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:
(3/2, -1/2)
Step-by-step explanation:
add the 2 inequalities together.
you get 2X<3 so x<3/2. plug X back in and solve for y and you get y= -1/2
distribute
-3y -9 = 2y+3
add 3y to each side
-9 = 5y +3
subtract 3 from each side
-12 = 5y
divide by 5
-12/5 = y
y = -2 2/5
Step-by-step explanation:
3(-30x - 15y = -30) ...........(i)
15(6x + 3y = 6) ..............(ii)
Now,
-90x -45y = -90
90x +45y = 90
_____________
Every term is cancelled. so this system has no any solution so it means solution does not exist (DNE)
Answer:
1.9099
Step-by-step explanation:
V = (PI) * r^2 * (h/3)
32 = (PI) * (16) * (h/3)
6/PI = h
1.9099 = h