A community theater uses the function \small p\left(d\right)=-4d^2+200d-100 to model the profit (in dollars) expected in a weekend when the tickets to a comedy show are priced at \small 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. Explain your reasoning.

Answers

Answer 1

Answer:

10 or 40

Step-by-step explanation:

We have the following equation

-4d²+200d-100= 1500

We want all the non zero on one side and so we subtract 1500

-4d²+200d-1600=0

Solve for d

4( -d²+50d-400)=0

factor (I can explain this part in depth if needed)

4(d-40)(d-10)=0

d=40

d=10

This means that the price either needs to be 40 or 10 dollars

Answer 2

The prices at which the theater would earn $1,500 in profit from the comedy show each weekend are $10 and $40 both.

How to evaluate a given mathematical expression with variables if values of the variables are known?

You can simply replace those variables with the value you know of them and then operate on those values to get a final value. This is the result of that expression at those values of the considered variables.

For this case, the profit function is specified as:

[tex]\small p\left(d\right)=-4d^2+200d-100[/tex]

where d denotes the price of each ticket of the theater.

We need such value of d, for which the profit evaluates to $1500

Since output of the expression is denoted by p(d), putting p(d) = 1500 gives us:

[tex]1500=p(d)\\1500=-4d^2+200d-100\\4d^2 - 200d + 1600 = 0\\d^2 -50d + 400 = 0\\d^2 - 40d - 10d + 400 = 0\\d(d-40) -10(d-40) = 0\\(d-10)(d-40) = 0\\\\[/tex]

This comes as 0 either because of (d-10) =0 or (d-40)=0 or both which means d =10 or d = 40 or both.

Checking both values of d and seeing if profit comes out at 1500, we get:

Case 1: d = 10:

[tex]\small p\left(d\right)=-4d^2+200d-100\\p(10) = -4(10^2) + 200\times 10- 100\\p(10) = -400 + 2000 - 100 = 1500[/tex] (in dollars)

Case 2: d=40:

[tex]\small p\left(d\right)=-4d^2+200d-100\\p(40) = -4(40)^2 + 200 \times 40 - 100\\p(40) = -6400 + 8000 - 100\\p(40) = 1500[/tex]

Thus, both prices of the ticket (as of $10 for each ticket and of $40 for each ticket) makes the theater earn $1500 as profit. (well since profits are same, keeping price at $10 would be good for general conditions)

Learn more about solving quadratic equations here:

https://brainly.com/question/26675692


Related Questions

if 36 is exactly divisible by a then the gcd of 36 and is​

Answers

Here it shows you how to do it

The value of  Greatest common divisor of 36 and a is a.

Here, 36 is exactly divisible by a.

What is Greatest common divisor?

The Greatest common divisor of two or more integers, which is not all zero, is the largest positive integer that divides each of integers.

Now, LCM of 36 and a;

36 = 2 x 2 x 3 x 3

a = 1 x a

Since, a divide 36 then the possible value of a are 2, 3, 4

⇒ gcd of 36 and possible value of a is given as;

⇒2, 3, 4

Clearly,

Greatest common divisor of 36 and a = a

Hence, The value of Greatest common divisor of 36 and a is a.

Learn more about the Greatest common divisor visit:

https://brainly.in/question/2692886

#SPJ6

Plssssssssssz help I need the answers plsssss

Answers

About 1.3 pers second
1.3 times 60 is 78. So about 78 yards per minute.

Box A has 2 rectangles with base 10 inches and height 4 inches. It has 2 rectangles with base 10 inches and height 3 inches. It has 2 rectangles with base 3 inches and height 4 inches. Box B has 2 rectangles with base 6 inches and height 5 inches. A rectangle with base 6 inches and height 8 inches. 2 triangles with base 8 inches and height 3 inches.

A shipping company is designing new cardboard packages to sell to customers. The options are a rectangular prism, Box A, or a triangular prism, Box B.

Which box is made with less cardboard?

PLS HELP I WILL GIVE BRAINLYEST

Answers

Answer:

Box A

Step-by-step explanation:

(-12)+(-18)+(-30) simplify this question​

Answers

Answer:

-60

Step-by-step explanation:

Well just follow the equation from left to right

Add it all up.

(+) + (-) = -

-12-18-30

-30-30

-60 is your answer

Hope this helped

what is 2/3 ÷ 4/5

2/3
5/6
1 1/5
3 1/3​

Answers

Answer:

5/6

Step-by-step explanation:

mental math

What is the expression for the perimeter of this rectangle.

Answers

Answer: y^2 -5 + y^2 -5 + 3y^2+7y+8 + 3y^2+7y+8

Step-by-step explanation: The order doesn't matter but... its just the sides added up together. Its a rectangle so the opposites are equal. You were given 2 sides and thats all you need, just repeat it. L plus l plus w plus w is there.

Answer:

P= 8y^2+14y+6

Step-by-step explanation:

Multiply the given expressions by 2.

Then add your two products together.

Based on the slopes of the side of the quadrilateral. Is this shape a trapezoid?​

Answers

the slopes of the sides do not matter. It's the fact that AD and BC are parallel and AB and DC are NOT parallel that determines it to be a trapezoid.

Answer:

Yes

Step-by-step explanation:

I believe it would be :) sorry if it's wrong I'm just a 8th grader

A stock is currently selling for $50.00 per share and it pays a dividend of $2.00 a share per year then the dividend yield is what percent?

Answers

Answer:

4%

Step-by-step explanation:

Calculation to determine what the dividend yield percent is

Using this formula

Dividend yield=Annual Dividend per share ÷Current stock price per share

Let plug in the formula

Dividend yield=$2.00/$50.00

Dividend yield=0.04*100

Dividend yield=4%

Therefore the dividend yield percent is 4%

The area please I’m so confused

Answers

LxWxH is the formula for area!

Xochitl bought 5 shirts all for the same price.
After using a coupon that took $10 off the
total price, her total before tax was $35. What
was the cost of each shirt?

Answers

Answer:

Each shirt costed 9 dollars.

Step-by-step explanation:

35+10=45 (initial price)

45/5=9 dollars per shirt

Consider the expression.

– (x + 3) – 2(4x – 3)

Which procedure correctly simplifies the expression?

A.
Step 1: –x + 3 – 8x + 6

Step 2: –9x + 9

B.
Step 1: –x – 3 – 8x – 3

Step 2: –9x – 6

C.
Step 1: –x – 3 – 8x – 6

Step 2: –9x – 6

D.
Step 1: –x – 3 – 8x + 6

Step 2: –9x + 3

Answers

Answer:

D

Step-by-step explanation:

Given

- (x + 3) - 2(4x - 3) ← distribute both parenthesis

step 1

= - x - 3 - 8x + 6 ← collect like terms

step 2

= - 9x + 3

what is the measure of QRS in this diagram?
A. 48
B. 42
C. 47
D. 41
don’t have much time help needed

Answers

Answer:

the answer is d 41

Step-by-step explanation:

What is the two ratios equivalent to 7/8

Answers

from 7/8 = 35/40, 35 is the answer. 7/8 and 35/40 are equivalent fractions.

Use algebra to find the measure of the angles in the pair of complementary angles below. Show your work.

Answers

Answer:

18 and 72

Step-by-step explanation:

4x+x=90

5x=90

divided by 5

x=18

for the first side, since you only have x, you put 18

for the second one, since 4x, 4(18)=72

hope this helps!

suppose f(x)=x^2 -8 evaluate f(2)-f(3)​

Answers

Answer:

f(2)= -4 f(3)= 1

Step-by-step explanation:

Giving brainlist to whoever answers

Answers

The answer would be X=28

A shirt sale for 10$ after discount 20% find the original price

Answers

Answer:

$12.50

Step-by-step explanation:

100%-20% -> $10

80% -> $10

100% -> [tex]\frac{100}{80}[/tex] × $10 = $12.50

Answer:

The original price was $12

30 POINTS !!

Which dimensions can create only one unique triangle?

three angles measuring 75 degrees, 45 degrees, and 50 degrees

three sides measuring 14 m, 11 m, and 18 m

three angles measuring 40 degrees, 50 degrees, and 60 degrees

three sides measuring 3 cm, 4 cm, and 8 cm



What is the circumference of the circle? Use StartFraction 22 over 7 EndFraction for Pi.


A circle with radius 21 centimeters.

44 cm

66 cm

132 cm

154 cm



Figure FGHJ is shown below.

Figure F G H J has 4 sides. Sides F J and G H are congruent and parallel, and sides G F and H J are congruent and parallel. Angles G and J are 130 degrees.


Which names accurately describe figure FGHJ? Select two options.

parallelogram

quadrilateral

rectangle

rhombus

trapezoid

Answers

Answer:

1. 14m, 11, 18m

2. 132 (rounded from 131.946)

3. Quadrilateral (duh it has 4 sides) and a rhombus?

Step-by-step explanation:

1 a unique triangle is a triangle with side lengths that are ALMOST exactly like a triangle. I used the pyragothem theory (a^2 + b^2 equals c^2) and this one was soo close to 18 (17.8)

2 the equation for the circumference of a circle is C=dpi. the radius is half of the diameter so 21 time 2 is 42 then multi[ply by pi.

3 is definitely already a quadrilateral (all of them have 4 sides) and the only shade i can think of that can have a 130 degrees for 2 angles would be a longgg rhombus ( or diamond)

2/5y + 1/2y = ???
help please.

Answers

Answer:

9/10y

Step-by-step explanation:

Somewhat inconclusive hope this helps!

Answer:

[tex]\frac{9}{10} y[/tex]

Step-by-step explanation:

[tex]\frac{2}{5}y +\frac{1}{2} y\\\\\frac{4}{10}y +\frac{5}{10} y\\\\\frac{9}{10} y[/tex]

Melanie is designing a new board game, and is trying to figure out all the possible
outcomes. How many different possible outcomes are there if she spins a spinner
with three equal-sized sections labeled Walk, Run, Stop and spins a spinner with four
equal-sized sections labeled Red, Green, Blue, Orange?

Answers

Answer:

12 possible outcomes

Step-by-step explanation:

If she's spinning them at the same time, this is how you do it:

There are 3 possible outcomes on the first spinner- Walk, Run, and Stop.

There are 4 outcomes on the second spinner- Red, Green, Blue, and Orange.

Since they're being spun at the same time, we need to consider all of the possible combinations, for example:

Walk & Red.

Walk & Green.

Walk & Blue.

Walk & Orange.

And so on.  Each outcome on the first gets multiplied by 4, since there are 4 sections on the 2nd spinner.  Same thing if you did it and switched- the 4 sections on the second spinner would each have 3 different outcomes.

In conclusion, you'd just multiply 3×4, and there you go.  Or, you can think of it as 4+4+4, if that's a little easier to understand.

BRAINIEST TO WHIVER RIGHT HELP

Answers

The least value is the smallest number in a set. So in this case it would be 3 since the first marker marks 3 on the box plot.

A window washer cleaned 32 windows in 2 hours at this rate how many windows did he clean in 6 hours?

Answers

Answer:

96 windows

Step-by-step explanation:

[tex]\frac{32}{2} =\frac{x}{6} \\\\2x=192\\x=96[/tex]

Answer:

96

Step-by-step explanation:

ANyone know the answer to this???

Answers

Answer:

Step-by-step explanation:

i) the solutions are the two x-intercepts, where y = 0.  

One such intercept is (-1/4, 0) and the other is at (5/4, 0).  In other words, the solutions are x = -1/4 and x = 5/4.

ii) To solve this, we draw a line through y = 2 and determine the x values at which the graph crosses this line.  

They are x = -1 and x = 3.

Can anyone help me with this math problem plss?

Answers

Answer:

14/24 ( simplified = 7/12)

Step-by-step explanation:

to find this we multiply the fractions 2/3 and 7/8

7/8 x 2/3 = 14/24

So Shannon ate 14/24 lb

You can simplify to = 7/12

Geometry help please. What is the perimeter of the larger square?

Answers

Answer:

Step-by-step explanation:

ratio of sides=8/3

perimeter of larger square=8/3 ×12=32 mm

Find/solve for x in the image above

Answers

Answer:

Step-by-step explanation:

Simply we know this is an isosceles triangle meaning that:

The other angle is also 35.

With this information, we can say that as a triangle adds up to 180, we can put this in a formula:

x+35+35 = 180

x+70 = 180

x = 110

12 in
9 in
What is the surface area of the triangular
prism shown?
10 in
576 in2
540 in 2
468 in2
700 in 2

Answers

5 thousand with alot of zeros

Determinar el espacio muestral de los siguientes experimentos aleatorio a) lanzar tres monedas simultaneas.

Answers

Answer:

asi

Step-by-stepnasi

asiwe sfefo :V

how do you write an equation for the graph of y=cos x translated up 2 units and left pi units

Answers

The answer is:

y = cos(x - pi) + 2

Step-by-step explanation:

how do you write an equation for the graph of y=cos x translated up 2 units and left pi units

Felicia got a designer job with a company that pay $55,000/year. What is Felicia's gross monthly income

Answers

*☆*――*☆*――*☆*――*☆*――*☆*――*☆*――*☆*――*☆**☆*――*☆*――*☆*――*☆

Answer: 4583.33$

Explanation:

55000 / 12

I hope this helped!

<!> Brainliest is appreciated! <!>

- Zack Slocum

*☆*――*☆*――*☆*――*☆*――*☆*――*☆*――*☆*――*☆**☆*――*☆*――*☆*――*☆

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