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
Tasya [4]
3 years ago
15

Prove that the sum of the squares of any two odd numbers is always even

Mathematics
1 answer:
ValentinkaMS [17]3 years ago
6 0

Answer:

proof below

Step-by-step explanation:

Remember that a number is even if it is expressed so n = 2k. It is odd if it is in the form 2k + 1 (k is just an integer)

Let's say we have to odd numbers, 2a + 1, and 2b + 1. We are after the sum of their squares, so we have (2a + 1)^2 + (2b + 1)^2. Now let's expand this;

(2a + 1)^2 + (2b + 1)^2 = 4a^2 + 4a + 4b + 4b^2 + 4b + 2

= 2(2a^2 + 2a + 2b^2 + 2b + 1)

Now the sum in the parenthesis, 2a^2 + 2a + 2b^2 + 2b + 1, is just another integer, which we can pose as k. Remember that 2 times any random integer, either odd or even, is always even. Therefore the sum of the squares of any two odd numbers is always even.

You might be interested in
Fraction Questions:
bagirrra123 [75]

Answer:

0

Step-by-step explanation:

3 0
2 years ago
Read 2 more answers
2. Select the situation below that result in zero. * 0 points A. A diver is at sea level, reaches a depth of 6 ½ feet and descen
Komok [63]

Answer: B and C only

Step-by-step explanation:

The temperature on a cold day starts at 0 degrees Celsius, falls 4 degrees, and rises 4 degrees

Initial temperature = 0

Temperature rise = 4

Fall in temperature = - 4

(Initial temperature + rise in temperature + fall in temperature)

Summing all : (0 + 4 - 4) = 0

carbon atom has 6 negatively charged electrons and 6 positively charged protons.

Net charge of atom :

(number of proton + number of electrons)

( 6 + (-6)) = 0

8 0
3 years ago
What is the slope of a line perpendicular to the line whose equation is 6x+4y=-56
alex41 [277]

Answer:

First, put the equation of the line given into slope-intercept form by solving for y. You get y = -2x +5, so the slope is –2. Perpendicular lines have opposite-reciprocal slopes, so the slope of the line we want to find is 1/2. Plugging in the point given into the equation y = 1/2x + b and solving for b, we get b = 6.Step-by-step explanation:

|\   /|

 \|_|/

 /. .\

=\_Y_/=

 {>o<}

5 0
2 years ago
What are the similarities and differences between comparing whole numbers and decimals
Helga [31]
There both types of numbers but a whole number is a number with no exponents or decimals, but decimals are like a broken un half whole number
3 0
3 years ago
Read 2 more answers
Pls pls help I no understand
vazorg [7]

Answer: 2p+1.50=11.50

               p = 5.00

<u>Step-by-step explanation:</u>

<em>Note: the tip is calculated on top of the total so this figure is a redherring</em>

<u>2 pancakes</u> <em>plus</em> <u>1 fruit cup</u> <em>equals</em> <u>total bill</u>

          2p       +        1.50          =         11.50

2p + 1.50 = 11.50

<u>      - 1.50 </u> <u> - 1.50  </u>

 2p         = 10.00

<u>÷2          </u>    <u> ÷2       </u>

    p         =  5.00

8 0
3 years ago
Other questions:
  • How do you turn a inproper mixed fraction proper
    15·2 answers
  • (x+1)(x+8)=<br><br><br> can somebody help me on this
    5·1 answer
  • Y=-5 sketch the graph
    11·1 answer
  • I neeeee helppppppppp
    15·1 answer
  • A flower shop ordered 1,176 flowers to make bouquets. Each bouquet will have 12 flowers. How many bouquets can the flower shop m
    5·1 answer
  • Helps with this math problem please
    12·1 answer
  • WILL MARK YOU AS BRAINLIEST!!!!!!!!!! PLEASE HELP DUE TODAY AT 1 :(((((
    6·1 answer
  • The temperature dropped 3 °F every hour for 6 hours. How much did the temperature drop in total
    14·1 answer
  • Solve -4x – 8y = -48<br> 8x + 3y = -34.
    15·1 answer
  • Can someone help me please?! :’)
    6·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!