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
Helpppp plssssss and thxxx
velikii [3]

Answer:

x ≤ 13

Step-by-step explanation:

hope this helps

5 0
3 years ago
Read 2 more answers
Solve the equation for all real solutions.<br> 8w2 + 2w + 2 = 3
fredd [130]

Answer:

Step-by-step explanation:

w=  1 /4   or w=  −1/ 2

3 0
3 years ago
The total revenue R earned (in dollars) from producing a gift box of candles is given by R(p)=-10p^2+800p, where p is the price
kherson [118]
A.) R(20) = -10(20)^2 + 800(20) = -10(400) + 16000 = -4000 + 16000 = $12,000

R(25) = -10(25)^2 + 800(25) = -10(625) + 20000 = -6250 + 20000 = $13,750

R(30) = -10(30)^2 + 800(30) = -10(900) + 24000 = -9000 + 24000 = $15,000

b.) For maximum revenue, dR/dp = 0
dR/dp = -20p + 800 = 0
20p = 800
p = 40

Therefore, the maximum revenue will be recorded when the price is set at $40.
4 0
3 years ago
15,16,13,22,14, 16 what is the outerlier
katovenus [111]
I would say that your answer is 22
5 0
3 years ago
The area of a rectangle whose perimeter is a fixed 80 feet is given by A=40w - w2 , where w is the width of the rectangle. Deter
Stolb23 [73]

Answer:

Width=20 feet

Since Length=Width=20 feet, the rectangle is a Square.

Step-by-step explanation:

Area, A=40w - w^2

To determine the width of the rectangle that gives the maximum area, we take the derivative of A and solve for its critical point.

A'=40 - 2w\\$When A'=0\\40-2w=0\\40=2w\\w=20 feet

The width of the rectangle that gives the maximum area =20 feet.

Perimeter of a rectangle=2(l+w)

Perimeter of the rectangle=80 feet

2(l+w)=80

2l+2(20)=80

2l=80-40

2l=40

l=20 feet

Since the length and width are equal, the special type of rectangle that produces this maximum area is a Square.

7 0
3 years ago
Other questions:
  • Find the least whole number that can replace to make the statement true.
    10·1 answer
  • What is the measure of &lt;1? (ON ALL THE PROBLEMS) And tell if 4 and 5 are right. ( d means degrees)
    11·1 answer
  • Choose a method the find the product 16x60
    10·2 answers
  • Create a 10 question survey with quantitative variables (number) on a topic you are interested in. Think of questions where 0 is
    11·1 answer
  • What’s the unit rate of y = 6x
    7·1 answer
  • A 222-inch pipe is cut into two pieces. One piece is five times the length of the other. Find the length of the shorter piece.
    6·1 answer
  • Use the number line below, where RS = 6y + 3, ST = 4y + 7, and RT = 60.​
    14·2 answers
  • Last someone someone helppp
    14·2 answers
  • I need help with this pls anybody if u know these pls help
    10·1 answer
  • Can you help me with this
    15·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!