3 4 5 6 8 10 9 40 41 20 21 29 9 12 15 ...and factors of those such as the first 2 examples.
If you drive 9 miles north from your house, then turn and drive 12 miles east, you can use the Pythagorean theorem to calculate that you wind up 15 miles from home. You don't need a graph at all to do that. You just have to know the Pythagorean theorem.
5 m. Using Pythagoras: Hypotenuse2 = side2 + other_side2 ⇒ Hypotenuse = √(side2 + other_side2) = √((3 m)2 + (4 m)2) = √(9 m2 + 16 m2) = √(25 m2) = 5 m 3, 4, 5 is a well known Pythagorean triple - the three sides of a right angle triangle (32 + 42 = 9 + 16 = 25 = 52) Another is: 5, 12, 13 (52 + 122 = 25 + 144 = 169 = 132) If you multiply each of these sides by the same number (that is scale the triangle) you get other Pythagorean triples, eg 3, 4, 5 → (x2) 6, 8, 10; (x3) 9, 12, 15; (x4) 12, 16, 20; etc are all Pythagorean triples 5, 12, 13 → (x2) 10, 24, 26; (x3) 15, 26, 39; (x4) 20, 48, 52; etc are also all Pythagorean triples.
3 It is 12 more than -9 and 12 less than 15 9 + 15 = 24 24/2 = 12 -9 + 12 = 3 15 - 12 = 3
The GCF of 9, 12, 15 is 3.
Yes
Yes.
15, since 15*2 = 9*2 + 12*2
Yes; for example (9, 12, 15) can not be found. However, all primitive triples are found.
3 4 5 6 8 10 9 40 41 20 21 29 9 12 15 ...and factors of those such as the first 2 examples.
3 4 5 6 8 10 9 40 41 20 21 29 9 12 15 ...and factors of those such as the first 2 examples.
Yes they do. We find this by applying the pythagorean theorum. Since 9^2 + 12^2 = 15^2, they form a right triangle.
If you drive 9 miles north from your house, then turn and drive 12 miles east, you can use the Pythagorean theorem to calculate that you wind up 15 miles from home. You don't need a graph at all to do that. You just have to know the Pythagorean theorem.
5 m. Using Pythagoras: Hypotenuse2 = side2 + other_side2 ⇒ Hypotenuse = √(side2 + other_side2) = √((3 m)2 + (4 m)2) = √(9 m2 + 16 m2) = √(25 m2) = 5 m 3, 4, 5 is a well known Pythagorean triple - the three sides of a right angle triangle (32 + 42 = 9 + 16 = 25 = 52) Another is: 5, 12, 13 (52 + 122 = 25 + 144 = 169 = 132) If you multiply each of these sides by the same number (that is scale the triangle) you get other Pythagorean triples, eg 3, 4, 5 → (x2) 6, 8, 10; (x3) 9, 12, 15; (x4) 12, 16, 20; etc are all Pythagorean triples 5, 12, 13 → (x2) 10, 24, 26; (x3) 15, 26, 39; (x4) 20, 48, 52; etc are also all Pythagorean triples.
The straight line distance between 9 miles west and 12 miles south is the hypotenuse of a right triangle with sides 9 and 12. Using the Pythagorean theorem, the distance would be √(9^2 + 12^2) = √(81 + 144) = √225 = 15 miles.
3 It is 12 more than -9 and 12 less than 15 9 + 15 = 24 24/2 = 12 -9 + 12 = 3 15 - 12 = 3
The GCF of 9, 12, 15 is 3.