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Yuki888 [10]
3 years ago
6

For all integers n, if n2 is odd, then n is odd. Use a proof by contraposition, as in Lemma 1.1. Let n be an integer. Suppose th

at n is even, i.e., n =
Mathematics
1 answer:
Reil [10]3 years ago
8 0
Let's assume that the statement "if n^2 is odd, then is odd" is false. That would mean "n^2 is odd" leads to "n is even"

Suppose n is even. That means n = 2k where k is any integer.

Square both sides

n = 2k
n^2 = (2k)^2
n^2 = 4k^2
n^2 = 2*(2k^2)

The expression 2(2k^2) is in the form 2m where m is an integer (m = 2k^2) which shows us that n^2 is also even. 

So this contradicts the initial statement which forces n to be odd. 
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natima [27]

Answer:

A. 18÷2/9

Step-by-step explanation:

A. 18÷2/9

B. 18×2/9

C. 2/9÷18

D. 9/2÷18

Let

Total length of box = 18 inches

Thickness of each book = 2/9 inches

Number of books that will fit into the box = x

Number of books that will fit into the box = Total length of box ÷ Thickness of each book

x = 18 ÷ 2/9

= 18 × 9/2

= 162/2

= 81 books

The correct answer is A. 18÷2/9

7 0
3 years ago
The shape below is constructed from six squares, and the lengths of the sides of the three smallest squares are written inside o
Maurinko [17]

Answer:

78

Step-by-step explanation:

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Mid Square: 3, Area of 9

Mid White Square: 5, Area of 25

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5 0
3 years ago
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Leviafan [203]

Answer:

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Step-by-step explanation:

7 0
3 years ago
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Find two consecutive odd integers whose sum is 116 (and please have steps) thank you
matrenka [14]
It's 57 and 59
Call (n) is the first odd interger => the second odd interger is (n+2)
=> n + (n + 2) = 116 
=> n + n + 2 = 116 
=> 2n = 114 
=> n = 57 
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Sorry my English so bad =)))
6 0
3 years ago
2/10 (4/5)-(5/2)+ (10)
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Answer:

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7 0
3 years ago
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