Use the Pythagorean identity, Latex: (x^2-y^2)^2+(2xy)^2=(x^2+y^2)^2\tex tsf{,} to create a Pythagorean triple. Follow these steps:

Choose two numbers and identify which is replacing Latex: x
x
and which is replacing Latex: y\textsf{.}

How did you know which number to use for Latex: x
x
and for Latex: y\textsf{?}

Explain how to find a Pythagorean triple using those numbers.

Explain why at least one leg of the triangle that the Pythagorean triple represents must have an even-numbered length.

Find the length of the diagonal of the rectangle. round your answer to the nearest tenth. || | | 8 m | | | | 11 m

The fraction of defective integrated circuits produced in a photolithography process is being studied. a random sample of 300 circuits is tested, revealing 17 defectives. (a) calculate a 95% two-sided confidence interval on the fraction of defective circuits produced by this particular tool. round the answers to 4 decimal places. less-than-or-equal-to p less-than-or-equal-to (b) calculate a 95% upper confidence bound on the fraction of defective circuits. round the answer to 4 decimal places. p less-than-or-equal-to

Write the point-slope form of the line passing through (2, -12) and parallel to y=3x.