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Vinvika [58]
3 years ago
14

Which combination of integers can be used to generate the Pythagorean triple (5,12,13)

Mathematics
2 answers:
Radda [10]3 years ago
7 0

Answer:

x=3 and y=2

Step-by-step explanation:

The Pythagorean triples can be generated by two values <em>x, y, </em>and a given system of equations:

x^{2}-y^{2}=5\\2xy=12\\x^{2}+y^{2}=13

You can see that each coordinate of the triple is included in each equation.

Remember that Pythagorean triples refers to the values of each side of a right triangle, where is used the Pythagorean Theorem. But, at a higher level, to construct this triples we use the system of equations, with two integers <em>x </em>and <em>y.</em>, like this case.

Now we solve the system, the best first step is to just sum the first and third equations, because they have like terms:

2x^{2}=18\\x^{2}=\frac{18}{2}=9\\x=3

Now, we just replace it in the second equation:

2xy=12\\y=\frac{12}{2x}=\frac{6}{3}=2

Therefore the integers that generate the Pythagorean triple (5,12,13) are x=3 and y=2

Kitty [74]3 years ago
3 0

Answer:

x=3 and y=2

Step-by-step explanation:

The pythagorean triples are generated by two integrers x and y that can be found by solving the following system of equations:

\left \{ {{x^{2}-y^{2}=5}\atop {2xy=12}} \atop {x^{2}+y^{2}=13}}\right.

Solve the system of equations, and we get that the solution is x=3 and y=2.

Therefore, the combination of integrers that ca be used to generate the pythagorea triple are: x=3 and y=2

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Solve for x 11x+4&lt;15 OR 12x−7&gt;−25
never [62]

Isolate the x in both cases. What you do to one side, you do to the other.


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-------------------------------------------------------------------------------------------------------------------


Again, isolate the x.


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-------------------------------------------------------------------------------------------------------------------



hope this helps

3 0
3 years ago
Read 2 more answers
Is the square root of 12 rational or irrational?
Andreyy89
<h3>Answer: Irrational</h3>

We cannot write sqrt(12) as a fraction of two whole numbers

Note how sqrt(12) = 3.464 and the decimal portion goes on forever without any known pattern (and it doesnt repeat either).

Compare this to something like sqrt(16) = 4 which can be written as a fraction 4/1, so sqrt(16) is rational

5 0
3 years ago
What is the domain of the following graph?
Morgarella [4.7K]

Answer:

[0,9]

Step-by-step explanation:

The domain is the first set of the ordered pair. When finding the domain you are supposed to find which x value it starts from to where it ends. The x value starts from 0 and ends and the 9th unit on the x-axis which would give us 0,9 now since both points are closed you would use these symbols [ ] to show that it is closed meaning the answer would be [0,9]

Note:

I'm sorry if this is wrong but this is what I believe the answer is.

4 0
3 years ago
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