1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
Archy [21]
2 years ago
9

N is a positive integer

Mathematics
1 answer:
Murrr4er [49]2 years ago
6 0

Part (1)

n is some positive integer. Let's say for now that n is even. So n = 2k, for some integer k

This means n-1 = 2k-1 is odd since subtracting 1 from an even number leads to an odd number.

Now multiply n with n-1 to get

n(n-1) = 2k(2k-1) = 2m

where m = k(2k-1) is an integer

The result 2m is even showing that n(n-1) is even

------------

Let's say that n is odd this time. That means n = 2k+1 for some integer k

And also n-1 = 2k+1-1 = 2k showing n-1 is even

Now multiply n and n-1

n(n-1) = (2k+1)(2k) = 2k(2k+1) = 2m

where m = k(2k+1) is an integer

We've shown that n(n-1) is even here as well.

------------

So overall, n(n-1) is even regardless if n is even or if n is odd.

Either n or n-1 will be even. If you multiply an even number with any number, the result will be even.

=======================================================

Part (2)

n is some positive integer

2n is always even since 2 is a factor of 2n

2n+1 is always odd because we're adding 1 to an even number. The sequence of integers goes even,odd,even,odd, etc and it does this forever.

-----------

Another way to see how 2n+1 is odd is to divide 2n+1 over 2 and you'll find that we get (2n+1)/2 = 2n/2+1/2 = n+0.5

The 0.5 at the end is not an integer, so there's no way that (2n+1)/2 is an integer; therefore 2n+1 is odd.

You might be interested in
How do you solve this?
konstantin123 [22]

Answer:

145

Step-by-step explanation:

180-137=43

43+102=145

4 0
3 years ago
Read 2 more answers
Use the graphing calculator to locate the solutions of this system of equations: y = x2 + x – 2 y = –x + 1
bonufazy [111]

Answer:

(–3, 4) and (1,0)

Step-by-step explanation:

5 0
3 years ago
Read 2 more answers
Based on previous sales, Ron predicted sales of 80 pen sets. He actually sold 100 pen sets. Find the error and absolute error fo
bagirrra123 [75]

Answer:

A=-20 B=20

Step-by-step explanation:

7 0
3 years ago
Read 2 more answers
What is the equation of a line that passes through points (2, 1)<br> and (3, 2)?
leva [86]

Good evening ,

______

Answer:

A. y=x-1

____________________

Step-by-step explanation:

Look at the photo below for the details.

:)

3 0
3 years ago
3. Find the values of the variables and the lengths of the sides of this kite.
Kazeer [188]

Answer:

So, the correct option is A. x = 9, y = 14 , Sides are 11 and 20

Step-by-step explanation:

P.S - the exact question is -

As given in the question ,

Side AB = Side AD

⇒y - 3 = x + 2

⇒y - x = 2 + 3 = 5

⇒y - x = 5                        .........(1)

Also, given

Side BC = Side CD

⇒2x + 2 = x + 11

⇒2x - x = 11 - 2

⇒x = 9

∴ equation (1) becomes

y - 9 = 5

⇒y = 5 + 9 = 14

⇒y = 14

∴ we get

x = 9, y = 14

Now,

as given ,

Side AB = y - 3

⇒ AB = 14 - 3 = 11

Side BC = 2x + 2

⇒ BC = 2(9) + 2 = 18 + 2 = 20

Side CD = x + 11

⇒ CD = 9 + 11 = 20

Side DA = x + 2

⇒DA = 9 + 2 = 11

∴ we get

The sides are 11 and 20

So,

The correct option is A. x = 9, y = 14 , Sides are 11 and 20

8 0
2 years ago
Other questions:
  • what is the sum of a 7-term geometric series if the first term is −6, the last term is −24,576, and the common ratio is −4? −32,
    8·1 answer
  • Your task is to build a road joining a ranch to a highway that enables drivers to reach the city in the shortest time. The perpe
    12·1 answer
  • PLZ HURRY, 20 POINTS. Is this equation true or false, if its true tell the answer, if its false than no answer.
    13·2 answers
  • Angelina factored (x - 48 ) and wrote that it was equal to (x^2 - 4^2)^2(x^2 + 4^2). Use complete sentences to explain how you c
    8·1 answer
  • Find the inverse of the function f(x) = x3 + 5
    5·1 answer
  • Given g(x)=30-6x, find g(-4)=____?
    8·1 answer
  • Which of the following angles is coterminal with - 2pi/3
    11·1 answer
  • The original price of an item was $20.00. It was marked up 25%. What is the new selling price?
    5·2 answers
  • Find an equation of the line that has a slope of 9 and a y intercept of -2.
    7·2 answers
  • Solve for x and explain the steps:<br> 3x-6=4(2-3x)-8x
    8·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!