduced yard?

The area of the reduced backyard is 112.5 square feet

Step-by-step explanation:

The initial length of the backyard is 40.5 feet long.

The initial width of the backyard is 25 feet wide.

In order to install a pool, the yard needs to be reduced by a scale of 1/3. This means that the new length of the backyard is would be

40.5 × 1/3 = 40.5/3 feet lonng

The new width of the backyard would be

25 × 1/3 = 25/3 feet wide

The backyard is rectangular in shape. Area of a rectangle is length × width. The area of the reduced backyard becomes

40.5/3 × 25/3 = 1012.5/9 = 112.5 square feet

112.5 square feet... edg2020

(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