what is the largest integer that always divides $(n 1)(n 3)(n 5)(n 7)(n 9)$ for all positive even integers $n$?

Answers

Answer 1

The largest integer that always divides (n+1)(n+3)(n+5)(n+7)(n+9) for all positive even integers n is 15.

What is positive integer?

Positive integers are numbers such as 1, 2, 3, etc. They are also called countable or natural numbers. A positive number is any number greater than zero.

Let P(n) = (n+1)(n+3)(n+5)(n+7)(n+9) be a polynomial for all positive even integers, n . We have to calculate the largest integer that always divides the P(n) .

Let "l" be the largest integer that divides P(n) for each n∈N . Then, l must divide both P(1) and P(2)

i.e, P(1) = (1+1)(1+3)(1+5)(1+7)(1+9) = 2×4×6×8×10

= 2^8×5×3

P(2) = 3×5×7×9×11 , hence , l divides 15.

Since, n + 5 ≡ (n+2) mod(3), one (and exactly one) of the numbers n+1 , n+3 , n+5 must be multiple of 3 . Thus, 3/P(n) for each n∈N.

Since, n+7 ≡ (n+2)mod(5) and n+9 ≡ (n+4)mod(5),

one (and exactly one) of the numbers n+1 , n+3 , n+5 , n+7 and n+9 , must be multiple of 5.

Thus, 5/P(n) for each n∈N.

Therefore, 15/p(n) for each n∈N , so that l = 15 .

So, required value of n is 15.

To learn more about positive integer , refer:

https://brainly.com/question/1367050

#SPJ4

Related Questions

7x −28 solve for inequality

Answers

Answer:

7(x-4)

Step-by-step explanation:

You can use an Algebra calculator btw.

Find the slope from the table:
X | Y
0 | -1
2 | 3
5 | 9
6 | 11

Answers

Answer:

The slope is 2

Step-by-step explanation:

Pick two points.

ex: (0,-1) and (2,3)

do the equation below where 0=x1, -1=y1, 2=x2, 3=y2

y2-y1 divided by x2-x1

3-(-1) divided by 2-0

4/2

sorry this was kind of hard to explain on a computer :/

I’m not completely sure but I think it’s x/y also I’m only in 7th sorry

A student cuts out a rectangular strip of paper that has an area of 2/3 square meter. If the width of the paper strip is 1/5 meter, what is the length of the strip, in meters?

Answers

Answer:

3 1/3

Step-by-step explanation:

Perform the inverse operation: l = a/w

(2/3)/(1/5)

Find the common denominator.

It is 15 in this case.

(10/15)/(3/15)

150/45

3 1/3

Check your work.

a = 3 1/3 x 1/5

a = 2/3

This is true.

The answer is 3 1/3

-Xax

IM RUNNING OUT OF TIME SO PLss ANYONEEE

Answers

Answer:

x= -2

Step-by-step explanation:

If the slope is zero, that means the line is horizontal.

Answer: y=7

Step-by-step explanation:

solve x , y , and z. Please help

Answers

Answer:

z and x equal 143

y equals 37

Step-by-step explanation:

37-180=143

The area of a square is 75 inches squared. A student correctly wrote the length of each side of the square as a√3. What is the value of a?

Answers

Answer: 5 in.

Step-by-step explanation:

Given

The area of the square is [tex]75\ in.^2[/tex]

The side length of the square is [tex]a\sqrt{3}[/tex]

Area of square[tex]=(\text{length})^2[/tex]

[tex]\therefore 75=(a\sqrt{3})^2\\\Rightarrow 75=3a^2\\\Rightarrow a^2=25\\\Rightarrow a=5\ in.[/tex]

Thus, value of a is 5 inch

Caleb made a scale drawing of a theater. He used the scale 7 inches = 10 feet. What is the scale factor of the drawing?

Answers

Answer:

10 feet = 120 inches

120 / 7 = 17.1428571429

So, the scale is 17.1428571429 to 1.

Step-by-step explanation:

What are the steps you would take to find the area of the shaded region? Check all that apply.

Answers

Answer:

THE ANSWER IS INCOMPLETE SO IM GOING TO REPORT:/

Step-by-step explanation:

8 ( x + 4) = 62. 4. x = _____

Answers

Answer: 0.05

Step-by-step explanation: Ur welcome

Step-by-step explanation:

8×x+8×4=62.4.x=_

8x+32=62.4.x=_

8x=62.4-32

8x=30.4

x=30.4:8

x=3.8

If the simple interest on a sum of money invested at 3% per annum for 242 years is N123, find the
principal

Answers

The principal is N16.94

Step-by-step explanation:

Simple Interest = (Principal × Rate × Time)/100

Principal = (Simple Interest × 100)/(Rate × Time)

Principal = (123 × 100)/(3 × 242)

Principal = 12300/726

Principal = 16.9421

Helppp I need to finish this !!!!!

Answers

Answer:

filled in dot on -2 and shade the rest to the right (see below)

Step-by-step explanation:

This can also be read as "x is equal to or greater than -2." The "alligator" mouth, aka the inequality sign, is "eating" the x, meaning it's greater than the -2.

First graph the -2. Because it's also equal to, the dot on the -2 is filled in.

The inequality also acts as an arrow. It's pointing to the right, so the rest of the number line to the right is shaded.

This arrow method works only when the variable is on the left side so that is read "x is greater/less than a number."

EAR is rotated 180° about the origin.

plsss help

Answers

Answer:

rotating ΔEAR 180° inside the right angle parallelogram circumscribed by.

original coordinates:

A (-6, 4)

R (-2, 2)

E (-5, -6)

post rotation coordinates:

A (-2, -6)R (-6, -4)E (-3, 4)

If a farmer sells 9.8 KL of apples and pears at the farmers market. 4/5 of this weight is apples,and the rest are pears. How many kl of pears did they sell the farmers market

Answers

Answer:

1.96

Step-by-step explanation:

A farmer sells 9.8 kl of apples and pears

4/5 of this weight is apples, while the rest are pears

Therefore the wight of pears can be calculated as follows

Let x represent the weight of pears

9.8= 4/5×9.8 + x

9.8= 0.8×9.8+x

9.8= 7.84+x

9.8-7.84= x

x= 1.96

i need help with this question plsss

Answers

Answer:

180

Step-by-step explanation:

because angles on the same line sum up to 180

A rectangular prism is 12 feet long, 8 feet wide and 11 feet tall. What is the
surface area? *
192
440
632
O
1056

Answers

Answer:

632 square feet

Step-by-step explanation:

Surface area of the prism = 2(lw+wh+lh)

L is the length = 12feet

w is the width = 8feet

h is the height = 11feet

Substitute

S = 2(12*8 + 12*11 + 8*11)

S = 2(96+132+88)

S = 2(316)

S = 632 square feet

Hence the surface are of the prism is 632 square feet

I need help with this pls I out 30 points

Answers

Answer:

Step-by-step explanation:

Age: Frequency:

50-54 2

55-59 5

60-64 3

65-69 3

Kiran cuts out a square piece of paper with side length 6 inches. Mai cuts out a paper sector of a circle with radius 6 inches, and calculates the arc length to be inches. Whose paper is larger? Explain or show your reasoning.

Answers

Arc length doesn’t matter. Area does.

Area of a square: bh = 6x6 = 36 inches squared

Area of a circle: 3.14(r^2) = 3.14(36)= 113 inches squared

Mai’s paper is much larger.

A circle is a curve sketched out by a point moving in a plane. The area of the circular paper is more than the area of the square.

What is a circle?

A circle is a curve sketched out by a point moving in a plane so that its distance from a given point is constant; alternatively, it is the shape formed by all points in a plane that are at a set distance from a given point, the centre.

The arc length of radius 6 inches is equal to,

Length of the Arc of a quarter = 2πr×(1/4) = 2×π×6×0.25 =0.9448 inches

The area of the circular paper = πr² = π×6×6 = 113.097²

The area of the square with a side of 6 inches = 36 in²

Therefore, the area of the circular paper is more than the area of the square.

Learn more about Circle:

https://brainly.com/question/11833983

#SPJ2

Brad had a small gathering at a local steakhouse. The steakhouse offers three dinner platters which vary by size and price. They ordered 4 of the 6-ounce platters, 3 of the 8-ounce platters, and 3 of the 11-ounce platters. Steak Platter Prices
• 6-ounce $9.95
• 8-ounce $12.95
• 11-ounce $15.95

If a gratuity of 16% was added to the bill, which of the following is closest to the total of the steak platters and gratuity, ignoring sales tax?

Answers

Answer:

Ok if you get this worng im so sorry but I got $6.21

Step-by-step explanation:

Which equation represents a line which is perpendicular to the line 4x + 3y = - 24 ?

Answers

Answer:

Step-by-step explanation:

4x+3y=-24

eq. of any line perpendicular to given line is

3x-4y=a

4y=3x-a

y=3/4x -a/4

where a is an arbitrary constant.

I’ll give brainliest! Help please!!!!

Answers

Don’t press that link please

in a school the number of girls exceeds the number of boys by 15% find the ratio number of boys to number of girls

Answers

Answer:

20:3

Step-by-step explanation:

no.of boys /no.of girls =20:3

Find the volume of the given figure.

Answers

364.5 cm sq

or

365 1/2 cm sq

HELPPPPPPPPPP
What is the value of x in the triangle?

Answers

Answer:

x=130

Step-by-step explanation:

Hello There!

Remember the sum of the angles in a triangle is 180

So we can find the missing angle by subtracting the given angles (25 and 25 in this case) from 180

so x = 180 - 25 - 25

180 - 25 = 155

155 - 25 = 130

x = 130

23. Daniel bought a gallons of paint at the store for a project. At the end of his project,
Daniel had 1 gallons of paint left. How much paint did Daniel use for his project?
A. 3. gallons
B.3 gallons
c. 2. gallons
D. 6 gallons

Answers

Answer:

Based on your responses and my understanding from what you have said the answer is B.

Step-by-step explanation:

That the wrong answer

Answers

Answer:

what's your question?

Step-by-step explanation:

I’m about to spam questions if you can answer them please do .

Answers

Answer:

id say anything between 15 to 30 i dont have the stuff i need to answer this 100% accurately

Step-by-step explanation:

Answer:

Step-by-step explanation:

90 plus 40 ,then you subtract it from 180

Please help me please

Answers

Answer:

1) g < -6

2) x < -5

3) f < 2

4) y ≤ -2

5) p ≥ 2

which point on the number line represents --3/4

Answers

Answer:

Step-by-step explanation:

Because it is 3 tics closer to 1. which would be 3/4 of 1

Anyone know how to do this?

Answers

Answer:

Step-by-step explanation:

Given the coordinates of A(3, 6), B(5, 2), and C(9, 4), which coordinates for D make ABCD a square?

Answers

Answer:

(7,8)

Step-by-step explanation:

The point D is (7, 8) for which the given coordinates of A(3, 6), B(5, 2), and C(9, 4), make a square.

What is a square?

It is defined as a two-dimensional geometry that has four sides and four vertices. The sides of the square are equal in length. It is a regular quadrilateral.

Line AB and CD are parallel to each other.

Line AB:

(y- 6) = -2(x-3)

y - 6 = -2x+6

2x+y = 12

Line CD:

2x + y = d

Plug (9,4)

18+4 = d

d = 22

2x + y = 22 ...(1)

Line BC:

(y - 2) = 1/2(x-5)

2y -4 = x-5

-x + 2y = -1

x - 2y = 1

Line AD:

x - 2y = e

3 - 12 = e

e = -9

x-2y = -9 ...(2)

The intersection point of (1) and (2)

x = 7 and y = 8

Thus, the point D is (7, 8) for which the given coordinates of A(3, 6), B(5, 2), and C(9, 4), make a square.

Learn more about the square here:

https://brainly.com/question/14198272

#SPJ2

Other Questions

Give practical this question answer TO PREPARE BARIUM SULPHATE BY THE PRECIPITATION REACTION BETWEEN BARIUM CHLORIDE AND SULPHURIC ACID Did Queen Gertrude cheat on King Hamlet? How many elements are in AlCl(OH) How do I organize my garage recycling bins? What is the mean of the following numbers 23 45 87 40 50? To diplay the ditribution of the length in inche of a ample of brook trout, you could ue Can my ex get in trouble for claiming my child on taxes? Why do you think that Chapter 23 ends with Jim tells Huck about the time he beat his daughter for not listening to him all the while not knowing that she was deaf? A community group is selling prize tickets to raise money for a city park. The group spent $300 on prizes and sells tickets for $30 each. How many tickets does the group need to sell to make a profit of $900?. A bakery records whether the customer is a loyalty program member or not on each receipt.Total purchase price for both members and non-members is skewed toward the higherprices.The bakery takes separate random samples of 45 receipts from members and non-members.They look at the difference in the mean total price from each group(member - non-member).What do we know about the shape of the sampling distribution of TM - IN, and why? Consider a town in which only two residents, Lorenzo and Neha, own wells that produce water safe for drinking. Lorenzo and Neha can pump and sell as much water as they want at no cost. Assume that outside water cannot be transported into the town for sale. The following questions will walk you through how to compute the Cournot quantity competition outcome for these duopolists. Consider the market demand curve for water and the marginal cost for collecting water on the following graph. Assume Lorenzo believes that Neha is going to collect 12 gallons of water to sell. On the graph, use the purple points (diamond symbols) to plot the demand curve (D1) Lorenzo faces; then use the grey points (star symbol) to plot the marginal revenue curve (MR1) Lorenzo faces. Finally, use the black point (plus symbol) to indicate the profit-maximizing price and quantity (Profit Max 1) in this case. Instead, now assume Lorenzo believes that Neha is going to collect 16 gallons of water to sell, rather than 12. On the following graph, use the purple points (diamond symbol) to plot the demand curve (D2 ) Lorenzo faces; then use the grey points (star symbol) to plot the marginal revenue curve (MR2 ) Lorenzo faces. Finally, use the black point (plus symbol) to indicate the profit-maximizing price and quantity (Profit Max 2) in this case. Fill in the following table with the quantity of water Lorenzo produces, given various production choices by Neha. Given the information in this table, use the green points (triangle symbol) to plot Lorenzo's best-response function (BRF) on the following graph. Since Lorenzo and Neha face the same costs for producing water, Neha's best-response function is simply the reverse of Lorenzo's; that is, the curve has the same shape, but the horizontal and vertical intercept values are switched. Therefore, you can derive Neha's best-response function by following the same analysis as in the previous question, but from Neha's perspective. Use the purple points (diamond symbol) to plot her best-response function on the graph. Finally, use the black point (plus symbol) to indicate the unique Nash equilibrium under Cournot quantity competition. True or False: According to her best-response function, Neha will always want to decrease her output as Lorenzo decreases his. O True O False Does Amazon usually deliver early or late? 2naoh + h2so4 na2so4 + h2o the equation is___because the number of hydrogen atoms and atoms____is____in the reactants and in the products. PLEASE HELP! Why is it possible that the oxygen and carbon dioxide on earth will never be used up in regard to photosynthesis and respiration? Which Kubernetes object is created in a deployment? When someone has the plaintext and the corresponding ciphertext which of the following will provide the crypto variable O Linear cryptanalysis attack O Chosen plaintext O Chosen ciphertext O Brute force What is the lewis structure of I3-? morrisey company has two investment opportunities. both investments cost $6,400 and will provide the same total future cash inflows. the cash receipt schedule for each investment is given below: Robert owns 50 shares of stock from a certain corporation. Each share is worth $3.00. After the corporation declares a two-for-one stock split, his shares are wortheach help again asap pls!!!!!!!!!