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

Answers

Answer 1

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.

Answer 2

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.


Related Questions

Problem of the Day 7.7
Joshua swims 18 laps every day at swim practice. If he swims every day for 32 days, how many laps has he completed?

Answers

Answer:

576

Step-by-step explanation:

18 x 32 = 576

Which segment is a reflection of segment AB over the line x = 1?
Line segment C D
Line segment E F
Line segment G H
Line segment I J

Answers

Answer:

EF

Step-by-step explanation:

this line is a mirror version of AB when you reflect it across x=1

Hope this is helpful! :))

Answer:

EF

Step-by-step explanation:

Edge2021

hey please help with giving brainliest

Answers

Answer:

I think second bullet point

Step-by-step explanation:

Answer:

B adjacent

Step-by-step explanation:

angles aren't complementary because complementary angles add up to 90 and we don't know the values.

they are not vertical because they are not vertical to each other

I hope this helped you :)

Find the surface area of the rectangular prism.
3 in.
2 in.
4 in.

1.)60 in 2
2.)84 in 2
3.)26 in
4.)52 in2

Answers

Answer:

52 Inches³

Step-by-step explanation:

The surface area formula for a rectangular prism is 2 x (height x width + width x length + height x length)

SA= 2(4x2+2x3+4x3)

please help thank you​

Answers

the perimeter of the square is 4cm

6 because the perimeter is the outside total of a shape each individual line is 1cm (yiu only count what’s outside the box) so your would get 6.

Help, please!!!!!!!!

Answers

y= 3/2 x+ 3 and 3x-2y=-6

Step-by-step explanation:

□y = -3/2x-9

□y=3x+3

□3x+2y=-9 = y=-9/2 -3/2x

□y=3/2x+3 correct

□3x-2y=-6 = y=3+ 3/2x correct

□2/3x +3

Pippin owns 2 cats, 3 dogs, and a lizard as pets. What is the ratio of the number of cats to the total number of pets Pippin owns?
Choose 1 answer:
is it
A 1/6
B 1/3
C 2/5
D 1/2
or E 2/3

Answers

Answer: B) 1/3

2 cats/6 total animals

simplified is 1/3

Step-by-step explanation:

Answer:

1/3

Step-by-step explanation:

plz make me brainliest

if there are 300 seventh graders, and 80% passed the benchmark, how many passed the benchmark

Answers

Answer:

240 seventh graders passed

Step-by-step explanation:

300 x 0.8 = 240

What is an equation of the line that passes through the point (-6,-2)(−6,−2) and is parallel to the line 3x-2y=23x−2y=2

Answers

Answer:

y = 3/2x + 7

Step-by-step explanation:

If two lines are parallel to each other, they have the same slope.

The first line is 3x - 2y = 2. First, let's put this into standard form.

3x - 2y = 2

Add 2y to both sides to make y positive.

3x = 2y + 2

Subtract 2 from both sides to isolate y.

3x - 2 = 2y

Isolate y further by dividing both sides by 2.

3/2x - 1 = y or y = 3/2x - 1

This is now your first line. Its slope is 3/2. A line parallel to this one will also have a slope of 3/2.

Plug this value (3/2) into your standard point-slope equation of y = mx + b.

y = 3/2x + b

To find b, we want to plug in a value that we know is on this line: in this case, it is (-6, -2). Plug in the x and y values into the x and y of the standard equation.

-2 = 3/2(-6) + b

To find b, multiply the slope and the input of x (-6)

-2 = -9 + b

Now, add 9 to both sides to isolate b.

7 = b

Plug this into your standard equation.

y = 3/2x + 7

This equation is parallel to your given equation (y = 3/2x - 1) and contains point (-6, -2)

Hope this helps!

4x – 2y = -8
y = 2x + 4

Answers

Answer:

Set any x and then compute y as 2x + 4. The pair solves the equations.

Step-by-step explanation:

4x - 2y = -8

4x = 2y - 8

2x = y - 4

y = 2x + 4

2x + 4 = y

2x = y - 4

Both equations are the same, so any pair of x and y for which 2x = y - 4 works.

Set any y and then compute x as (y - 4)/2

Alternatively

2x = y - 4

2x + 4 = y

Set any x and then compute y as 2x + 4.

Write equivalent fractions for 2 2/5 and 1 3/4 using a common denominator

Answers

Answer:

12/5 and 15/5

Step-by-step explanation:

I think this is the answer based on ur question but sry if I'm incorrect. boom roasted.

See screenshot Please! :) and help ASAP thank youu!! <33

Answers

Answer:

A.

Step-by-step explanation:

A. makes the most sense out of all of them. But if it had to be another one, I'd say D. Sorry! I'm not the best at these either. :)

Find the circumference and area of a circle with a diameter of 22 inches. Leave your answers in terms of pi. (4 points) a C = 110; A = 440. b C = 22n; A = 440 C C = 110; A = 1210 C = 22n; A = 1210​

Answers

Answer:

C = 22[tex]\pi[/tex]

A = [tex]121\pi[/tex]

Step-by-step explanation:

Please let me know if you want me to write an explanation for my answer :)

Between which two consecutive whole numbers does \sqrt{5} 5 Between which two consecutive whole numbers does \sqrt{5} 5 lie? Fill out the sentence below to justify your answer and use your mouse to drag \sqrt{5} 5 to an approximately correct location on the number line.

Answers

Answer:

2 and 3

Step-by-step explanation:

Sqrt(5) will lie between the square root of the perfect square before 5 and the square root of the perfect square after 5

Perfect square before 5 = 4

Perfect square after 5 = 9

sqrt(4) and sqrt(9)

2 and 3

write an equation perpendicular to y=1/5 x+9 that passes through the point (-2,-2)

Answers

Answer:

-2= 1/5x-2 +9

-2= -0.4 +9

Step-by-step explanation:

Find the slope of the line passing through (3, 7) and (6, 11). Note: Use the y-y/x-x formula!

Answers

Answer:

Slope of the line       [tex]m = \frac{4}{3}[/tex]

Step-by-step explanation:

Explanation:-

Given points are ( 3,7) and (6,11)

Slope of the line

        [tex]m = \frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]

       [tex]m = \frac{11-7}{6-3}[/tex]      

        [tex]m = \frac{4}{3}[/tex]

Slope of the line       [tex]m = \frac{4}{3}[/tex]

Find the difference in slopes. Can anyone help me with this? I need it, its a grade for my mah class.

Answers

Answer:

Slope of the graphed line, using 2 points (-1, 3) and (0, 0):

m₁ = 3/-1 = -3

Slope of the line containing the points (-6, 2) and (-9, 5):

m₂ = (5 - 2)/(-9 - (-6)) = 3/-3 = -1

The difference in number between the slopes:

-3 - (-1) = -2

The difference in slopes:

The slope of the graphed line is 3 times steeper.

Answer:

i like to know this answer

List and appraise a piece of music base on timbre

Solve the following equation by using properties of logarithms.

500 / (1 + e^-5x) = 300

Answers

Step-by-step explanation:

in the 6 th process I've used natural logarithm ln and ln(e)=1.

if the answer is required in decimal u can substitute the value in calculator.

hope it helps

Mr falcone pizza shop offers three sizes of pizza the large pizza has a diner tee of 12 inches what is the largest pizza

Answers

Answer:

37.68

Step-by-step explanation:

A factory can fill 225 bottles of orange juice each hour. Each bottle of juice contains 24 fluid ounces of juice. Each bottle of juice sells for $5.50. How many pints of juice are filled in each 12-hour shift?

Answers

Answer: 4050 pints

Some information provided is irrelevant to the problem. The question asks how many pints are filled for each 12-hour shift.

Relevant information

A factory can fill 225 bottles of orange juice each hour.Each bottle of juice contains 24 fluid ounces of juice.

Fact

One pint is the same as 16 fluid ounces.

Plan

Calculate the total number of bottles the factory can produce in 12 hours. Then, convert the total number of bottles to the total number of fluid ounces. Lastly, convert fluid ounces to pints.

Solution

If then factory can produce 225 bottes in one hour, then, in 12 hours, 225*12=2700 bottles are produced. Since each bottle is 24 fluid ounces, then the factory produced 2700*24=64800 fluid ounces in total. Converting this to pints, the factory produced 64800/16=4050 pints

One week Tony bought 6 soft shell tacos and 2 hard shell tacos for $12. The next week he bought 3 soft shell tacos and 1 hard shell tacos for $6. Write a system to find the cost for each type of taco. Explain your answer.

Answers

S - Soft
H- Hard

6s + 2h = 12
3s + 1h = 6

Answer: $1.50 each for soft taco
$1.50 each for hard taco

Linda received 3/5 of the votes in the election for student council president. What percent of the votes did Linda receive

Answers

Answer:

60.

Step-by-step explanation:

Answer:

[tex]60%[/tex][tex]%[/tex]%

Can u gimme brain plz!

w – 9 = 22 what is w

Answers

Answer:

31............

Step-by-step explanation:

22+9=31

Answer:

it is -13

Step-by-step explanation:

9-9-x=22-9 x=-13. 9-(-13)=22 brainliest please

3) Given P = 5y , find the positive values of x and y that will give P its maximum value if ^2 + 5 = 7.

Answers

Answer:

were the hell is x

Step-by-step explanation:

where is x in it holy........

Y=2(-8)+7. How do I do this ???

Answers

Answer:

y=−9

Step-by-step explanation:

Let's solve for y.

y=(2)(−8)+7

Answer:

y=-9

Step-by-step explanation:

Y=2(-8)+7

first multiply

Y=-16+7

add like terms

y=-9

I struggle on this one to

Answers

Answer:

13. acute

14. right

15.  36

16. x = 14

Step-by-step explanation:

A carnival is selling red tickets for rides and yellow tickets for games. The red tickets are $1.25 each and the yellow tickets are $0.75 each. The total number of tickets sold was 1,032 and the total sales was $979. Let r represent the number of red tickets sold and y represent the number of yellow tickets sold. Which pair of linear equations can be used to find the number of red tickets sold?
{ r + y = 979 0.75 r + 1.25 y = 1,032
{ r + y = 1,032 0.75 r + 1.25 y = 979
{ r + y = 979 1.25 r + 0.75 y = 1,032
{ r + y = 1,032 1.25 r + 0.75 y = 979

Answers

Answer:

Your answer.

Equation is D

R = 622

Y = 410

Thank you. And give my answer as Brainlist answer. Follow me for more

Step-by-step explanation:

do you guys know this please help

Answers

Answer:

I'm pretty sure 44cm2

Step-by-step explanation:

If  im  wrong sorry if Im right give me 5 stars pls  

PLEASE HELP ME!! I WILL GIVE A BRAINLIEST AND 30 POINTS:))))))

Answers

Answer:

(2,-2)

Step-by-step explanation:

Im pretty sure

What is the result when we simplify the expression ( 1 + 1 /x ) ( 1 − 2/x + 1 ) ( 1 + 2/ x − 1 ) ?

Answers

Step-by-step explanation:

Let y be 1/x. Then 2y = 2/x.

We wish to simplify (1 + y)(2 - 2y)(2y).

(1 + y)(2 - 2y)(2y)

= 4y(1 + y)(1 - y)

= 4y(1 - y²)

= 4y - y³

= 4/x - 1/x³.

P.S. Writing it as (4x² - 1)/x³ is fine.

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