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Bingel [31]
3 years ago
10

PLEASE ANSWER & EXPLAIN *****100 POINTS******

Mathematics
2 answers:
Zarrin [17]3 years ago
8 0

Answer: B

Step-by-step explanation:

line 1: 10

line 2: 9

line 3: 8

line 4: 7

line 5: 6

line 6: 5

kogti [31]3 years ago
8 0

Answer:

Step-by-step explanation:

Given the first line has 10 marbles and each following line has one less, the general equation is the nth line will have 10-(n-1) marbles.

So the sixth line has 10-(6-1) = 5 marbles.

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Answer and Step-by-step explanation:

(a) Given that x and y is even, we want to prove that xy is also even.

For x and y to be even, x and y have to be a multiple of 2. Let x = 2k and y = 2p where k and p are real numbers. xy = 2k x 2p = 4kp = 2(2kp). The product is a multiple of 2, this means the number is also even. Hence xy is even when x and y are even.

(b) in reality, if an odd number multiplies and odd number, the result is also an odd number. Therefore, the question is wrong. I assume they wanted to ask for the proof that the product is also odd. If that's the case, then this is the proof:

Given that x and y are odd, we want to prove that xy is odd. For x and y to be odd, they have to be multiples of 2 with 1 added to it. Therefore, suppose x = 2k + 1 and y = 2p + 1 then xy = (2k + 1)(2p + 1) = 4kp + 2k + 2p + 1 = 2(kp + k + p) + 1. Let kp + k + p = q, then we have 2q + 1 which is also odd.

(c) Given that x is odd we want to prove that 3x is also odd. Firstly, we've proven above that xy is odd if x and y are odd. 3 is an odd number and we are told that x is odd. Therefore it follows from the second proof that 3x is also odd.

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