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victus00 [196]
2 years ago
13

Prove each of the following statements about integers by proving thecontrapositive of the statement.A. If 3nis even, thennis eve

n.B. Ifx y zis odd, then at least one ofx; yandzis odd.
Mathematics
1 answer:
frozen [14]2 years ago
6 0

Answer and Step-by-step explanation:

(A) Suppose 3n is even, this implies that the product of 3n is a multiple of two, let's say 2(3k) where k is a real number. Rearranging that, we have 3(2k), let 2k = n. Therefore, n is even.

(B) Suppose xyz is odd, then let x = 2k, y = 2p + 1 and z = 2q + 1. xyz = 2k(2p + 1)(2q + 1) and this is obviously even since it is a multiple of 2.

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3 years ago
Marneshia walked three over eight of a mile in three over five of an hour. What equation can be used to calculate her unit rate
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Answer:

\frac{3}{8} / \frac{3}{5} = \frac{5}{8}

Step-by-step explanation:

Given

Distance =\frac{3}{8}

Time =\frac{3}{5}

Required

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The unit rate is calculated as:

Unit\ Rate = \frac{Distance}{Time}

Unit\ Rate = \frac{3}{8} / \frac{3}{5}

Convert to multiplication

Unit\ Rate = \frac{3}{8} * \frac{5}{3}

Unit\ Rate = \frac{1}{8} * \frac{5}{1}

Unit\ Rate = \frac{5}{8}

Hence, the expression can be represented as:

\frac{3}{8} / \frac{3}{5} = \frac{5}{8}

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Step-by-step explanation:

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