A community theater uses the function p(d)=−4d2+200d−100 to model the profit (in dollars) expected in a weekend when the tickets to a comedy show are priced at d dollars each. Write and solve an equation to find out the prices at which the theater would earn $1,500 in profit from the comedy show each weekend. Show your reasoning. At what price would the theater make the maximum profit, and what is that maximum profit. Show your reasoning.

price = $25

maximum profit is $2400

Step-by-step explanation:

Given the function modeled by the community theatre as

p(d)=−4d^2+200d−100

The maximum profit will be ,ade at dP/dd = 0

dP/dd = -8d + 200

0 = -8d + 200

8d = 200

d = 200/8

d = 25

hence he theatre will make maximum profit at a price of $25

Substitute d = 25 to get the maximum profit

p(25)=−4(25)^2+200(25)−100

p(25) = -2500+5000-100

p(25) = 2400

Hence the maximum profit is $2400

dalila is incorrect. the whisker on the left is very long, going all the way out to 5. the whisker goes from 5 to 30, so it has a spread of 25. the rest of the box plot values are closer together, so 5 is an outlier

a.   we have two

lines:   y = 4-x   and  

y = 8-x^-1

given two simultaneous equations that are both to be

true, then the solution is the points where the lines cross. the intersection is

where the two equations are equal. therefore the solution that works for both

equations is when

4-x = 8-x^-1

this is where the two lines will cross and that is the

common point that satisfies both equations.

b.   4-x = 8-x^-1

  x           4-x       8-x^-1

-3           7        

8.33

-2           6         8.5

-1           5         9

  0           4        

-

  1           3        

7

  2           2        

7.5

  3           1         7.67

the table shows that none of the x values from -3 to 3 is

the solution because in no case does

4-x = 8-x^-1

to find the solution we need to rearrange the equation to

find for x:

4-x = 8-x^-1

multiply both sides with x:

4x-x^2 = 8x-1

x^2+4x-1=0

x= -4.236, 0.236

therefore there are two points that satisfies the

equation.

find y:  

x=-4.236

y = 4-x   = 4 – (-4.236)

= 8.236

y = 8-x^-1 =   .236)^-1

= 8.236

x=0.236

  y = 4-x   = 4 – (0.236) = 3.764

y = 8-x^-1 =   8-(0.236)^-1

= 3.764

thus the two lines cross at 2 points:

(-4.236, 8.236) & (0.236, 3.764)

c.   to solve

graphically the equation 4-x = 8-x^-1

we would graph both lines: y = 4-x   and   y

= 8-x^-1

the point on the graph where the lines cross is the

solution to the system of equations.

just graph the points on part b on a cartesian coordinate

system and extend the two lines.   the

solution is, as stated, the point where the two lines cross on the graph.

step-by-step explanation:

mark brainliest!