Find all triples of natural numbers (a, b, c) satisfying the system of equations​

Find All Triples Of Natural Numbers (a, B, C) Satisfying The System Of Equations

Answers

Answer 1

9514 1404 393

Answer:

(±7, ±1, ±4)(±13, ±11, ±16)

Step-by-step explanation:

Solution of the system by the usual means yields the parametric equations ...

  (a², b², c²) = (41 +t, t -7, 2t)

Since we want t-7 to be a perfect square, we can let ...

  t -7 = n²

  t = n² +7

Then the solutions are ...

  (a, b, c) = (±√(n²+48), n, ±√(2(n² +7)))

The only integer solutions are for n=±1 and n=±11. Then the 16 possible triples are ...

  (±7, ±1, ±4) and (±13, ±11, ±16) . . . where the signs can have any combination


Related Questions

A sports tournament has b teams. Each team has 8 players. Using b, write an expression for the total numbers of players in the tournament.

Answers

Answer:

The answer is 8b

Step-by-step explanation:

Hey, a variable is a filler for an unknown number. Don't let it confuse you too much!

If there were 5 teams, there would be 8(5) = 40 players, right??

With b teams, there are 8b players. We are lazy as mathematicians and don't say 8(b) or 8 x b. It's just 8b.

Thus, The answer is 8b

-TheUnknownScientist 72

2319471, how is this number read?

Answers

Step-by-step explanation:

#G

enjoy. my son haha. lol

What is an equation of the linethat passes through the points (3,-8) and (1,-2)

Answers

Answer:

y=3x+1

Step-by-step explanation:

m= [tex]\frac{-2-(-8)}{1-3} =\frac{-6}{2}[/tex] or -3

-8= -3(3) + b

-8= -9 + b

+9     +9

1=b

Then put in slope intercept form:

y= 3x+1

Hope this helps! :)

an example of an abelian group which is not cyclic

Answers

G=Z6×Z2G=Z6×Z2 will do (where ZnZn denotes the cyclic group of order nn). As a direct product of cyclic (so abelian) groups, GG is again abelian. Given any element (x,y)∈G(x,y)∈G, the order of (x,y)(x,y) will be the least common multiple of the orders of x,y.x,y.  

The order of xx must divide 66 and the order of yy must divide 2,2, so the order of (x,y)(x,y) is at most lcm(6,2)=6.lcm⁡(6,2)=6. But |G|=|Z6|⋅|Z2|=6⋅2=12.|G|=|Z6|⋅|Z2|=6⋅2=12. Since no element of GG has order 12,12, then GG is not cyclic.

draw a square and its diagonals how many angles are formed by the intersection of the diagonals?

Answers

A square has 2 diagnals. imagine 2 lines connecting every opposite angle of the square. that leaves 2 intersecting lines. Sinse the two lines are intersecting, they form angles. Because there are only 2 lines, there are 4 angles. The answer is 4.

A square is a four-equal-sided figure with the diagonals of the square cut perpendicular to each other as shown below and the number of angles formed by diagonals is 4.

What is a square?

A square is a geometrical figure in which we have four sides each side must be equal and the angle between two adjacent sides must be 90 degrees.

Area of square = Side²

The perimeter of the square = 4× side

A square is a geometrical figure in which we have four sides each side must be equal and the angle between two adjacent sides must be 90 degrees.

There are two diagonals in every square.

The angle of intersection between both diagonals is 90 degrees.

The number of angles formed by diagonals = 4

Hence "A square is a four-equal-sided figure with the diagonals of the square cut perpendicular to each other as shown below and the number of angles formed by diagonals is 4".

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Please answer this question!!

Answers

I believe the answer is A A and A. pls mark me as brainliest!

x + 4y = 23
-2x + 3y = -2

Answers

Answer:

  (x, y) = (7, 4)

Step-by-step explanation:

I find a graphing calculator to give a solution quickly and easily.

  (x, y) = (7, 4)

__

Here, we can solve the first equation for x, then substitute into the second.

  x = 23 -4y

  -2(23 -4y) +3y = -2 . . . . . substitute for x

  -46 +8y +3y = -2 . . . . . eliminate parentheses

  11y = 44 . . . . . . . . . . . collect terms

  y = 4 . . . . . . . . . . . . divide by the coefficient of y

  x = 23 -4·4 = 7 . . . . use the expression for x to find x

  (x, y) = (7, 4)

Which best describes how the graph of g(x) = square root of 25/9 x relates to the graph of the parent function, f(x) = square root of x?

The graph of g(x) is shrunk vertically by a factor of 5/3.
The graph of g(x) is stretched vertically by a factor of 5/3.
The graph of g(x) is shrunk vertically by a factor of 25/9.
The graph of g(x) is stretched vertically by a factor of 25/9.

Answers

Answer:

The graph of g(x) is stretched vertically by a factor of 5/3.

Step-by-step explanation:

f(x) = √x

g(x) = √25/9 x = 5/3 √x

5/3 > 1 .. vertical stretch by a factor of 5/3

Yesterday, Kofi earned 50 Cedis mowing lawns. Today, Kofi earned 60% of what he earned yesterday mowing lawns. How much money did Kojo earn mowing lawns today?

Answers

The amount of money that Kojo earn mowing lawns today is 30 cedis

To determine the amount of money that  Kojo earn mowing lawns today we are going to multiply the amount she earn by the her earning percentage.

Using this formula

Amount=Earning × Earning rate

Where:

Earning=50 cedis

Earning rate=60%

Let plug in the formula

Amount=50×.60

Amount=30

Inconclusion The amount of money that Kojo earn mowing lawns today is 30 cedis

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Since Kofi earned 60% of what he earned yesterday mowing lawns, today he earned 30 Cedis.

Given the following data:

Amount earned yesterday = 50 Cedis.Percentage today= 60%

To find how much money Kojo earn mowing lawns today:

In this exercise, you're required to find the amount of money earned by Kofi, if he was able to make certain amount of money the previous day.

Hence, we would determine what percentage of the money he earned today.

[tex]Today's\;earnings = \frac{60}{100} \times 50\\\\Today's\;earnings = \frac{3000}{100}[/tex]

Today's earnings = 30 Cedis

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A water tank holds 1500 liters of water when it is full. If 2/3
of the tank is full, how

much more liters of water are needed to make the tank full?


fraction word problem

Answers

Answer: 500

Step-by-step explanation: A third of 1,500 is 500, and 2/3 of 1,500 is 1,000. So, 1,500 - 1,000 = 500 liters. Therefore, in order to make the tank full, 500 liters of water are needed.

algebra ii question!

Answers

It’s the first answer because it’s greatest value is 6.

a. Exactly 117.125 b. Correct to 2 significant figures c. Correct to 2 decimal places d. In standard form ​

Answers

Answer:

b) 11

c)117.12

1.1×10^2

Those are my answer that try

Complete the equation so that it has infinitely many solutions.

13(3−z)=

Answers

Answer:

13(3 − z) = 39 - 13z

Step-by-step explanation:

13(3 − z)

= 39 - 13z

So, the equation will be 13(3 − z) = 39 - 13z

Find the midpoint of the line segment joining the points (10, 13) and (−7, 7).

Answers

Answer:11.5and 0

Step-by-step explanation:

Please answer #1 hurry!!! Will give brainliest

Answers

Answer:

1a) O is the steepest

1b) because it is more angled

1c) all lines are positive

Step-by-step explanation:

1a) plot the coordinates on the graph and find the steepest

Answer:

1a) O) y = 5x

1b) The slope value is greater than M and N

1c) They all meet on the point of (0,0) because there is no b value and are all positive slopes.

What’s the greatest common factor of (280, 168)

Answers

Answer:

Greatest common factor of 280 and 168 is 56

-NULL

Brainliest will be appreciated thank you!

pls help me with question 3

Answers

No. I can’t. Just wanting to get some points man, 5 would be nice.

Use a truth table to determine whether to two statements are equivalent

Answers

Answer:

equivalent yan kasi pareho lang den nmn letters lng naiba

(5x+5)-2x
No scam.....​

Answers

Answer:

=3x+5

Step-by-step explanation:

Let's simplify step-by-step.

5x+5−2x

=5x+5+−2x

Combine Like Terms:

=5x+5+−2x

=(5x+−2x)+(5)

=3x+5

Answer:

=3x+5

Answer:

[tex]\boxed{\boxed{\sf 3x+5 }}[/tex]

Step-by-step explanation:

[tex]\sf (5x+5)-2x[/tex]

[tex]\sf \left(a\right)=a[/tex]

⇒ First step is to get rid of expression parentheses:

[tex]\longmapsto[/tex] [tex]\sf 5x+5-2x[/tex]

⇒ Now, we need to combine like terms:

[tex]\longmapsto[/tex] [tex]\sf (5x-2x)[/tex] [tex](5)[/tex]

[tex]\longmapsto[/tex]  [tex]\sf 3x+5[/tex]

__________________________________

heeelllllllllpppppppp meeeeee

Answers

Answer:

32

Step-by-step explanation:

36-4

Use Pythagorean theorem

Answer:

B=4

Step-by-step explanation:

1/3 x 2/5 in simplest form

Answers

Answer:

2/15

Step-by-step explanation:

1/3 x 2/5

= ( 1 x 2 ) / ( 3 x 5 )

= 2/15

Answer:

2/15

Step-by-step explanation:

1/3*2/5

(1*2)/(3*5)

2/15

811570 rounded to nearest hundred thousand

Answers

Answer:

800,000

Step-by-step explanation:

8 is in the hundred thousands, 1 is in the ten thousands, 1 is in the thousands, 5 is in the hundreds, 7 is in the tens, 0 is in the ones place

It rounds down as its nowhere near 900,000 which changes all its digits.

Can someone help me on what I could do to do better for my classes cause most on them I got a low grade and I think I might have to go to summer school if I don’t do good, also I have this huge test today and I think I’m gonna fail on it

Answers

Answer:

Dont worry man take a deep breath just try your best and if worse case you do bad and on the test take your time and don’t feel pressured

Step-by-step explanation:

Answer:

nope. you only go to summer school if you flunked about 60% of your core subjects. and/or if you also flunked your PAT'S/SAT'S. don't worry buddy.

Brianna works for a large fast food chain recording and publishing training videos for employees. Which job title would Brianna MOST likely have?

Answers

Answer:

Multimedia Specialist

Step-by-step explanation:  

Had a question like this before

Peter owns a store that sells men's clothing. His most significant monthly expenses to run the store are the cost of retail items and the power bill. This month, he purchased 50 suits for his store. He also
needed to buy 35 pairs of shoes, which cost $25 dollars more than each suit. The expression shows Peter's total expenses for this month:
50 (x) + 35 (x + 25) + 450
What does (x + 25) represent?

А-the cost of 25 suits

B-the cost of each pair of shoes

C-the total cost of the pairs of shoes

D-the price of one suit and one pair of shoes

Answers

Answer:

B-the cost of each pair of shoes

Step-by-step explanation:

This is because each pair of shoes cost $25 dollars more than each suit (which is represented by x)

x + 25, represents the cost of each pair of shoes. Option B is correct.

Given that,
This month Peter purchased 50 suits for his store. He also needed to buy 35 pairs of shoes, which cost $25 dollars more than each suit. The expression shows Peter's total expenses for this month
50 (x) + 35 (x + 25) + 450, What x + 25 represents the equation is to e determined.

What is a polynomial function?

A polynomial function is a function that applies only integer dominions or only positive integer powers of a value in an equation such as the quadratic equation, cubic equation, etc. ax+b is a polynomial.

Here,
Let x be the rate of each suit,
and the cost of the shoe is $25 dollars more than each suit. So,
50 (x) + 35 (x + 25) + 450
In the equation, x + 25  represent the cost of each pair of shoe.

Thus, x + 25, represents the cost of each pair of shoes. Option B is correct.

Learn more about polynomial function here:

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solve the equation 3/4x-5=x
give your answers correct to 2 decimal places

Answers

Given :

3/4x - 5 = x

To find :-

The value of x .

Solution :-

Taking the given equation ,

3/4x - 5 = x x - 3/4x = -5 4x - 3x /4 = -5x/4 = -5x = -5*4x = -20

-79=7w+3(4w-1) all steps please and quick

Answers

step 1:
3(4w-1)= 12w-3

step 2:
7w+12w-3
=19w-3

step 3:
-79=19w-3 (so add 3 to -79)

step 4:
-76=19w (just divide by 19 to get w)

step 5:
-4=w

Who do you agree with? Explain why.


David states -15 divided by a negative integer will produce a positive quotient less than or equal to 15.

Lesly states -15 divided by a negative integer will produce a positive quotient greater than or equal to 15.

Answers

David Because if u divide any number has to be smaller or the same.

The local newspaper has letters to the editor from 80 people. If this number represents 2​% of all of the​ newspaper's readers, how many readers does the newspaper​ have?

Answers

Answer:

The local newspaper has letters to the editor from 80 people. If this number represents 2% of all of the newspaper's readers, how many readers does the newspaper have?

Step-by-step explanation:

2%ofx=80

or, 2/100 *X = 80

or, 2x =800

or, x = 400

A cyclist rides her bike at a rate of 10 kilometers per hour what is this rate in miles per hour? How many miles will the cyclist travel in 3 hours? In your computations, assume that 1 mile is equal to 1.6 kilometers l. Do not round your answers

Answers

Answer:

cyclist will travel 64 kilometres in 4 hours

Step-by-step explanation:

speed of cyclist = 10 miles per hour

given 1 mile is equal to 1.6 kilometres.

1*10 miles will be equal to 1.6*10 kilometres

thus , 10 mile is equal to 16 kilometres

using 16 km in place of 10 miles in 10 miles per hour

we have

speed of cyclist = 16 kilometres per hour

we know that distance = speed * time

speed is 16 kilometres per hour

time 4 hours

thus , distance = 16*4 kilometres= 64 kilometres.

cyclist will travel 64 kilometres in 4 hours.

(Hope this helps can I pls have brainlist (crown)☺️)

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