1. Suppose that a theater charges a school group $4.50 per student to show a special film. Suppose that the theater's operating expenses include $130 for the staff and a film rental fee of $1.25 per student.

a. What equation relates the number of students x to the theater's income I?

b. What equation relates the theater's operating expenses E to the number of students x?

c. Copy and complete the table below.

Theater Income and Expenses
Number of Students, x 0 10 20 30 40 50 60 70
Income, I ($) box box box box box box box box
Expenses, E ($) box box box box box box box box
d. On the same set of axes, graph the theater's income and operating expenses for any number of students from 0 to 100.

e. Describe the patterns by which income and operating expenses increase as the number of students in a group increases.

f. Write and solve an equation that you can use to answer the question “How many students need to attend the movie so that the theater's income will equal its operating expenses?”

g. Write an equation that represents the theater's profit. Compare your equation to those your classmates wrote.

h. Find the number of students that make each of the following inequality statements true.

i. E < 255

ii. I > 675

Answers

Answer 1

The functions I(x) and E(x) of the theatre's income and expenses are illustrations of linear functions.

The equation of the theatre's income

The theatre charges $4.50 per student.

Assume the number of students is x, the equation of the theatre's income would be:

I(x) = 4.5x

The equation of the theatre's expenses

The theatre expense per student is $1.25, and the operating cost on the staff is $130

The equation of the theatre's expenses would be:

E(x) = 1.25x + 130

Complete the table

Using the formulas I(x) = 4.5x and E(x) = 1.25x + 130, the complete table is:

Students, x  0       10        20     30      40      50      60    70

Income, I      0      45        90     135     180    225    270   315

Expenses, E 130  142.5   155    167.5   180   192.5   205  217.5

The graph of the theatre's income and expenses

See attachment

The pattern by which theatre's income and expenses increase

The functions I(x) and E(x) are linear functions.

So, the pattern with which the functions increase is a linear pattern.

The number of students when the theatre's income and expenses are equal

This means that:

I(x) = E(x)

So, we have:

4.5x = 1.25x + 130

Subtract 1.25 from both sides

3.25x = 130

Divide both sides by 3.25

x = 40

Hence, the number of students is 40

The theatre profit

This is the difference between the theatre expenses and their income.

So, we have:

P(x) = E(x) - I(x)

This gives

P(x) = 1.25x + 130 - 4.5x

Simplify

P(x) = 130 - 3.25x

Solution to the inequalities

We have:

E(x) < 255

This gives

1.25x + 130 < 255

Subtract 130 from both sides and divide by 1.25

x < 100 students

Also, we have:

I(x) > 675

This gives

4.5x > 657

Solve for x

x > 146 students

Hence, the number of students for the inequalities are less than 100 and greater than 146

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1. Suppose That A Theater Charges A School Group $4.50 Per Student To Show A Special Film. Suppose That

Related Questions

please help i am confused.

Answers

Answer:

12.16 inches.

Step-by-step explanation:

Use pythagoras thereom since they are right angle triangles. A² = c² - b².

For NP triangle:

10² - 4² = 84. square root of 84 is 9.165.

For MN triangle:

5² - 4² = 9. square root of 9 is 3.

finally, add them up:

3 + 9.165 = 12.165, to 2 d.p., it is 12.16 inches.

Sam has a cylindrical storage container 7 inches tall with a radius of 5 inches. How much cat litter will fit in the container? Round your answer to the nearest tenth.

Answers

Answer:

549.8 inches³

Step-by-step explanation:

Volume of Cylinder = height × base, where base = [tex]\pi[/tex]r².

The radius (r) is given, 5 inches, and so is the height, 7 inches.

We simply substitute these values into the equation.

V(volume)  = 7 × [tex]\pi[/tex] × 5²

                  = 175[tex]\pi[/tex]

                  = 549.77871437821...

when we round that to the nearest tenth,

                  ≈ 549. 8

Eliminate the parameter to complete the statements describing the equations
x = 3cos(t) - 2 and y = 2sin(t) + 1.
The rectangular form of this equation is
A. 4(x + 2)2 + 9(y – 1)2 = 36
B. 9(x + 2)2 + 4(y - 1)2 = 36
C. 4(x - 2)2 + 9(y + 1)2 = 36
D. 9(x - 2)2 + 4(y + 1)2 = 36
The equations represent a/an

Answers

Answer:

A

ellipse

Step-by-step explanation:

Answer:

1.) The rectangular form of this equation is (A)

.2.) The equations represent a/an (ellipse)

.

Step-by-step explanation:

Edge 2022

The graph of g is a translation 2 units left of the graph of f(x) = x−−√x. What is the domain of g? A. all real numbers B. x ≥ −2 C. x ≥ 0 D. x ≥ 2

Answers

y=x√x

4 units left means change in x

y=x√x+2

So

Solve for domain

x+2≥0x≥-2

Domain=[-2,oo)

Option A

The domain of g is x ≥ -2, which is option B.

What is Translation?

Translation is a type of transformation of geometrical figures. After translation, the original figure is shifted from a place to another place without affecting it's size.

Given that,

the graph of g is a translation 2 units left of the graph of f(x) = x√x.

When f(x) is translated k units to the left, the new function will be f(x + k).

So the new function g is,

g(x) = (x + 2) √(x + 2)

In order for the function to be defined, the part inside the square root must be greater than or equal to 0.

x + 2 ≥ 0

x ≥ -2

Hence the domain is x ≥ -2.

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How many different triangles can you make if you are given the measurments or two sides an angle that is not between those two sides

Answers

Answer:

2.

Step-by-step explanation:

This is called the ambibuous case where  2 sides are given and angle opposite one of these sides.

2 traingles are possible.

solve: 15x = 180.75
please and thanks

Answers

Answer:

x = 12.05

Step-by-step explanation:

Given:

15x=180.75

Divide both sides by 15

15x             180.75

------  =         --------

15                   15

x = 12.05

Hence, x = 12.05

~lenvy~

Answer:

12.05

Step-by-step explanation:

Divide both sides by the same term

15x/15 = 180.75/15

180.75/15

= 12.05

Hence, x = 12.05

Check Answer:

15(12.05) = 180.75

[RevyBreeze]

3a+2(4a-b)
please simplify this equation with processing

Answers

[tex]\bf \colorbox{black} {\bf {\textcolor{blue}{topic= }{ \bf { \textcolor{orange}{mathematics= }{ \bf{ \textcolor{cyan}{answer = }}}}}}}[/tex]

3a+2(4a-b)=

3a+8a-2b=

[tex] \bf \textcolor{green}{ \underbrace{11a - 2b}}[/tex]

xLasersx✨

How much money would you have after 7 years if you invested$12,000 at 2% in order to have compounded annually?

Answers

Answer:

$1,680

Step-by-step explanation:

i think it is right because 12,000 at 2 percent=280 then 280×7= 1,680

Damian needs to buy 5 pints of juice but the store doesn't sell juice in pints, so damian buys 3 quarts of juice. does damian buy enough juice if not how much more does he have left or need to have enough?

Answers

Answer:

Damain has bought enough juice.

Step-by-step explanation:

1 qt(quart) = 2 pints.

3 qt = 6 pints.

6 pints > 5 pints (6 pints is bigger than 5 pints)

Therefore, Damain has bought enough juice.

Please mark as brainliest!

4x^2 - y^2 - 2x- y

Factorise each of the following expressions completely

Answers

Answer:

(2x + y)(2x - y - 1)

Step-by-step explanation:

4x² - y² - 2x - y

4x² - y² is a difference of squares and factors in general as

a² - b² = (a - b)(a + b) , then

4x² - y²

= (2x)² - y²

= (2x - y)(2x + y)

expression is now

(2x - y)(2x + y) - (2x + y) ← factor out (2x + y) from each term

= (2x + y)(2x - y - 1)

Help me understand how to do this please. (?)

Answers

Step-by-step explanation:

part 1: the exponent is the power or the number you see ontop of n. it indicates how many times n is multiplied by itself. so for the first question n is multiplied by itself 6 times. so the answer should be n×n×n×n×n×n.

part 2 is similar to part 1.

since there is a total of 6 ns we can say that it is n^6.

feel free to ask if you need any further guidance.

HELLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLO

Answers

Answer:

hi

Step-by-step explanation:

what is pi and why do we need it

Answers

pi or 3.14 is known as the ratio between a circle’s circumference and diameter.

Answer:

Pi is used to find the area and circumference of a circle. Pi can be used to find an area by multiplying the radius of the circle squared times pi.


Step-by-step explanation:

Have a great rest of your day

#TheWizzer

What is the area of the polygon given below?

Answers

Answer:

C. 120 square units

Step-by-step explanation:

Easy just divide this into 2 shapes.

The area of a rectangle is lenght Times Width.

2 Rectangles. So the One on the left would be

5X12=60 is the area of the first one.

The Second rectangle is

6X10=60

Both rectangles have the same area.

Now just add up both areas

60+60= 120 square units

SonicIsCoool, if you need more help I'm at your service

:)

Answer:

C. 120 units² or square units

Step-by-step explanation:

View the attached picture

Hope it helps!

Identify the key characteristics of the exponential function.
y =
2(1)"

Answers

Answer:

2x1 mabe

Step-by-step explanation:

im just doing that because they are next to eatch other but im in 6 grade so if i get it wrong dont blame me

A parabola has a vertex at (0,0). The equation for the directrix of the parabola is x = –4. In which direction does the parabola open? up down right left.

Answers

The parabola with vertex at (0,0) and directrix at x=-4, will open towards the right.

What is a directrix?

A parabola is a collection of points on a plane that are all at the same distance from a particular point and line. The point is called the focus of the parabola while the line is called the directrix. The directrix is perpendicular to a parabola's axis of symmetry and does not contact it.

As we know that the directrix is perpendicular to the axis of the parabola, now since the directrix is at x=-4, the parabola will be horizontal and will be opening either towards the left or the right.

As it is given that the vertex of the parabola is at (0,0) and we know that the parabola can not touch the directrix, therefore, the parabola's vertex will be at (0,0) and will open towards the right side. As shown below.

Hence, the parabola with vertex at (0,0) and directrix at x=-4, will open towards the right.

Learn more about Directrix:

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Answer:

right

Step-by-step explanation:

Step by Step solution please.
Thanks

Answers

Derivation of f(x):

   [tex]f'(x) = \frac{g(x)*8x-4x^2*g'(x)}{(g(x))^2} -\frac{1}{x+2}[/tex]

    Since g(3) = 6 and g'(3) = 3

   [tex]f'(3) = \frac{g(3)*8*3-4(3)^2*g'(3)}{(g(3))^2} -\frac{1}{3+2} \\f'(3) = \frac{6*8*3-4*9*3}{36} -\frac{1}{5} \\f'(3) = \frac{36}{36} -\frac{1}{5} =1-\frac{1}{5} =\frac{4}{5}\\ f'(3) = 0.8[/tex]

Thus f'(3) = 0.8

Hope that helps!

A couple of identities I used in derivation:

[tex]\frac{d}{dx} (ln x) = \frac{1}{x}[/tex]

Which statement is true about the transformation?

It is isometric because not all side lengths and angle measures remained the same.
It is isometric because all side lengths and angle measures remained the same.
It is not isometric because not all side lengths and angle measures remained the same.
It is not isometric because all side lengths and angle measures remained the same.

Answers

Answer:

B. It is isometric because all side lengths and angle measures remained the same

Step-by-step explanation:

Answer:

B) It is isometric because all side lengths and angle measures remained the same.

Step-by-step explanation:

Got it right on edge <3

Solve for k.

Give an exact answer.

2.5(4k+2)=12k2.5(4k+2)=12k

Answers

Answer:

The answer would be k=5/2

Step-by-step explanation:

2.5 (4k+2)12k <- distribute the 2.5 into the parentheses  

10k+5=12k <- take the parentheses out of the equation

10k-12k= -5 <- Move the like terms to one side and change the sign

-2k= -5 <- Collect the like terms & divide by -2 on both sides of the equation

k=5/2 <- Answer at the end

Elena drives for 3 hours at 44mph claire drives 144miles in 4 hours how far would elena travel if she drove for 3hours at the same speed as claire?

Answers

Answer:

108 miles

Step-by-step explanation:

144m/4h = 36m/1h or 36mph

36mph · 3 = 108m

10 A grocery store bought 1,600 cans of
vegetables in different sizes. Of the cans,
25% contained less than 400 grams of
vegetables, 15% contained between 400
and 500 grams of vegetables, and the
rest contained more than 500 grams of
vegetables.
How many cans contained more than 500
grams of vegetables?
F 1,120
H 640
G 800
J 960

Answers

Answer:

1020 cans

Step-by-step explanation:

100-25

=75%

0.75x1600

1200cans

100-15

=85%

0.85x1200

=1020 cans

A tank that is 20% full contains 125 gallons of water. How many gallons would be needed to fill the entire tank? How many gallons are there if thetank was 30% full? What percent of the tabk is full if tgerd are 500 gallons? ​

Answers

Answer:

625

Step-by-step explanation:

becuase 20% is equivilant to 1/5 you need to multiply by 5 to get 1t or full.

part b: 187.5

part c: 125 gallons is 25%. this is because you can fit 4 of it into one 500 gallon tank

Answer:

625 gal, 187.5 gal, 80%

Step-by-step explanation:

[tex]\frac{125}{x}[/tex]=[tex]\frac{20}{100}[/tex] 125*100/20=625

[tex]\frac{x}{625}=\frac{30}{100}[/tex] 30*625/100=187.5 or 625*.3=187.5

[tex]\frac{500}{625}=\frac{x}{100}[/tex] 500*100/625=80

Visible light waves that our eyes see as the color red have a wavelength of about 6.7 x 10-7 meters. What is the frequency of these waves? The speed of light is 3.0 x 10 8 m/s. [v = 1f]

Answers

The frequency of these visible light waves that our eyes see is equal to [tex]4.47\times 10^{-14}\;Hz[/tex]

What is wavelength?

Wavelength refers to the distance between two (2) successive crests (troughs) of a wave.

How to calculate frequency.

Mathematically, the frequency of a wave is given by this formula:

[tex]F = \frac{V}{\lambda}[/tex]

Where:

F is the frequency of a wave.V is the speed of a wave.[tex]\lambda[/tex] is the wavelength of a wave.

Substituting the given parameters into the formula, we have;

[tex]F=\frac{3 \times 10^8}{6.7 \times 10^{-7}} \\\\F=4.47\times 10^{-14}\;Hz[/tex]

Read more on frequency here: https://brainly.com/question/19250621

reflect the shape A in the line

x=1

What are the coordinates of the vertices of the image?
its for a maths test!!!!!!!!!!!!!!!!!!!!!!!!!!
correct answers to be awarded brainley
.

Answers

i dont knowkkkkkkkkkkkkk

pls help ill give 15 brainliest and 5 starts question is down below

Answers

Answer:

1 is 9 sq units

2 is 12

3 is 24cm^2

Step-by-step explanation:

help!!

For what value of x is the value of the square of the binomial 2x +3
is 9 greater than the value of the square of the binomial 2x -3?

Answers

Answer:

  x = 3/8

Step-by-step explanation:

The difference of the two squares can be found several ways. One way uses the "difference of squares" special form.

  a² -b² = (a -b)(a +b)

For the given squares, this is ...

  (2x +3)² -(2x -3)² = ((2x +3)-(2x -3))((2x +3) +(2x -3)) = 6(4x) = 24x

We want to find x that makes this difference be 9:

  24x = 9

  x = 9/24 = 3/8

For the value x = 3/8, the difference between the squares of the binomials will be 9.

I WILL GIVE YOU BRAINLIEST PLEASE HELPPPPP

Answers

Answer: 3/2

Step-by-step explanation:

Let's consider the points (6,9) and (4,6).

The difference in the y coordinates is 3, and the diffeence in the x coordinates is 2.

So, the slope is 3/2.

Help me due in 5 mins!

Answers

In order: 6, 6, 12
1st: l x w | 3 * 2
2nd: 1/2(l x w) | 1/2(12)
3rd: 1st + 2nd | 12

how to tell if something is cubed or squared being ft^3 or ft^2

Answers

Answer:

Check the power

Step-by-step explanation:

You can tell if a quantity has been cubed or squared by looking at its power.

For example, ft^3 has a power of 3 (meaning feet is raised to 3) which means whichever number ft^3 is used with, has been cubed, generally volume of any shape

Similarly, ft^2 has a power of 2 (meaning feet is raised to 2) which means whichever number ft^2 is used with, has been squared, generally area of any shape

hello!

===========================================================

If something is squared, it's multiplied times itself 2 times.

Example:-

[tex]\bigstar\boxed{\pmb{4*4=4^2}}\longleftarrow\sf{4~squared~}[/tex]

You should also notice that the exponent of 4 is 2.

So if something is squared, its exponent is 2.

If something is cubed, it's multiplied times itself 3 times.

Example:-

[tex]\bigstar{\boxed{\pmb{4*4*4=4^3}}\longleftarrow\sf{4~cubed}[/tex]

You should also notice that the exponent of 4 is 3.

So if something is cubed, its exponent is 3.

=======================================================

note:-

Hope everything is clear; if you need any clarification/explanation, kindly let me know, and I will comment and/or edit my answer :)

WILL GIVE BRAINLIEST TO BEST ANSWER, THANKS, 5 STARS!
PLEASE HELP!!
What are the zero(s) from the function f(x)=-4x^2-16x-12
(Select all that apply)
(4,0)

(-12,0)

(-4,0)

(1,0)

(-3,0)

(-1,0)

(3,0)

Answers

Answer: (-3, 0) and (-1, 0)

Step-by-step explanation:

[tex]-4x^2-16x-12[/tex]

[tex]\mathrm{Rewrite\:}-16\mathrm{\:as\:}-4\cdot \:4[/tex]

[tex]\mathrm{Rewrite\:}-12\mathrm{\:as\:}-4\cdot \:3[/tex]

[tex]=-4x^2-4\cdot \:4x-4\cdot \:3[/tex]

[tex]\text{Factor out common term -4}[/tex]

[tex]=-4\left(x^2+4x+3\right)[/tex]

[tex]x^2+4x+3[/tex]

[tex]=\left(x^2+x\right)+\left(3x+3\right)[/tex]

[tex]=x\left(x+1\right)+3\left(x+1\right)[/tex]

[tex]\mathrm{Factor \ out \ common \ term \ x+1}[/tex]

[tex]=\left(x+1\right)\left(x+3\right)[/tex]

[tex]=-4\left(x+1\right)\left(x+3\right)[/tex]

Roots:

x + 3 = 0    and    x + 1 = 0

x = 0 - 3               x = 0 - 1

x = -3                   x = -1

Therefore, the zeroes of the function are (-3, 0) and (-1, 0)

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