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
Elenna [48]
3 years ago
5

Prove the following statement.

Mathematics
1 answer:
gayaneshka [121]3 years ago
6 0

Answer:

You can prove this statement as follows:

Step-by-step explanation:

An odd integer is a number of the form 2k+1 where k\in \mathbb{Z}. Consider the following cases.

Case 1. If k is even we have: (2k+1)^{2}=(2(2s)+1)^{2}=(4s+1)^{2}=16s^2+8s+1=8(2s^2+s)+1.

If we denote by m=2s^2+2 we have that (2k+1)^{2}=8m+1.

Case 2. if k is odd we have: (2k+1)^{2}=(2(2s+1)+1)^{2}=(4s+3)^{2}=16s^2+24s+9=16s^{2}+24s+8+1=8(2s^{2}+3s+1)+1.

If we denote by m=2s^{2}+24s+1 we have that (2k+1)^{2}=8m+1

This result says that the remainder when we divide the square of any odd integer by 8 is 1.

You might be interested in
Adrian took out a simple interest loan for $2000. The rate on this loan is 7% and he will pay it back in 5 years. How much money
laila [671]

Answer:

i think its 700

Step-by-step explanation:

7%of 2000 is 140 and 140 x 5 is 700

8 0
3 years ago
Read 2 more answers
Can you solve this problem please im having trouble with this question ​
Degger [83]

Answer:

The answer is 3.7

Step-by-step explanation:

Use cross multiplication to set up the equation then simplify,

17y = 63

  y = 63/17

  y = 3.705

Round to the nearest tenth.

Solution is y = 3.07

Good luck!

3 0
3 years ago
Read 2 more answers
Tina's age is 4 years less than 3 times her niece's age. If her niece's age is x years, which of the following expressions best
zubka84 [21]
3x-4 is the answer, you have to see that if its 3 times her nieces age it would be 3x and if its four less than that it is 3x-4
7 0
3 years ago
Read 2 more answers
Tim drives at an average speed of 80 km per hour for 3 hours and 45 minutes. work out how may kilometers Tim drives.
lara31 [8.8K]
Hey there!


Tim drives 300 kilometers.


Work: 80 x 3 = 240
Then, 45 minutes is 3/4 of an hour, so if you were to do 3/4 of 80  it is 60
Now, add 240 + 60 = 300

Hope I was able to help!
6 0
3 years ago
Read 2 more answers
35-2.4(7-5) <br> What is the answer to this question
laila [671]
30.2 is correct according to PEMDAS
8 0
3 years ago
Other questions:
  • What is the value of x in the equation 2(x-3)+9=3(x+1)+x?<br> x = -3<br> х=-1<br> x = 0<br> х= 3
    11·2 answers
  • Work out the balance for £4500 invested for 2 years at 4% per annum
    12·1 answer
  • Which is equivalent to 9+2i -(6+ 4i)?<br> [A] 3-212<br> [C] 15+6i<br> [B] 3-6<br> [D] 3-2i
    8·1 answer
  • PLS HELP HOMEWORK. Complete the function table. Then write a rule for the function. Explain
    14·1 answer
  • What’s the correct answer for this question? Select all that Apply
    7·1 answer
  • In order to safely land, the angle that a plane approaches the runway should be no more than 15°. A plane is approaching Ottawa
    9·1 answer
  • Helpppppp pleaseeeeeeeeee
    12·2 answers
  • Help plz assap with these 4 questions :(:)))
    11·2 answers
  • What is the perimeter of the figure
    13·1 answer
  • Which expressions have the same value as the product of 0.06 X 3.9?
    12·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!