find the explicit formula for the following sequence.
15, 29, 49, 75, 107,....

Answers

Answer 1

Answer:

Step-by-step explanation:

We are given the sequence

[tex]15, 29, 49, 75, 107\\15->29 = 14\\29 -> 49 = 20\\49->75 = 26\\75 -> 107 = 32\\14, 20, 26, 32\\14 -> 20= 6\\20 -> 26 = 6\\26 -> 32 = 6\\\\6, 6, 6\\6->6 = 0[/tex]

Since we had to find the differences twice, it is a second degree polynomial

[tex]y = an^2 + bn + c\\plugging \: in \: n = 1, 2, 3...\\the \: sequence \: is \\a+b+c, 4a + 2b + c, 9a + 3b + c...\\the \: diff \: under \: is \\3a + b, 5a + b, 7a + b...\\the \: diff \: under \: is \\2a, 2a, 2a...\\so, \\2a = 6\\a = 3\\3(3) + b = 14\\b = 5\\\\a +b + c = 15\\3 + 5 + c = 15\\c = 7\\[/tex]

so,

[tex]y = 3n^2 + 5n + 7[/tex]


Related Questions

expand and simplify

2(x+7)+ 3(x+1)

Answers

Answer:

2(x+7)+3(x+1)

2x+14+3x+3

5x+17

Answer:

Step-by-step explanation

2(x+7)+ 3(x+1)

2x+14+3x+3

5x+17 is the answer

Ignore the 1 and the 2. That’s just where you put your answer.

Answers

Answer:

4500000

40

Step-by-step explanation:

*^*^*^*^*^*^*^*^*^*^*^*^*^*^*^*^*^*^*^*^*^*^*^*^*^*^*^*^*^*^*^*^*^*^*^*^*^*^*^*^*^*^

In the equation, we are told that d(t) = 300,000t, where t is the time in seconds and d(t) is the distance in kilometers.

1. In this part of the question, it asks for the distance after 15 seconds. To solve we plug 15 in for t.

d(t) = 300,000(15)

d(t) =  4500000  kilometers

2. In this part of the question, it is asking for time after going 12,000,000 kilometers (twelve million). To solve, we solve for t by dividing 300,000.

12,000,000 = 300,000(t)

40 = t

*^*^*^*^*^*^*^*^*^*^*^*^*^*^*^*^*^*^*^*^*^*^*^*^*^*^*^*^*^*^*^*^*^*^*^*^*^*^*^*^*^*^

#teamtrees #WAP (Water And Plant)

2x-3=x+1
Show the work on what x is

Answers

Answer:

x=4

Step-by-step explanation:

Let's solve your equation step-by-step.

2x−3=x+1

Step 1: Subtract x from both sides.

2x−3−x=x+1−x

x−3=1

Step 2: Add 3 to both sides.

x−3+3=1+3

x=4

Answer:

x=4

2x - 1x = x

x-3= 1

3+1 =4

so x=4

And I is throwing money at birthday party. She has $100 to spend. She buys a cake for $30, a giant balloon for $20, and 10 cups that each cost the same price. Create and solve any equation to determine the cost of each cup.

Answers

Answer:

$5 per cup

Step-by-step explanation:

Step one:

given data

total amount = $100

cost of cake=$30

cost of balloon=$20

let the cost of 1 cup be x

so cost of ten cups = 10x

Step two:

The expression for the total amount is given as

100=30+20+10x

100=50+10

100-50=10x

50=10x

divide both sides by 10

x=50/10

x=$5

the cost of one cup is $5

the cost of ten cups is 5*10= $50

HELP PLZZ BTW I NEED THE WORK so plz include it if you do I will mark you brainliest

Answers

Answer:

C

C

C

I hope this help

The answer is C hit helpp

Marco needs to buy some cat food. At the nearest​ store, 5 bags of cat food cost ​$18.75. How much would Marco spend on 3 bags of cat ​food?

Answers

Answer:

$11.25

Step-by-step explanation:

5 bags = $18.75

To find the amount for three bags, we need to find the price for each bag.

Divide 18.75 by 5.

18.75/5 = 3.75

So each bag is 3.75, and since we need to know the price for 3 bags, we need to multiply 3.75 by 3, which is 11.25.

HELPPP

Solve for b 2 in A = h(b 1+b 2), if A = 16, h = 4, and b 1 = 3.

b 2 =

Answers

Answer:1

Step-by-step explanation: substitute all the corresponding terms so you get, 16=4(3+b2)

Then you multiply and get 16=12+4b2 then subtract 12 from both sides to get 4=4b2 and then divided both sides by 4 and you get 1=b2

Answer:1

Step-by-step explanation: A = h(b 1+b 2)

16=4(3+b2)

16/4=3+b2

4=3+b2

B2 =4-3=1

Do the organic prices vary directly with the conventional prices? If so, identify k. Does the total cost of organic apples vary directly with the number of pounds of organic apples purchased? If so, identify k.
THE RIGHT ANSWER IS (i just had to answer my own question so that other people can get it but just copy and paste this thanks :) )

no, this is not a direct variation
yes this is a direct variation with k=2.34

2

Answers

Answer:

1: No, this is not direct variation

2: Yes, this is direct variation with k= 2.34

Step-by-step explanation:

I’m Just Built Different

Elvira used 4 cups of grape juice, 1 1/2 cups of cranberry juice, and 1/2 cup of pineapple juice to make punch. One liter
is approximately equal to 4.23 cups.
Which measurement is closest to the number of liters of punch Elvira made?

Answers

4+1.5+.5= 6 cups

6 cups = 1.42 liters

Closest measurement is 1.42L

Yousef typed a 36-word paragraph in 2/3 minute. What is his typing speed, in words per minute?

Answers

If he types 36 words in 2/3 of a minute, we first need to find out what his speed is in 1/3 of a minute.

To do this, we divide 36 by 2 which gives us 18.

So if Yousef can type 18 words in 1/3 of a minute, we multiply 18 by 3 to work out how many words he types per minute.

18 x 3 = 54

Therefore Yousef types 54 words per minute.


Another method:

Another method to do this would be to take the 36 and divide it by 2/3 which would give us 54.

$59.99 DVD box set, 6.5% tax

Answers

Answer:

$63.89

Step-by-step explanation:

59.99 * 6.5% = 3.89935. we can round that to $3.90.

59.99 + 3.90 = $63.89 total

Answer:

$3.90

Step-by-step explanation:

6.5% of $59.99 is $3.90.

Feel free to give brainliest.

Have an outstanding day!

is 12x+6y=18 parallel or perpendicular to 9x-3y=4

Answers

Answer:

perpendicular

Step-by-step explanation:

Yolanda has a 1/6 -cup ladle that she uses to pour gravy over potatoes. She uses one full ladle for each serving of potatoes. Yolanda has 6 cups of gravy. How many servings of potatoes can she make?

Answers

Answer: For 6 cups of gravy, Yolanda will have 36 servings of potatoes

Step-by-step explanation:

Step 1

Since  Yolanda has a  1/6-cup of ladle for one full serving

Then for every serving the 1/6- cup ladle  is used and can be expressed as

1 serving  =1/6-cup of ladle

Step 2--- Solving

Serving of potatoes for  1 cup is

1 serving  =1/6 cup of ladle

?? servings=1 cup of ladle ( cross multiply)

=  1 x 6/1 =  6 servings

Therefore  6 cups of gravy =  6 servings x 6 = 36 servings of potatoes

A restaurant freezes a cherry and lime juice mixture to create slushes. Cherry juice costs $5 per quart, and lime juice costs $3 per quart. Each day, the restaurant spends a total of $36 on 8 quarts of juice. The restaurant manager organizes the information in the table below.

Answers

Answer:

Answer is at the bottom!

Step-by-step explanation:

Cherry juice=5+5+5+5+5+5=30

Lime juice =3+3=6

6 cherry slushes and 2 lime slushes were sold.

Hope this helps!!

Answer:

6 cherry slushes and 2 lime

Step-by-step explanation:

What is 2.53 Times 57.62

Answers

Answer:

145.7786

simplified to 145.78

Step-by-step explanation:

Answer:

The answer is 145

What is the equation of the line with a slope of 2 through (–4, 6) in point-slope form?

Answers

In point-slope form, the equation is :

Y-6=2(x+4)

Hope this helps✨❤️

I have 2 questions

Transform the equation.
Stretch y=5x by a factor of 3
What is the transformed equation?

Transform the equation.
Shift y=5√x+5 horizontally, 5 units to the right and a stretch by a factor of 4
What is the transformed equation?

Answers

Answer:

1. I assume that stretching vertically by factor of 2 means that every point on the transformed curve is twice as far from the x axis as the original curve.

Imagine that you have plotted y=5x.  you want to change the y scale so that each point on the original curve is two times as high.  For example, one point on the original curve is (1,5).  This point must be relocated to (1,10).  Similarly, the point (2,10) on the original curve must be relocated to (2,20).

You can see that these relocations are accomplished if we transform the function to y=2(5x)=10x.

Step-by-step explanation:

hope this helps! even though it's just the first one...

helppp i’ll give brainliest

Answers

Answer:

6 x 10^-4 (B)

Step-by-step explanation:

It is the greater number.

B- is the bigger number 6x ^10-4

whats 100000x 109888888 -4000 + 185637?
ill give brainliest or whatever you want

Answers

Answer:

1.0988889e+13

Step-by-step explanation:

and i oop

Is 3 x 1/2 greater than 5?

Answers

No it is not greater than 5

When ever you are multiply a number by 1/2 you are halving the number. So in the us case 3 x 1/2 is 1.5.

And 1.5 is not greater than 5

So the answer is no



Can you please mark brainleist

5(y + 2) = 6(y - 1)
Show work
Please and thank you

Answers

Answer:

5 ( y + 2) = 6 ( y - 1)

- distribute the number outside into the parenthesis by multiplying it with each value

5y + 10 = 6y - 6

- subtract like terms, in this case 5y and 6y

-y + 10 = -6

- isolate the variable ( y)  by getting rid of 10 by subtracting it to both sides

-y = -16

-1y = -16

- isolate variable (y) by getting rid of the -1 next to it by dividing it to both sides

y = -16 / -1

y = 16

solve the question, thank you

Answers

Answer:

A . m = 11/6

its going to be a

the answer is A because when you do y2 - y1 / x2- x1 you are doing 18-7/ 4- (-2) and 18-7 is 11 and 4-(-2) is 6 so your answer will be 11/6 which is A

Which statement is true about figures ABCD and A'B'C'D?

Answers

Answer:

Step-by-step explanation:

To understand the transformation better we will take a point B first.

Coordinates of B → (3, 0)

When we rotate this point by 180° counterclockwise about the origin, rule to be followed,

(x, y) → (-x, -y)

By this rule, coordinates of B'' will be,

B(3, 0) → B''(-3, 0)

Now we translate the point B by 2 units right.

Rule for the translation is,

(x, y) → [(x + 2), 0]

Following this rule,

B''(-3, 0) → B'[(-3+2), 0]

             → B'(-1, 0)

We can conclude with the statement, "Figure ABCD was rotated by 180° about the origin followed by the translation of 2 units to the right" to get the new figure A'B'C'D' similar to pre-image ABCD.

A garden bed has 4 sections of vegetables. The garden 8 1/2 yards long.
If each section is equal in the length, what is the length of each section?​

Answers

i think its 12 1/2 because 4 + 8 1/2 = 12 1/2

Answer: 12 1/2

Step-by-step explanation: It is 12 1/2 because you have to multiply 4 times 8 1/2 and you'll get 12 1/2

Thats how you do It and make sure to subscirbe to GamerPlayzSupreme2 BYE!!

You are at a fruit stand to get some fresh produce. You notice that the person in front of you gets 5
apples and 4 pears for 10 dollars. You get 5 apples and 5 pears for 11 dollars. Write a system of
equations that could be used to find the price of an apple and the price of a pear.

Answers

Answer:

[tex]5A + 4P = 10[/tex]

[tex]5A + 5P = 11[/tex]

1 apple costs $1.2

1 pear costs $1

Step-by-step explanation:

Represent Apples with A and Pears with P

For the person in my front, the expression is:

[tex]5A + 4P = 10[/tex]

For me, the expression is

[tex]5A + 5P = 11[/tex]

Hence, the system of equation is:

[tex]5A + 4P = 10[/tex]

[tex]5A + 5P = 11[/tex]

Solving for the values of A and P.

Substract equation (2) from (1)

[tex]5A - 5A + 4P - 5P = 10 - 11[/tex]

[tex]-P = -1[/tex]

[tex]P = 1[/tex]

Hence, 1 pear costs $1

Substitute 1 for P in [tex]5A + 4P = 10[/tex]

[tex]5A + 4 * 1 = 10[/tex]

[tex]5A + 4 = 10[/tex]

[tex]5A = 10 - 4[/tex]

[tex]5A = 6[/tex]

[tex]A = \frac{6}{5}[/tex]

[tex]A = \$1.2[/tex]

Hence, 1 apple costs $1.2

A new amusement park has a sign posting the cost for rides.
How much would it cost for 18 rides?

Answers

Answer:

It would cost $51 for 18 rides

Step-by-step explanation:

if it costs $8.50 for 3 rides, you could easily just multiplied the price of 3 by 6 because 6 x 3 = 18 rides

And 8.5 x 6 = $51

The average cost per unit c(x) to produce x units of lumber is given byc * (x) = 400/(x + 25) if the cost per unit is \$1.00 how many units have been produced if necessary round your answer to the nearest whole unit. the answer is 375

Answers

Answer:

The number of units of lumber that have been produced is 375

Step-by-step explanation:

From the question,

The average cost per unit c(x) to produce x units of lumber is given by

c(x) = 400/(x + 25).

Now, to determine how many units have been produced (that is, x) if the cost per unit is $1.00 (that is, c(x) = $1.00), we will put in the value into the given equation to determine x.

c(x) = 400/(x + 25)

c(x) = $1.00

∴ 1.00 = 400/(x + 25)

Then,

(x + 25) × 1.00 = 400

x + 25 = 400

x = 400 - 25

x = 375

Hence, the number of units of lumber that have been produced is 375.

There are 48 students in the dass. They arrange their desks in rows with 8 desks in each row.
How many rows are there?

Answers

Answer:

6 rows

Step-by-step explanation:

We know that 48 desks are split up into rows of 8

If we divide the 48 total desks by the 8 desks in each row... we find the number of rows.

48/8 = 6

Find the zero of the function f(x) = 5x-3

Answers

The answer is x= 3/5

simplify:
3х + 5y-x+ 2y
&
3g + 5h +4g - 2h​

Answers

♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️

[tex]3x + 5y - x + 2y = [/tex]

[tex]3x - x + 5y + 2y = [/tex]

[tex](3 - 1)x + (5 + 2)y = [/tex]

[tex]2x + 7y[/tex]

_________________________________

[tex]3g + 5h + 4g - 2h = [/tex]

[tex]3g + 4g + 5h - 2h = [/tex]

[tex](3 + 4)g + (5 - 2)h = [/tex]

[tex]7g + 3h[/tex]

♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️

Other Questions
Anybody know the answer to this? Which statement about the Articles of Confederation is true? They officially announced the independence of the United States and started the Revolutionary War.(a) They were the first constitution of the United States, and they united the newly independent states under a national government with limited power.B) They established the United States as a protectorate of Great Britain, capable of creating its own laws but relying on the British armed forces to defend it.C) Question 1 of 5In which way are electromagnetic waves different from mechanical waves? 25. The picture below shows a model of the rock cycle. During which part of therock cycle does water break rocks apart?sedimentaryheating and pressingmetamorphiccementingmeltingsedimentsweathering and erosionigneousa. part 1b. part 2C. part 3d. part 4 what are the solutions for the dependent population? Una caja registradora contiene $1782 en monedas de cinco pesos, de diez y de un peso. Hay 802 monedas en total, y 10 veces ms de 5 que de a 10 Cuntas monedas hay de cada una en la caja registradora? HELP WILL GIVE BRAINIEST AND 20 POINTS!! What organs can be found in the circulatory system?GIVE ABOUT 5 OR 6 13. Keep ato help you identify trends in your fitness habits that are particularly effective. (1 point)grade booksharp memoryvideo blogfitness journal which position represents a basic disagreement between Democrats and Republicans Sam needs to create a spreadsheet for his coworkers. They will need to follow across a long row of data. Sam would like to make his spreadsheet easy to read. Sam should _____. Pls answer (10 points!) Lionel works for an energy company interested in drilling for oil off the coast of a small island. The representative for the local fishing industry, Rochelle, says that locals are vigorously opposed to Lionels idea. A town meeting is held. Lionel explains how his company is dedicated to practicing the safest drilling techniques. He explains that oil piped from the oceans floor is purer and that it can be harvested in a more efficient way than an oil rig on land. Lionel also emphasizes how much the trucks carrying fish to the markets all over the country would save if local oil was able to be used. Rochelle fires back that in the past, serious accidents with offshore oil drilling have been reported. She points out that if there were a spill, the resulting death of fish would cost the local fisherman their livelihood. Local opinion on the issue is split. Before the town agrees to side with Lionels energy company or Rochelles local fish industry, officials order a report from a biotechnologist. Everyone agrees to go with what the biotechnologist recommends. Which side do you think the biotechnologist will agree with? Why?hurry please How would you say I watch in Spanish in a way that fits into this crossword Due Nov 3, 2:30 PM Attendance Question: What is the best candy to get on Halloween? Add class comment By using Euler's formula, find the number of edges of a polyhedron with 16 faces and 20 vertices why is sin(90 degrees) = 1. I know that that is the answer you get when you plug it into a calculator. I need an explanation as to why it equals 1 X - 2x- 11x + 30x - 20 entre x + 3x - 2 I need an example of Nuclear Chemistry.Any suggestions... Help quick plzThe options are:jeilnousilstuellevouselles Was perestroika successful?