Show that n^2-1 is divisible by 8,if 'n' is an odd positive integer.

Answers

Answer 1

Answer: $n-an\ odd\ positive\ integer\ \ \ \Rightarrow\ \ \ n=2k+1\ \ \ and\ \ \ k\in Natural\n\nn^2-1=(2k+1)^2-1=(2k)^2+2\cdot2k\cdot1+1^2-1=4k^2+4k=\n\n=4k(k+1)\n\nif\ k-odd\ \ then\ (k+1)-even,\ \ \ then\ k(k+1)-even\n\n\ \ \ \Rightarrow\ \ \ k(k+1)=2m\ \ \ and\ \ \ m\in N\ \ \ \Rightarrow\ \ \ 4k(k+1)=4\cdot2m=8m\n\n\nif \ k-even,\ \ \ then\ k(k+1)-even\n\n\ \ \Rightarrow\ \ \ k(k+1)=2p\ \ \ and\ \ \ p\in N\ \ \ \Rightarrow\ \ \ 4k(k+1)=4\cdot2p=8p\n\n$

$------------------------\n\n for\ each\ k \in N\ the\ product\ of\ \ \ k (k +1)\ \ \ is\ even,\ so:\n\nif\ 'n'\ is\ an \ odd\ positive\ integer,\ then\ \ \ n^2-1\ \ \ is\ divisible\ 8.$

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Nine times the sum of a number and 2 is 189. I need to make it to an equation.

Given x varies inversely with y and xy = 2, what is the value of x when y = 1?a) -1

b) 1/2

c)1

d) 2

Answers

Answer is (d).

Let's take the constant as K.
x=K. (1/y)----(1)'
K= xy
so; according to the data given above K=2.

Let's substitute K=2 & y=1 to ----(1)'

x=2x (1/1)
x= 2×1
so x = 2... :)

Helpppppp which of the following features of the online textbook will allow you to receive extra instruction on a topic? A. Companion workbook
B. Visual glossary
C. Practice and problem solving workbook
D. Homework video tutors

Answers

Answer:

Option: D is correct.

( D. Homework video tutors )

Step-by-step explanation:

" Homework Video tutors:

Narrated by real school teachers, these online video tutorials provide students with homework help on key concepts of every lesson "

Hence, Homework video tutors are the online textbook which allow you to receive extra instruction on a topic.

Hence, option D is the correct answer.

i'd say D. because that's what a lot of mine have

hope this helped :D

Tile costs $28 per square meter. how much will it cost to cover the countertop with new tile? (48 square Feet)

Answers

You multiply 48 by28. You get 1344.So it would cost $1,344.00.

The Line Of Symmetry Divides A Design So That Every Point On One Side Of The Line _____ A Point On The Other Side Of It. A. Coincides With B. Is Equal To C. Is Rotated To D. Becomes

Answers

The Line Of Symmetry Divides A Design So That Every Point On One Side Of The Line coincides with a point on the other side

The correct answer is A. Coincides with

Answer: The answer is A. Coincides with

Step-by-step explanation:

4x²+8x=1 by completing the square

Answers

First thing you do is subtract both sides by 1.
Then divide everything by 4, to remove the 4x².
After completing the square, you multiply the 4 back in.

Photo attached.
Hope the answer is right >-<
Have a Brainly day!

A set of face cards contains 4 Jacks, 4 Queens, and 4 Kings. Carlie chooses a card from the set, records the type of card, and then replaces the card. She repeats this procedure a total of 60 times. Her results are shown in the table.How does the experimental probability of choosing a Queen compare with the theoretical probability of choosing a Queen?

The experimental probability is 4 less than the theoretical probability.
The experimental probability is 1/15 less than the theoretical probability.
The experimental probability is 1/15 more than the theoretical probability.
The experimental probability is 4 more than the theoretical probability.

Answers

The experimental probability is 1/15 less than the theoretical probability.

Given

A set of face cards contains 4 Jacks, 4 Queens, and 4 Kings.

Carlie chooses a card from the set, records the type of card, and then replaces the card.

She repeats this procedure a total of 60 times. Her results are shown in the table.

What is experimental probability?

Theoretical probability describes how likely an event is to occur.

The theoretical probability of choosing a Queen is;

$\rm Theoretical\ probability= (Observed \ frequency)/(Probability \ of \ selecting \ Queen)\n\n Theoretical\ probability= (16)/(4)\n\n Theoretical\ probability= (4)/(1)$

What is experimental probability?

Experimental probability describes how frequently an event actually occurred in an experiment.

The experimental probability of choosing a Queen is;

$\rm Experimental \ probability = Relative \ frequency\n\nExperimental \ probability = (4)/(15)$

For comparing the theoretical and experimental probability of both equations.

$\rm =(Experimental \ probability)/(Theoretical \ probability)\n\n= ((4)/(15))/((4)/(1))\n\n= (4)/(15)* (1)/(4)\n\n= (1)/(15)$

Hence, the experimental probability is 1/15 less than the theoretical probability.

To know more about Experimentalprobability click the link given below.

brainly.com/question/3733849

Answer:

the answer is b

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