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
telo118 [61]
3 years ago
15

Prove that the sum of the squares of two consecutive integers is odd

Mathematics
2 answers:
iren2701 [21]3 years ago
8 0

Answer: Every even number can be expressed in the form (2n) where n is an integer. So we have an even number, 2n, and an odd number, 2m+r. Adding them together we get 2n + 2m + r, which can be expressed as 2 (n+m) + r.

seraphim [82]3 years ago
4 0

Answer:

Step-by-step explanation:

Start by breaking up the question into parts:'always an odd number' . An even number is any number divisible 2 e.g. 2n, an odd number is always 1 higher or lower than an even number e.g. 2n+1 or something similar. Getting an answer at the end of working of this form will prove the theory'any two consecutive integers' means two numbers that are next to each other on the number line.To prove this, we can do this in terms of n i.e. n and n+1'the squares' square the two terms we have just written down to give n2 and (n+1)2The 'sum of the squares' tells us to add these two parts together. We would then hope to work through this and get something similar to the idea of 2n+1 or something similarn2+(n+1)2=2n2+2n+1=2(n2+n) +1. The first part of this is even because it is divisible by 2. By adding 1 it must become odd.

You might be interested in
The graph of g(x) is obtained by reflecting the graph of f(x)=2|x| over the x-axis.
Lera25 [3.4K]
Answer: Choice C) 
g(x) = -|2x|

You get this answer by simply sticking a negative out front of the original function. In other words, g(x) = -f(x) or more technically, g(x) = -1*f(x).

The negative will flip every y coordinate from positive to negative (or vice versa)

You'll also use the idea that |2x| = 2|x|. The two can be pulled out since we can say |x*y| = |x|*|y|
So |2*x| = |2|*|x| = 2|x|

4 0
3 years ago
A car rental company charges a daily rate of $ 23 plus $ 0.20 per mile for a certain car. Suppose that you rent that car for a d
MAXImum [283]

Answer: 105 miles?

I am not sure but that"s what I got

Step-by-step explanation:

8 0
3 years ago
Read 2 more answers
What’s the value of 1 2/3 divided by 1 7/18 In mixed number fraction form someone please help :)
JulsSmile [24]
12/3=4
4 divided by 17/18 equals to 4* 18/17=72/17= 4 4/17
Thus the answer is 4 4/17
4 0
3 years ago
Which expression is equivalent to sec^2x − 1? a. cot2x b. tan2x c. csc2x d. cos2x
Nesterboy [21]
Sec^2 x - 1 = tan^2x

Proof:
Sec^2x = 1+ tan^2x

1/cos^2x = 1 + sin^2x/cos^2x

<span>1/cos^2x - sin^2x/cos^2x = 1
</span>Using common denominator:
(1-sin^2x)/cos^2x = 1
sin^2x + cos^2 x = 1
cos^2 x = 1 - sin^2x
Substituting : 
cos^2x/<span>cos^2x = 1
</span>1 = 1
Left hand side = right hand side 
4 0
3 years ago
Read 2 more answers
What is the slope of the line.
makkiz [27]
-4/5 is the skip of the graph
4 0
3 years ago
Read 2 more answers
Other questions:
  • Add or subtract them in simplest form please help me as fast as possible
    10·1 answer
  • Find the length of the missing side: the lengths are 14m &amp; 5m
    14·1 answer
  • Help me please it is important
    14·1 answer
  • Circle O has a circumference of approximately 44 in.
    13·2 answers
  • 8. Let α, β, γ be the angles made by a vector u ∈ R 3 with positive x, y, z−axis respectively. Then, the numbers l = cos α, m =
    10·1 answer
  • What is a.missing term in each proportion 6:n = 8:12
    11·2 answers
  • Silas claims that the equation y=2+mx, where m is a real number, represents a function whose graph is a straight line.
    7·2 answers
  • NEvermind ..............
    11·2 answers
  • Anu and Aji solve an equation. In solving Anu commits a mistake in constant term and finds the roots 8 and 2. Aji commits a mist
    15·1 answer
  • Find the product.<br> 0.18 × 4
    7·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!