SYSTEMS OF EQUATIONS WORD PROBLEM: The members of the city cultural center have decided to put on a play once a night for a week. Their auditorium holds 500 people. By selling​ tickets, the members would like to raise ​$3,350 every night to cover all expenses. Let d represent the number of adult tickets sold at ​$8.50. Let s represent the number of student tickets sold at ​$5.50 each. If all 500 seats are filled for a​ performance, how many of each type of ticket must have been sold for the members to raise exactly ​$3,350​? At one performance there were two times as many student tickets sold as adult tickets. If there were 360 tickets sold at that​ performance, how much below the goal of ​$3,350 did ticket sales​ fall?

Given:

First term of a geometric series = a

Common ratio of the geometric series = [tex]\sqrt{3}[/tex]

To prove:

[tex]S_{10}=121a(\sqrt{3}+1)[/tex]

Solution:

The sum of first n terms of geometric series is

[tex]S_n=\dfrac{a(r^n-1)}{r-1}[/tex]

Where, a is the first term and r is the common ratio.

Putting n=10 and [tex]r=\sqrt{3}[/tex] in the above formula, to get the sum of 10 terms.

[tex]S_{10}=\dfrac{a((\sqrt{3})^{10}-1)}{\sqrt{3}-1}[/tex]

[tex]S_{10}=\dfrac{a(243-1)}{\sqrt{3}-1}[/tex]

[tex]S_{10}=\dfrac{242a}{\sqrt{3}-1}[/tex]

Rationalizing the denominator, we get

[tex]S_{10}=\dfrac{242a}{\sqrt{3}-1}\times \dfrac{\sqrt{3}+1}{\sqrt{3}+1}[/tex]

[tex]S_{10}=\dfrac{242a(\sqrt{3}+1)}{(\sqrt{3})^2-1^2}[/tex]

[tex]S_{10}=\dfrac{242a(\sqrt{3}+1)}{3-1}[/tex]

[tex]S_{10}=\dfrac{242a(\sqrt{3}+1)}{2}[/tex]

[tex]S_{10}=121a(\sqrt{3}+1)[/tex]

Hence proved.

Answer:

4x

3x

Step-by-step explanation:

1.)

we see that when x=0 y=0 which means that our equation

y=mx+b

b=0

(this is shown if we plug in 0 for x)

0= 0x+b

0=b

Next, we notice that each time it's increasing by four which means our slope is just 4

the answer is 4x

The y intercept (or b) is the same deal as question one

we can also see that when x=1 y=3 which means that

3=x+0

3=x

our slope is 3

Answer:

a triangle, I'm guessing 20ft and 24 ft on the outsides,

would be:

Equation to get the area of a triangle: (A*B)/2

(20*24)/2=Area

20*24= 480

480/2= 240

area= 240

Answer: 240 ft²

Step-by-step explanation:

1. Multiply the base and the height.

2. Divide the product you get by 2.

=> 20 * 24 = 480

=> 480 / 2 = 240

Answer:

y=5200(0.15)^t

Step-by-step explanation:

this is the answer y=5200(0.15)^t

Answer:

B. -1/3

Step-by-step explanation:

replace x with 34 and solve it.

Answer:

55%

Step-by-step explanation:

Make 11 out of 20 as a fraction:

[tex]\frac{11}{20}[/tex]

11 ÷ 20 is 0.55.

To make a decimal a percent, you multiply it by 100. So,

0.55 x 100 = 55

                  = 55%

So, the answer is 55%

The requried,  percentage of 11 out of 20 is 55%.

To find the percentage of 11 out of 20, you can use the following formula:

Percentage = (Part / Whole) * 100

In this case, the "part" is 11 and the "whole" is 20. Plug these values into the formula:

Percentage = (11 / 20) * 100

Calculate the value:

Percentage = 0.55 * 100

Percentage = 55%

So, 11 is 55% of 20.

Learn more about percentages here:

https://brainly.com/question/13162258

#SPJ6

Answer:

13 each

Step-by-step explanation:

40/3= 13.3

Answer:

30

Step-by-step explanation:

This is a 30 60 90 triangle. Since it tells us it a right triangle (which means it has a 90 degree angle). Also it tells us that there is a 30 degree. Using the triangle interior theorem, the third angle is a 60 degree

angle

The longest side or hypotenuse is twice the length of the shortest side. So the hypotunes is 30.

Answer:

Aqua para chica gamer? te sirve?

Answer:

Your answer......6480 Rs

WANT MORE THEN FOLLOW ME, LIKE & MARK MY ANSWER AS BRAINLIST ANSWER

Answer:

After calculating, your answer should be:

(0.80-0.5 m/s)/(4.0 s) = (0.075 m)/s^2

I hope this helps you! (This was for the 100 point brainly thing you said you wiuld give me 100 points?)

Answer:

avg speed= total distance / total time

total time= 0.5+1.5= 2 h

d1= v1 t1=1.5×3=4.5

d2=v2t2

v2=x...let

d2=0.5x

atq....4.5+0.5x/2= 4

4.5+0.5x=8

x= v2=7mph

Answer:

7 mph

Step-by-step explanation:

Answer:

I plot the points to a graph but I don't have access to a 14 I only have a 10 grid graph but I was able to plot the other points this is wht I got

Step-by-step explanation:

let me know if u can't see it..... I would say it's nonlinear

eㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤ

watch wonder egg priority & sk8 Infinity

on 4anime dot to

Answer:

Meat

Step-by-step explanation:

The only thing he can practically think about is Meat, Pirate King, and his pirate crew.

Answer:

length =12 cm breadth =10 cm height =5 cm

TSA=2(lb+bh+lh)=2[12×10+10×5+5×12]

TSA=2[120+50+60]=2×230

[TSA=460cm 2 ]

Step-by-step explanation:

Hope it is helpful....

Step-by-step explanation:

length=12cm

breadth =10cm

height =5cm

we know that,

T.S.A of cuboid= 2(lb+lh+bh)

=2(12*10+12*5+10*5)

=2* 230

=460.

Hope it will help

Answer:

4 pitches

Step-by-step explanation:

if a cylinder with height 9 inches and radius r is filled with water, it can fill a certain pitcher. how many of these pitchers can a cylinder with height 9 inches and radius 2r fill? explain how you know.

Solution:

The volume of a cylinder is given by:

V = πr²h;

where V is the volume, r is the radius of the cylinder and h is the height of the cylinder.

A cylinder with height 9 inches and radius r can fill a certain pitcher. Therefore the volume of the cylinder is:

V = πr²h = πr²(9) = 9πr²

V = volume of pitcher = volume of cylinder with radius r = 9πr²

For a cylinder with height 9 inches and radius 2r its volume is:

V2 = πr²h = π(2r)²(9) = 36πr²

Therefore, the number of pitchers a cylinder with height 9 inches and radius 2r can fill is:

number of pitches = 36πr² / 9πr² = 4

Therefore a cylinder with height 9 inches and radius 2r can fill 4 pitches.

Answer: 25

Step-by-step explanation:

If 1 inch equal to 5 feet in this equation than. 5 inches=25 because 5 inches and each inch is 5 feet so 5x5=25

hope this helps

Answer:

Step-by-step explanation:

(10 - 4)/(4 -1)= 6/3= 2

y - 4 = 2(x - 1)

y - 4 = 2x - 2

y = 2x + 2

9514 1404 393

Answer:

  ML = 7.5

Step-by-step explanation:

The parallel lines divide the transversals proportionally.

  ML/LK = JH/HG

  ML/10 = 6/8

  ML = 10(6/8) = 7.5

The length of ML is 7.5.

__

We don't need to solve for x. If ML = x-2, then x=9.5.

Answer:

Step-by-step explanation:

a₂₁ = -10 + 5(21) = 95

Answer:

42.54 inches

Step-by-step explanation:

Answer:

572.555

Step-by-step explanation:

A=Πr²

A=3.14×13.5²

A=572.555

Answer:

2.5198421 is yhe answer of 3^√16

Answer:

okay bro, but I need some time

Answer:

72

Step-by-step explanation:

.75x96=72

Answer:

5.75 days

Step-by-step explanation:

Given data

let the number of days be x and the number and the number of miles be y

so that the cost of the rental will be

c= 38.38x+ 0.14y---------1

we are told that the amount at hand is $270

hence

270=38.38x+ 0.14*(350)

solve for x

270= 38.38x+49

270-49= 38.38x

221= 38.38x

divide both sides by 38.38

x= 221/38.38

x= 5.75 days

Hence the  number of days is 5.75 days

Answer:

perimeter goes with the one that has 5x^2

i dont know the second im sorry

Step-by-step explanation:

Answer:

1

Step-by-step explanation:

I did it in the calculator

Answer:

-7/2

Step-by-step explanation:

Answer:

1. 40

2. 124

3. 160

Step-by-step explanation:

1. 12x - 20 = 60 - 20 = 40

2. 12x - 20 = 144 - 20 = 124

3. 12x - 20 = 180 - 20 = 160