Write an explicit equation for the sequence based on the graph at right.

Write An Explicit Equation For The Sequence Based On The Graph At Right.

Answers

Answer 1

Answer:

[tex]t(n)=12 \cdot 3^{n-1}[/tex]

Step-by-step explanation:

From inspection, the points on the graph are:

(1, 12)(2, 36)(3, 108)

Therefore, as terms of a sequence:

[tex]t_1=12\\\\t_2=36\\\\t_3=108[/tex]

The difference between the y-coordinates is not equal, therefore the sequence is geometric.

Geometric sequence formula: [tex]t_n=t_1r^{n-1}[/tex]

As [tex]t_1=12 \implies t_n=12r^{n-1}[/tex]

To find r, divide one term by the previous term:

[tex]r=\dfrac{t_3}{t_2}=\dfrac{108}{36}=3[/tex]

Therefore, geometric sequence formula: [tex]t_n=12 \cdot 3^{n-1}[/tex]


Related Questions

I DONT GET THIS!!!!


QUESTION HERE : IN 140 CHARACTERS. OR LESS CREATE. A
TWEET. ABOUT WHAT INTELLIGENCEIS OR
MEANS TO YOU. THE GRID BELOW CAN BE USED TO MAKE SURE YOU DONT GO OVER 140 CHARACTERS.​

Answers

Answer:

you just have to calm down and search it online it helps sometimes

rewrite the equation without the exponent
3^-4

Answers

[tex]3^{-4}=\dfrac{1}{3^4} =\dfrac{1}{81}[/tex]

The perimeter of the triangular park shown in the picture is 13x - 4. You have been given 2 of the 3
sides of the park. What is the missing side length?

Answers

Answer:

8x-3

Step-by-step explanation:

I hope it helps you

Which statements about the graph of the function f(x) = –x2 – 4x 2 are true? Select three options.

Answers

The domain of the function is the real number and the range of the function is (-∞, 6].

What is a function?

The function is an expression, rule, or law that defines the relationship between one variable to another variable. Functions are ubiquitous in mathematics and are essential for formulating physical relationships.

The function f(x) = -x² - 4x + 2

The function can be written as

[tex]\rm f(x) = -x^2- 4x +2\\\\f(x) = -x^{2}- 4x - 4 + 4 +2 \\\\f(x) = -(x^{2} +4x +4) + 6\\\\f(x) = -(x+ 2)^2 + 6[/tex]

The domain is the real number and the range is (-∞, 6].

More about the function link is given below.

https://brainly.com/question/5245372

Felix can paint a room, working alone, in 8 hours. Sandy can paint the same room, working alone, in 6 hours. How long will it take them if they work together?

Answers

It will take them 4 hours if they work together.

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Graph the linear function y = 5. Plot two points and connect them with a line.

Answers

Answer: (1,5)(-1,5)
It’s a horizontal line going through y=5, so you can just plot these two points in and draw a line through them

graph of the linear function y = 5 is attached below. which is true for all the values of x.

What is a linear function?

a function whose equation is of the form y = ax + b, where a and b are constants, a does not equal zero, and x is any real number, and whose graph is a straight line.

Given a linear function y = 5 here

The graph of that linear function will be a straight line that is attached below.

this function will be the same for all the values of x. since it is not dependent on the variable x

it will pass through points (0, 5),  (1, 5),  (-6, 5),  (5, 5),  (-9, 5),.... and so on.

therefore, Below is a graph of the linear function at y = 5. This holds true regardless of x's value.

Learn more about linear functions here:

https://brainly.com/question/20286983

#SPJ2

Complete and submit the W4 form using the personal information provided for Addison.
Addison Marie Smith
2222 W. Pine
Anytown, USA 55555
Social Security Number: 222 22 2222
Addison will only have one job, and there is no need to have any additional taxes withheld from her
paycheck.

Answers

The steps for completing a W-4 form include the following:

You should provide your information such as name, address, Social Security Number (SSN).You should indicate that Addison has one job only.You should indicate whether or not Addison has dependents.You should state that there is no need to have any additional taxes withheld from Addison's paycheck.You should provide a signature and date.

What is a W-4 form?

A W-4 form can be defined as an internal revenue service (IRS) tax form which is used to indicate the correct federal income tax that should be withheld from an employee's paycheck in the United States of America.

After an employee fills a W-4 form, it must be submitted to the internal revenue service (IRS) by the employer.

How to complete a W-4 form.

Basically, the steps for completing a W-4 form include the following:

Step 1: You should provide your information such as name, address, Social Security Number (SSN).

Name: Addison Marie Smith                          Address: 2222 W. Pine Anytown, USA.Social Security Number: 222 22 2222

Step 2: You should indicate that Addison has one job only.

Step 3: You should indicate whether or not Addison has dependents.

Step 4: You should state that there is no need to have any additional taxes withheld from Addison's paycheck.

Step 5: You should provide a signature and date.

Read more on W-4 form here: https://brainly.com/question/15507745

expand this expression
x(2x-3)

Answers

Answer:

2x² - 3x

Step-by-step explanation:

multiply the outside with the inside brackets

x × 2x = 2x²

x × (-3) = -3x

Answer:

x(2x-3)

Step-by-step explanation:

x(2x-3)

x times 2x equals 2x².

x times -3 is -3x.

2x²-3x.

PLS help!! This is due tomorrow

Answers

Answer:

x = 18

Step-by-step explanation:

So there is two ways, but I'm going with the way I remember

1/6 x = 3

1x/6 = 3 multiply by 1

x/6 = 3 then multiply by 6

x = 18

Which of the following rational functions is graphed below?

Answers

Answer: C) F(x)=1/(x+5)^2

the surface area of a pyramid is 85 square meters the side length of the base is 5 meters what is the slant height

Answers

Answer:

6 meters

Step-by-step explanation:

[tex]A=a^2+2a\sqrt{\frac{a^2}{4}+h^2} [/tex]is the formula that you use

h=vertical altitude and

a=side length of the base

[tex]85=5^2+(2*5)\sqrt{\frac{25}{4}+h^2}[/tex]

[tex]85-25=10\sqrt{\frac{25}{4}+h^2}[/tex]

[tex]\frac{60}{10}=\sqrt{\frac{25}{4}+h^2}[/tex]

[tex]6=\sqrt{\frac{25}{4}+h^2}[/tex]

[tex]36=\frac{25}{4}+h^2[/tex]

[tex]36-\frac{25}{4}=h^2[/tex]

[tex]36-6.25=h^2[/tex]

[tex]29.75=h^2[/tex]

Vertical altitude (h) and [tex]\frac{1}{2}a[/tex] and the slant height form a right triangle with the slant height being the hypotenuse

[tex]h^2+(2.5)^2=s^2 [/tex]where s=slant height

[tex]29.75+6.25=s^2[/tex]

[tex]36=s^2[/tex]

s=6 meters

Answer:

slant height = 6 meters

Step-by-step explanation:

surface area of pyramid: 2bs + b²

2*5*s + 5² = 85

10s = 85 - 25

10s = 60

s = 6

The slant height is 6 meters.

your car travels 308 miles on 11 gallons of gasoline. how many miles can it travel with 1 gallon of gas

Answers

Answer:

28 miles

Step-by-step explanation:

308/11 = 28 miles per gallon of gas

Solve for h.

10 = 2h

Answers

h would be 5
10= 2(5)

The equatin of line AB is y = 2x + 4. What is the equation of a line parallel to line AB in slope-intercept form that contains the point (3, -2)2

Answers

Answer:

Step-by-step explanation:

Parallel lines have the same slope, so if the slope of the given line is 2, the slope of the "new" line is also 2, and the slope-intercept equation becomes:

y = 2x + b.  

Here you seem to have a "misprint," as "(3, -2)2 is not a valid expresion.

Supposing that y ou meant (3, -2), then our equation becomes

-2 = 2(3) + b, or -8 = b.

The desired equation is then y = 2x - 8

If this is not what you expected, please focus on your (3, -2)2 and rewrite it properly.

100 POINTS EASY QUESTION

Simplify the polynomial expression.

3x(-2x + 7) - 5(x - 1)(4x - 3)

Answers

Answer:

[tex]-26x^2+56x-15[/tex]

Step-by-step explanation:

[tex]3x(-2x + 7) - 5(x - 1)(4x - 3)[/tex]

Expand the brackets:

[tex]\implies -6x^2+21x-5(4x^2-7x+3)[/tex]

[tex]\implies -6x^2+21x-20x^2 +35x-15[/tex]

Collect like terms:

[tex]\implies -6x^2-20x^2+21x +35x-15[/tex]

Combine like terms:

[tex]\implies -26x^2+56x-15[/tex]

Answer:

Step-by-step explanation:

This is late reply. You can try searching online next time you need an answer in a hurry - most questions have been asked before: like here https://brainly.com/question/11412899

3x(-2x + 7) - 5(x - 1)(4x - 3)

= (-6x^2 + 21x) - 5(4x^2- 7x +3)

= -6x^2 + 21x - 20x^2 + 35x - 15

= -26x^2 + 56x -15

Please answer with clear instructions so that i can apply this to other questions.

Answers

Answer:

10 terms

Step-by-step explanation:

equate the sum formula to 55 and solve for n

[tex]\frac{1}{2}[/tex] n(n + 1) = 55 ( multiply both sides by 2 to clear the fraction )

n(n + 1) = 110 ← distribute parenthesis on left side

n² + n = 110 ( subtract 110 from both sides )

n² + n - 110 = 0 ← in standard form

Consider the factors of the constant term (- 110) which sum to give the coefficient of the n- term (+ 1)

the factors are + 11 and - 10 , since

11 × - 10 = - 110 and 11 - 10 = + 1 , then

(n + 11)(n - 10) = 0 ← in factored form

equate each factor to zero and solve for n

n + 11 = 0 ⇒ n = - 11

n - 10 = 0 ⇒ n = 10

However, n > 0 , then n = 10

number of terms which sum to 55 is 10

PLEASE HELPP!!!URGENT!!!!!!

This scale drawing shows a reduction in a figure.

What is the value of x?

Enter your answer as a decimal in the box.

x =

Answers

Answer:

2.25

Step-by-step explanation:

Because if you do 8/6 you get 1.33333333333 so you would need to do 3/1.33333333333 and you would get 2.25.

Answer:

x = 2.25

Step-by-step explanation:

Since this is simply a reduction of a figure, we can assume the ratio is constant. With this in mind, we can set up the following proportion to solve for x.

8 / 3 = 6 / x

8 * x / 3 = 6

8 * x = 6 * 3

x = 6 * 3 / 8

x = 18 / 8

x = 9 / 4 = 2.25

Cheers.

whats the answer for this oneeeeeeeeeee

Answers

Answer:

1.35

Step-by-step explanation:

the explanation to the question is in the photo I sent

rounding off to the nearest tenth

then the final answer is 1.4

Which is the graph of y = 3sin(x) - 1

Answers

Answer:

It should look like the graphs above.

Hope this helps!

Josan and Adamas want to play a video game together. Their parents let them earn credits for video game time by reading books.

Josan's credits are each worth 5
5
minutes of play, and Adamas's credits are each worth 10
10
minutes of play. Josan also starts each day with 6
6
free credits, and she has already used 10
10
minutes of her video game time.

They each want to earn enough credits so that they will have the same number of minutes to play video games.

Which equation will solve for the number of credits,
z
, they must earn to have the same amount of play time?

Answers

Both Josan and Adama must have to earn 6 credits for they to have the same amount of play time.

Equation

An equation is an expression used to show the relationship between two or more numbers and variables.

Let z represent the number of credits they must earn to have the same amount of play time. Hence:

5z + 6(5) = 10z

5z = 30

z = 6

Both Josan and Adama must have to earn 6 credits for they to have the same amount of play time.

Find out more on Equation at: https://brainly.com/question/2972832

Answer:

5(z+6) −  10=10z

Step-by-step explanation:

A plane can fly 312 miles with the wind in 3 hours, while it takes the same plane 4 hours to fly the same distance against the wind. Find the speed of the plane in still air, and the speed of the wind.

Answers

The  speed on the plane is 104mph while that of the wind is 78mph

Speed and distances

The formula for calculating distance is expressed as:

Speed = Distance/Time

If the plane is flying with the wind;

3(r+ w) = 312

r + w = 104 ................... 1

If against the wind

4(r - w )= 312

r- w = 78 .................. 2

Add both equations

2r = 104  + 78

2r = 182

r = 91

Since r + w = 104

w = 104 - 91

w = 13

Speed on the plane  = r + w  = 91 + 13 = 104mi/hr

Speed on the wind = 91 - 13 = 78mi/hr

Learn more on speed here: https://brainly.com/question/4931057

Please help!

Eleven subtracted from a number

A) 11- x
B) 11x-11
C) C x/11
D) x- 11

Answers

Answer:

[tex]x-11[/tex]

Step-by-step explanation:

Let the number be x

Then we have,

x-11

I need help anything can help idc honestly​

Answers

Answer:

s=sqrt(60) => the second one is the correct answer.

Step-by-step explanation:

It’s given that A=60.

Formula: A=s^2.

=> s=sqrt(A)=sqrt(60)

Given the net with dimensions below, find the surface area of the shape.

Answers

Answer:

184cm^2

Step-by-step explanation:

(5+5+6) * 10 = 160

6*4 = 24

160+24=184

there are 2 triangles so I am assuming they have the same dimensions

6. An ant travels at a constant rate of 30 cm every 2 minutes.-
a. At what pace does the ant travel per centimeter?
b. At what speed does the ant travel per minute?
(From Unit 2, Lesson 18.)

Answers

A:

4 seconds per centimer:

30cms               15 cms

----------------       -------------

2 minutes           1 minute

1 minute= 60 seconds

15 cms                       1cm

-----------------     =     ----------------

60 seconds              4seconds

B: 15 cms per minute

30cms/2minutes

(divide by 2 to get speed for one minute)

15cm/1 minute

x2−14x−32=0 What are the roots of the polynomial equation?

Answers

Answer:

x= - 8/3

Step-by-step explanation:

1- Multiply the monomials

2- Combine like terms

3- Rearrange variables to the left side of the equation

4- Divide both sides of the equation by the coefficient of the variable

5- Cross out the common factor

PLEASE HELP. I don’t get it at all and I’d really appreciate it. Thank you!

Answers

Answer:

was this the whole question cause it depends on what the plane is

Step-by-step explanation:

what is the circumference of a circular swimming pool with a diameter of 6 1/2 feet use 22 over 7 for pi

Answers

Answer:

20.428571

Step-by-step explanation:

C=(22/7)d

C=(22/7)6.5

C=20.428571

Answer:

20.4285714289

or ≈20.4

Step-by-step explanation:

2*pi*r

radius = diameter/2 = 6.5/2

r=3.25

22/7=3.1428571429

2*3.1428571429*3.25

PLSSS HELP IF YOU TURLY KNOW THISS

Answers

Answer:

4 X 3= 12

6 X 3= 18

Please mark as Brainliest

Answer:

12

Step-by-step explanation:

View the question mark as x then cross multiply

18×4= 6×x

72= 6x

x is 12



2. At a school shop, pens are sold at dallars each and ruler at y dollars each. Mr. James bought 4 pens and 5 rulers for $20. Mr. Pike bought 2 of the same pens and 4 of the same ruler for $16 a. Write two equations in and y to represent the information given above. b. Solve the equations

Help pleaseee :)​

Answers

Answer:

x = 0, y = 4

Step-by-step explanation:

1 pen = x dollars

4 pen = 4x

1 ruler = y dollars

5 rulers = 5y

now,

a) = 5y + 4x = 20

2x + 4y = 16

Now,

2x + 4y = 16

or, 2x = 16 - 4y

or, x = (16 - 4y)/2

Now,

5y + 4x = 20

or, 5y + 4{(16 - 4y)/2} = 20

or, (10y + 64 - 16y) = 40

or, 64 - 6y = 40

or, 64 - 40 = 6y

or, 6y = 24

so, y = 4

now,

x = (16 - 4(4))/2

or, x =(16 - 16)/2

so, x = 0

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