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.
Suppose there are x number of clubs in the pack
P( draw a diamond) = 13 / 59
P( draw a club) = x / 58
so P( diamond then a club) = 13x / (58*59) = 13x / 3422
so we have the equattion
117 / 1711 = 13x / 3422
234 / 3422 = 13x / 3422
therefore x = 234 / 13 = 18 clubs :-
that is 5 more clubs than in a normal pack
So the number of extra spades = 59 - 52 - 5 = 2
If the annual rate increases nothing will happen to the monthly payment, so the answer is C as the annual rate increases, the monthly payment stays the same. Once the fixed-rate payment (loan) is processed there is no chance for any changes as this procedure means that lender is under a fixed-rate loan each payment period.
Answer:
£2.85
Step-by-step explanation:
Lucy paid this amount she used six coin remember you have to calculate them to get the 85 and u can't use £1
three different ways she could have paid
50+20+10+5=85(£2.85)
50+10+10+10+5=85(£2.85)
20+20+20+10+10+5=(£2.85)