Community Theater Owner A community theater currently sells 200 season tickets at $50 each. In order to increase its season-ticket revenue, the theater surveys its season ticket holders to see if they would be willing to pay more. The survey finds that for every $5 increase in the price of a season ticket, the theater would lose 10 season-ticket holders. What action, if any, should the theater owner take to increase revenue? a. Let n be the number of $5 price increases in the cost of a season ticket. Write an expression for the cost of a season ticket after n price increases, and an expression for the number of season-ticket holders after n price increases. b. Use the expressions from part a to create a revenue function, R (n) , from the survey information. c. Graph the revenue function. Be sure to label the axes with the quantities they represent and indicate the axis scales by showing numbers for some grid lines.

Answer: 25

Step-by-step explanation:

Find the distance from (3, 0) to (6,4).  That is the side length (s).

Area (A) = s²

[tex]s=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}\\\\s^2=(x_2-x_1)^2+(y_2-y_1)^2\\\\s^2=(6-3)^2+(4-0)^2\\\\s^2=3^2+4^2\\\\s^2=9+16\\\\s^2=25\\\\\\A=s^2\\\\\large\boxed{A = 25}[/tex]

Answer:

25 units squared

Step-by-step explanation:

Distance between (3, 0) and (6, 4)

√(3-6)²+(0-4)² = 5

Area = 5 * 5 = 25 units squared

Answer:

Step-by-step explanation:

14. x=4

vertical line(no slope) with one coordinate being (4,0)

15. y=2

horizontal line(no slope) with one coordinate being (0,2)

16. 2x-y=5

slope= 2; two coordinates are (0,-5) and (2,-1)

17. y-1=(x+3)

slope= 1; two coordinates are (-4,0) and (0,4)

HOPE THIS HELPS!!! :)

Answer:

43

Step-by-step explanation:

(9r-5s+3^3)

Let r = 2/3  and s = -2

(9 * 2/3-5* -2+3^3)

(6+ 10+27)

43

Answer:

Step-by-step explanation:

[tex]9r - 5s + {3}^{3} [/tex]

plug the values

[tex] = 9 \times \frac{2}{3} - 5 \times ( - 2) + {3}^{3} [/tex]

Reduce the numbers with Greatest Common Factor 3

[tex] = 3 \times 2 - 5 \times ( - 2) + {3}^{3} [/tex]

Multiply the numbers

[tex] = 6 + 10 + 27[/tex]

Calculate the sum of positive numbers

[tex] = 43[/tex]

Hope I helped..

Best regards!

Answer:

b<0

Step-by-step explanation:

b(b-a)>10

-5=b and -10=a for instance plug in

-5(-5-10)>10

-5(-15)>10 (negative x negative is positive)

75>10

Answer:

22ft^2

Step-by-step explanation:

I am not sure if this is the correct answer since there were no numbers to the question you wrote out.

Answer:

$30

Step-by-step explanation:

i think i did the right math

Answer:

Hey there!

40% of 50 dollars is 20

Thus, the price of the backpack is now 50-20, or 30 dollars.

Hope this helps :)

Answer:

A = 27π

P =

Step-by-step explanation:

Well if it follows the same proportions as a square then the dotted line is 6 cm.

                                                      Triangle                                                                

So the area of a triangle is b*h / 2

b = 6

h = 6

6*6 = 36

36 / 2 = 18

A = 18cm^2

So to find the missing side or c we do 6^2 + 6^2 = c^2,

36 + 36 = c^2

72 = c^2

≅8

6 + 6 + 8

= 20cm

                                                       Half circle                                                                  

Now the area of a semicircle is,

pi r^2 / 2

So if the diameter is 6 then the radius is 3.

So we do 3*3 = 9

9 * pi = 9π^2

Perimeter: 6π

____________________________________________________________

Thus,

the area is 27π and the perimeter 26π.

Hope this helps :)

Answer:

[tex]\large \boxed{\sf \ \ \sum_{n=1}^{n=4} (5n + 2) = 58 \ \ }[/tex]

Step-by-step explanation:

Hello,

We need to compute the following:

[tex]\displaystyle \sum_{k=1}^{k=4} (5\cdot k + 2)= (5*1+2) + (5*2+2)+ (5*3+2) + (5*4+2)\\\\=7 + 12 + 17 + 22 = 19 + 39 = 58[/tex]

Hope this helps.

Do not hesitate if you need further explanation.

Thank you

Answer:

B(4,-9) D(11,-2)

Step-by-step explanation:

Example: we have a 2 by 3 rectangle with area of 2*3 = 6. If we cut the first dimension in half, then we have a 1 by 3 rectangle that has area 1*3 = 3. The area has decreased. To keep the area the same, we would have to increase the other dimension some specific amount.

The area of the figure decreases when the dimension is decreased

The area of the rectangle is given by the product of the length of the rectangle and the width of the rectangle

Area of Rectangle = Length x Width

Given data ,

Let the figure be represented as ABCD

where ABCD is a rectangle

Now , the measures of the sides of the rectangle be

The length of the rectangle = L

The width of the rectangle = W

And , Area of Rectangle = Length x Width

On simplifying , we get

Area of rectangle = LW

when the dimension of one of the unit is decreased , we get

when L = L/2

Area of rectangle = ( LW) / 2

So , the area of the figure is decreased bu ( 1/2 )

Hence , the area of the figure decreases

To learn more about area of rectangle click :

https://brainly.com/question/15225905

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Answer:

221.12 cm^3

Step-by-step explanation:

Imagine that you have the 6cm side of the prism base facing you, and that you cut the prism in half through the vertex.  Doing this will form two triangles.  The hypotenuse of the triangle is the same as the "diagonal" that is 10√2 cm.  The base of this triangle is half of the 6" side, or 3 cm.

Use the Pythagorean Theorem to determine the height (h) of the prism:

h^2 + 3^2 = (10√2)^2, or

h^2 = 200-9 = 191

Then the height is √191 cm

and the base area is 6cm times 8 cm, or 48 cm^2

and so we end up with the volume V = (1/3)(base area)(height), or

                                                           V = (1/3)(48 cm^2)(√191 cm), or

                                                                  roughly 221.12 cm^3

Answer:

y = -6x + 6

Step-by-step explanation:

To make an equation you need to find the slope first

To do that use the expression y2-y1/x2-x1 (-6)

Now plug that in to y = mx + b

Lastly you substitute any coordinate and find b

y = -6x + 6

Answer:C

Step-by-step explanation:

Answer:

The answer is 39.

Step-by-step explanation:

You have to substitute the value of x into the expression :

[tex]3x + 12[/tex]

[tex]let \: x = 9[/tex]

[tex]3(9) + 12 = 27 + 12 = 39[/tex]

Answer:

39

Step-by-step explanation:

To solve your question we must replace x with the given number which is 9 so,

3 (9) +12 =

We can now solve it by multiplying 3 * 9 which will give us 27. Then we can add 27 to 12.

27 + 12 = 39

Hope this helps!!

Answer:

156

Step-by-step explanation:

3 ml of compound A used for every 4 ml of compound B in total it's 7 ml

To calculate how many ml of A used in a 364 ml drug we can divide 364 by 7

364 ÷ 7 = 52 which means there are 52, 7 ml in the 364

since 7 ml drug contains 3 ml conpound A there is

52 × 3 = 156 of compound A in the 364 ml drug

Answer:

[tex]BC=\sqrt{73}[/tex]

Step-by-step explanation:

Notice that A, B, and C constitute the vertices of a right angle triangle, with the right angle at the vertex A.

If we count the number of squares separating B and A (one of the legs of the right angle triangle) we find 8 units.

If we count the number of squares separating C from A (the other leg of the right angle triangle), we get: 3 units.

Then, we apply the Pythagorean theorem to find that length of the triangle's hypotenuse which is the segment BC:

[tex]BC=hyp=\sqrt{8^2+3^2} =\sqrt{64+9} =\sqrt{73}[/tex]

Answer:

the answer is d 73

Step-by-step explanation:

Answer: 50,499

Step-by-step explanation:

Since you are calculating the salary after 4 years, 4 would be the value of T. you then just solve the equation, so because of PEMDAS you plug in 1.06 to the 4th and then multiply it by 40,000, resulting in 50,499.

Answer: Initial Value is 18,500. Value after 12 years is about 2,283

Step-by-step explanation:

The initial value assumes you have just bought the car, which means 0 years have passed. If zero is substituted as an exponent in ANY NUMBER, it equals 1. Therefore, the value is 18,500.

The value after 12 years can be found by substituting 12 in the space of t. Then, use a calculator to approximate the value of 0.84¹² which is equal to about 0.12. DO NOT ROUND, HOWEVER. Then, the previous value is multipled by 18,500, equalling about 2,283.

Answer:

c. x ≤ 6

Step-by-step explanation:

Well we can tell the line is solid so we can cross out answers,

b.

And it is 6 units to the right where x is less than or equal to 6.

Thus,

the answer is c. x ≤ 6.

Hope this helps :)

Answer:

C

Step-by-step explanation:

x less than or equal to 6

If there had been a dashed vertical line at 6, it would have just been less than

Answer: it will be 3.7 cuz its perpendicular

have a good day,     hey thechesguy nice name and the guy under copied from me.

Answer:

y + 4 = (x - h)^2

Step-by-step explanation:

"vertex form" is y - k = a(x - h)^2.  Here, the vertex (h, k) is (-3, -4), and so we have:  

y + 4 = a(x + 3)^2.  To find the coefficient a, substitute -1 for x and 0 for y:

0 + 4 = a(-1 + 3)^2, or

4 = a(2^2).  Thus, a = 1, and the desired equation is

y + 4 = (x - h)^2

Answer:

The answer is C.

Step-by-step explanation:

First, you have to make expressions for all the flags :

[tex]let \: blue \: flag = x[/tex]

Green flag cost 10 times the price of blue flag,

[tex]green \: flag = 10 \times x = 10x[/tex]

Red flag is half the price of green flag,

[tex]red \: flag = 10x \div 2 = 5x[/tex]

Orange is 10 dollars less than red flag,

[tex]orange \: flag = 5x - 10[/tex]

Assuming that the total cost of all 4 different coloured flags is $200. So you have to solve the value of x :

[tex]x + 10x + 5x + 5x - 10 = 200[/tex]

[tex]21x - 10 = 200[/tex]

[tex]21x = 200 + 10[/tex]

[tex]21x = 210[/tex]

[tex]x = 210 \div 21 = 10 \: dollars[/tex]

Then, you have to substitute the value of x into the expression of orange flag :

[tex]orange flag = 5x - 10[/tex]

[tex]orange flag = 5(10) - 10[/tex]

[tex]orange flag = 50 - 10[/tex]

[tex]orange flag = 40 \: dollars[/tex]

Answer:

10 cm

Step-by-step explanation:

The perimeter of a equilateral triangle is

P = 3s where s is the side length

30 = 3s

Divide each side by 3

30/3 = 3s/3

10 = s

Answer:

92°

Step-by-step explanation:

We know that [tex]\overline{QV}[/tex] is a straight line which means that we know that ∠QTU + ∠VTU = 180

11x+4+∠VTU = 180

∠VTU = 180-11x-4

∠VTU = 176-11x

Then, using the triangle inequality, we know that ∠VTU+∠TUV+∠UVT = 180

3x+14+54+176-11x=180

-8x+244=180

-8x = -64

x=8

Now we can substitute and solve for ∠UTQ

11(8)+4 = 88+4 = 92°

Answer: 92°

Step-by-step explanation:

Answer:

The second choice

Step-by-step explanation:

So first we would plug in the first term which is 2 so we would get [tex]an=2[/tex] times [tex]rn-1[/tex] so next we would see that the common ration is -3 since every time the number is being multiplied by -3. so then our equation would be [tex]an= 2[/tex] times [tex]-3n-1[/tex]. Now we would just find the choice that matches and it would be the second choice.

Answer:

option 2

Step-by-step explanation:

First term [tex]a_{1} = 2\\[/tex]

common ratio = r = second term ÷ first term

                            = -6 ÷2 = -4

Plug in the values of  [tex]a_{1}[/tex] & r in the formula

[tex]a_{n} = a_{1}*r^{n-1}\\\\\\a_{n}=2 * (-3)^{n-1}[/tex]

Answer:

45°

Step-by-step explanation:

There are sets of formulas you can refer to for different situations like this. In your case here, you need to apply the formula and solve for the unknown. My work is in the attachment.

Answer: 45 degrees

Step-by-step explanation:

This is the same as h(x) = x/4

In decimal form, it would be h(x) = 0.25x

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

Explanation:

Inverses undo the original function. The original function tells us to take any input (x) and multiply by 4 to get the output y = f(x) = 4x

To get the inverse, we reverse the operation applied here. The opposite of multiplication is division. So we'll divide by 4 instead of multiply by 4. This is why the answer is x/4 or (1/4)x

-----------

Another approach is to do the following: Replace f(x) with y. Swap x and y. Solve for y

f(x) = 4x

y = 4x

x = 4y

4y = x

y = x/4

h(x) = x/4

We end up with the same result as before.

-----------

Extra info:

For any real number x, the following two equations are true

h( f(x) ) = x

f( h(x) ) = x

Answer:

y=-3x+4

Step-by-step explanation:

Use rise/run to find slope. Rise= -3, Run= 1

Y-Intercept is found where the line intersects y.

Answer:

The slope of the line is -3.

Step-by-Step Explanation:

You need to find any two points on the line.

I'll chose (0, 4) and (2, -2).

To find slope, you need to use the formula m = y2 - y1 divided by x2 - x1.

m = y2 - y1 / x2 - x1

m = (-2 - 4) / (2 - 0)

m = -6 / 2

Then you must reduce to lowest terms.

m = -3

Answer:

HIG=28°

Step-by-step explanation:

HI is a diameter therefore it's measure is 180°

HI-IG=HG

180-128=HG

52°=HG

HIG=1/2HG

HIG=1/2(56°)

HIG=28°

Answer:

Step-by-step explanation:

The line is vertical, so it is on x

the line is on x=5

the line is whole so it is less or greater than and equal to

the shaded part is to the left, so it is less than

So, the inequality represented by the graph is x≤5