10. What are the break-even points of the profit function (the values of x where profit equals 0)? Use the quadratic formula. (4 points: 2 points for each x-value)

r = 50000

P (r) = 0.7r - 35000

Step-by-step explanation:

Given cost function is

C (r) = 0.85r + 35000

and revenue function is

R (r) = 1.55r

At break even point, revenue is equal to cost

R(x)= C(x)

1.55r = 0.85r+35000

Subtract 0.85 from both sides

0.7r = 35000

divide by 0.7 on both sides

r = 50000

Profit function

P(x)= R(x)- C(x)

P(r) = 1.55r - (0.85r+35000)

P(r) = 1.55r - 0.85r - 35000

P(r) = 0.7r - 35000

solution:

the given function is ,

      =

the three roots of this quadratic function is , 0 ,8 and 10.all the roots are real and rational.

if a quadratic equation is of the form ,

sum of the roots = a + b +c= 0+8+10=18=  

product of roots taken two at a time = a b + b c+ c a = 0+80+0=80 =  

product of roots = a b c = 0=  

there are 11 doors in a hall starting from 0 to 11.the entry in the hall is permitted through gate number 0 and exit is allowed through only gate number 8 and 10.so, three roots(0,8,10) of quadratic function is given by entry and exit route of this hall.

when rotating a figure 180 degrees, imagine that you are able to take the figure and turn it clockwise or counterclockwise around a center point. to rotate a figure 180 degrees, you will need to apply the rule (x, y) → (-x, -y). start by using a coordinate grid with coordinates for each vertex of the figure. the center point of the coordinate grid is located at (0, 0), which is what you will rotate the figure around. write down the original coordinates of the shape you are going to rotate. then, apply the rule. for example, coordinate (1, 2) becomes (-1, -2). another example would be, coordinate (-4, -2) becoming (4, 2). after you change each original coordinate to the rotated coordinate, you will draw your new figure.

step-by-step explanation: