70 ! find the missing x- and y-values and pythagorean triples using the identity given 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: ?

A Pythagorean triple consists of three positive integers a, b, and c, that satisfy the equation from the Pythagorean theorem, thus, a² + b² = c², such triple is commonly written (a,b,c).

We are given the equation : (x²-y²)² + (2xy)² = (x²+y²)² since this, we have :

a = (x²-y²)

b = (2xy)

c = (x²+y²)

Question 1)

X Value: 4

Y Value: 3

Pythagorean triples: ?

Now we can replace the values of x and y, to determine a, b and c.

a = (x²-y²) = (4²-3²) = 16-9 = 7

b = (2xy) = (2*4*3) = 24

c = (x²+y²) = (4²+3²) = 16+9 = 25

Answer 1 : Pythagorean triples : (7,24,25)

Question 2)

X Value: 5

Y Value: ?

Pythagorean Triples: (9,40,41)

Now we have a, b, and c, to determine Y

b = (2xy) = 40

Y = 40/2x = 40/2*5 = 40/10 = 4

Answer 2 : Y = 4

Question 3)

X Value: ?

Y Value: 3

Pythagorean Triples: (27,36,45)

Now we have a, b, and c, to determine X

b = (2xy) = 36

X = 36/2y = 36/2*3 = 36/6 = 6

Answer 3 : X = 6

Question 4)

X Value: 7

Y Value: 5

Pythagorean Triples: ?

Now we can replace the values of x and y, to determine a, b and c.

a = (x²-y²) = (7²-5²) = 49-25 = 24

b = (2xy) = (2*7*5) = 70

c = (x²+y²) = (7²+5²) = 49+25 = 74

Answer 4 : Pythagorean triples : (24,70,74)

Hope this helps!

step-by-step explanation:

12: 00 p.m. to 7: 00 p.m. is a total of 7 hours.

4: 00 p.m. to 7: 00 p.m. is a total of 3 hours.

this means that from 4: 00 p.m to 7: 00 p.m. this represents 3/7 of what was lost from 12: 00 p.m. to 7: 00 p.m.

after knowing this, after doing 11,600 - 6,800 = 4,800

4,800 represents 3/7 of what was lost for 7 hours.

we then divide 4,800 by 3 which gets 1,600.

because we know that 1,600 represents 1/7 of how much water was lost, we just have to multiply by 7, which gets 11,200.   after adding 11,200 to how much water was left at 7: 00 p.m. which was 6,800. 11,200 + 6,800 = 18,000

this means that the pool originally had 18,000 gallons in the pool.

you can also check your work by doing 18,000 - 4(1600), which becomes           1800 - 6400 which gets you 11,600.