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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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After a 90% reduction, you purchase a new clothes dryer on sale for $62. What was the original price of the clothes dryer?
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Answer:

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Step-by-step explanation:

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When we finish this equation we get 54.8, which is what we need to subtract from 62 to see what 90% off is.

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Jamie and Stella are saving money to sign up for a school trip to Washington, D.C. In order to sign up for the trip, they must p
DanielleElmas [232]

Answer:

1. Let, Jamie needs "$ g" for the  trip. Then, according to the question,

g = 600 -------------------(1)

2. Let, Stella needs "$ m" for the trip. Then, according to the question,

m = 600 -------------(2)

3. If Jamie washes x no. of cars and Stella makes y no. of pies, then,

25x ≥ 600 ≥ 15y -------------(3)

4. Yes, Stella can afford to sign up for the trip with the money she earns.

Step-by-step explanation:

Let, Jamie needs "$ g" for the  trip. Then, according to the question,

g = 600 -------------------(1)

Let, Stella needs "$ m" for the trip. Then, according to the question,

m = 600 -------------(2)

if Jamie washes x no. of cars for $25 each and Stella makes y no. of pies

for $ 15 each, then, according to the question,

25x ≥ 600 ≥ 15y -------------(3)

Yes,  Stella can afford to sign up for the trip with the money she earns. Because, she can make at most 40 pies for $15 each and

$ 40 \times 15 = $ 600 = The amount of money Stella needs for the trip.

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3 years ago
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