Answer:
a = 5
b = 4
c = 2
Step-by-step explanation:
5 - 0 = 5
8 + 4 = 12 and 4 + 8 = 12
6 + 8 and 12 + 2 is 14
The beam of light hit the dolphin at the common point that is the solution of a system:
.
From the second equation express y: y=10-x and substitute it into the first equation:
.
Therefore, the horizontal distance in feet is x=5 ft and the height above water is y=10-5=5 ft.
Answer: the beam of light hit the dolphin at 5 ft above water
The distance between the horizontal legs be the distance between the 'x' values '-5' and '2'. 2+5=7 (It is +5 because the distance between -5 and 0 is 5*)
The distance between the horizontals is 7
Same with the vertical points, as the distance is 2. (1+1=2)
Considering that the pythagorean theorem is the a^2+b^2=c^2, and 'a' and 'b' are the sides, then you plug in '7' and '2', making the equation 7^2+2^2=c^2
49+4=c^2
53=c^2
c=sqrt(53)
Hope this helps.
If we know your Pythagorean Triples we can immediately recognize that the last choice is a right triangle:
8² + 15² = 17²
If you don't know your Pythagorean Triples, it's worth learning the first few off the list because teachers use them in problems all the time. But for now let's just exhaustively check the Pythagorean Theorem for each triangle. We don't have to multiply everything out; we can analyze the common factors. If two have a common factor that the third one doesn't have, there's no way for the Pythagorean Theorem to add up.
Clearly 5²+15² is a multiple of 5 but 18² isn't so that one isn't a right triangle.
6²+12² is a multiple of 6, 16² isn't a multiple of 6, not an RT.
15²-5² is a multiple of 5, 13² isn't, no joy.
8²+15² = 64 + 225 = 289 = 17² -- that's a real right triangle, a valid Pythagorean Triple.
Answer:
(3, 1)
Step-by-step explanation:
Midpoint of the diameter is the center
Since endpoints are (9, 7) and (-3, -5)
Midpoint will be:
- ((9 - 3)/2, (7-5)/2) = (3, 1)
So the center is (3, 1)