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2 years ago

A photo booth’s profit as a function of users is represented in the table. The function is quadratic.

Mathematics

1 answer:

Luda [366]2 years ago

3 0

Answer:

The vertex represent the minimum amount of profit

Step-by-step explanation:

Plot the function to better understand the problem

Let

x ----> the number of users in thousands

y ---> the Monthly profit in thousands

using a graphing tool

see the attached figure

we have a vertical parabola open upward

The vertex represent a minimum

In the context of this problem

The vertex represent the minimum amount of profit

In this problem the vertex is the point (0.4,-4)

0.4 represent -----> 0.4(1,000)=400 users

-4=-4(1,000)=-$4,000 (profit negative)

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Please help! determine the measure of the missing angles. show your work.

IrinaVladis [17]

Top triangle: if the know angle measures are 90 and 55 and there are a total of 180, 90 + 55 + a = 180. This means that angle a = 35°

Bottom triangle: if a is 35, the angle connected to it is 35 because they are vertical angles. The angles of this triangle are 35 + 120 + b = 180. Angle b = 25°

5 0

3 years ago

the area of a rectangular volleyball court is 1800 square feet the courts length is twice it width write a system of equations t

Marianna [84]

Answer:

The dimensions of the rectangular volleyball court are 60 ft x 30 ft

Step-by-step explanation:

Let

x ----> the length of rectangular volleyball court

y ---> the width of the rectangular volleyball court

we know that

The area of the rectangular volleyball court is equal to

$A=xy$

$A=1,800\ ft^2$

$1,800=xy$ ----> equation A

$x=2y$ -----> equation B

substitute equation B in equation A

$1,800=(2y)y$

$1,800=2y^2$

Solve for y

Simplify

$900=y^2$

take square root both sides

$y=30\ ft$

Find the value of x

$x=2y$

substitute the value of y

$x=2(30)=60\ ft$

therefore

The dimensions of the rectangular volleyball court are 60 ft x 30 ft

7 0

3 years ago

a falling stone is at a certain instant 230 feet above the ground. 3 seconds later it is only 14 feet above. From what height wa

vazorg [7]

The falling stone is a certain instant 230 feet above the ground. 3 seconds later it is only 14 feet above. The height that it was dropped is 32 feet. The equation for the answer is;

16t2+h0=230 −16(t+3)2+h0=14

4 0

2 years ago

Read 2 more answers

An apple sells for 25 cents and a peach sells for 15 cents. A total of 10 fruits were sold for a total of $2.10. How many apples

hammer [34]

Answer:

6 apples

Step-by-step explanation:

A = 0.25

P = 0.15

----------------

A + P = 10

0.25A+0.15P=2.10

----------------

I did this: 0.25*10 = 2.50

2.50-2.10=.40

0.25-0.15=0.10

0.40/0.10 = 4 so 4 peaches

10 fruits - 4 peaches = 6 apples

5 0

2 years ago

Eben, an alien from the planet Tellurango, kicks a football from field level. The equation for the football’s height in meters,

Luden [163]

The maxima of a differential equation can be obtained by getting the 1st derivate dx/dy and equating it to 0.

Given the equation h = - 2 t^2 + 12 t , taking the 1st derivative result in:

dh = - 4 t dt + 12 dt

dh / dt = 0 = - 4 t + 12 calculating for t:

t = -12 / - 4

t = 3 s

Therefore the maximum height obtained is calculated by plugging in the value of t in the given equation.

h = -2 (3)^2 + 12 (3)

h = 18 m

This problem can also be solved graphically by plotting t (x-axis) against h (y-axis). Then assigning values to t and calculate for h and plot it in the graph to see the point in which the peak is obtained. Therefore the answer to this is:

The ball reaches a maximum height of 18 meters. The maximum of h(t) can be found both graphically or algebraically, and lies at (3,18). The x-coordinate, 3, is the time in seconds it takes the ball to reach maximum height, and the y-coordinate, 18, is the max height in meters.

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2 years ago