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hodyreva [135]
3 years ago
13

....................​

Mathematics
1 answer:
Goryan [66]3 years ago
6 0

................................................i dont know

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Find the missing x- and y-values and Pythagorean triples can be generated using the identity given. Write the triple in parenthe
ddd [48]

The complete question is:

Find the missing x- and y-values and Pythagorean triples using the identity given:

(x² - y²)² + (2xy)² = (x² + y²)²

X Value: 4

Y Value: 3

Pythagorean Triples: ?

X Value: 5

Y Value: ?

Pythagorean Triples: (9,40,41)

X Value: ?

Y Value: 3

Pythagorean Triples: (27,36,45)

X Value: 7

Y Value: 5

Pythagorean Triples: ?

Step-by-step explanation:

Pythagorean triples are three numbers p, q, r, that satisfy Pythagoras' theorem.

That is, they are numbers such that

r² = p² + q².

Given the identity

(x² - y²)² + (2xy)² = (x² + y²)²

We can say tha

p = x² - y²

q = 2xy

r = x² + y²

Now, let us use this to solve the given problems.

X Value: 4

Y Value: 3

p = 4² - 3² = 7

q = 2×3×4 = 24

r = 3² + 4² = 25

Pythagorean Triples: (7,24,25)

X Value: 5

Y Value: ? = (4)

q = 2xy = 40

2×5×y = 40

y = 40/10 = 4

Pythagorean Triples: (9,40,41)

X Value: ? = (6)

Y Value: 3

2xy = q = 36

2×3×x = 36

x = 36/6 = 6

Pythagorean Triples: (27,36,45)

X Value: 7

Y Value: 5

p = 7² - 5² = 24

q = 2×7×5 = 70

r = 7² + 5² = 74

Pythagorean Triples: ? = (24,70,74)

8 0
3 years ago
Which set of ordered pairs does not represent a function? { ( − 3 , − 1 ) , ( 8 , − 1 ) , ( 0 , − 5 ) , ( − 9 , − 2 ) } {(−3,−1)
inysia [295]

Answer:

\{(2,8),(2,1),(-9,-5),(-8,9)\} is not a function

Step-by-step explanation:

Given

\{(-3,-1),(8,-1),(0,-5),(-9,-2)\}

\{(5,9),(-3,-5),(0,4),(-9,9)\}

\{(9,0),(-5,4),(5,0),(6,3)\}

\{(2,8),(2,1),(-9,-5),(-8,9)\}

Required

Which is not a function

A function is of the form (x,y)

Assume a function is:

\{(x_1,y_1),(x_2,y_2),(x_3,y_3).....,(x_n,y_n)\}

In simple terms:

For an ordered pair to be regarded as a function, no x value must be repeated

Analyzing the options:

1. \{(-3,-1),(8,-1),(0,-5),(-9,-2)\}

This is a function because none of the x values (-3, 8, 0 and -9) appeared more than once

2. \{(5,9),(-3,-5),(0,4),(-9,9)\}

This is a function because none of the x values (5, -3, 0 and -9) appeared more than once

3. \{(9,0),(-5,4),(5,0),(6,3)\}

This is a function because none of the x values (9, -5, 5 and 6) appeared more than once

4. \{(2,8),(2,1),(-9,-5),(-8,9)\}

This is not a function because one of the x values (2) appeared more than once.

i.e.

(2,8)   and   (2,1)

7 0
3 years ago
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