A small company manufactures a certain item and sells it online. The company has a business model where the cost C, in dollars, to make x items is given by the equation C = 20/3x + 50band the revenue R, in dollars, made by selling x items is given by the equation R = 10x . The break-even point is the point where the cost and revenue equations intersect.

Graph the cost and revenue equations on the xy-coordinate plane provided. Select the "Line" tool. Plot two points, then a line will connect the points.

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  see attached

Step-by-step explanation:

The break-even point is on both curves. The y-intercept can be used for the other point in each case.

The break-even point is where cost and revenue are the same:

  20/3x +50 = 10x

  50 = 10/3x . . . . . . . . subtract 20/3x

  15 = x . . . . . multiply by 3/10

  r = c = 10(15) = 150 . . . . for x = 10

Two points you can use for graphing the lines are ...

  cost: (0, 50) and (15, 150)

  revenue: (0, 0) and (15, 150)

(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:

3 bags of apples and 2 bags of oranges.

step-by-step explanation: