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goldenfox [79]
3 years ago
14

Use a proof by contradiction to prove that the sum of two odd integers is even.

Mathematics
1 answer:
Troyanec [42]3 years ago
4 0

Answer:

Step-by-step explanation:

to prove that the sum of two odd integers is even.

Let a and b be two odd integers.

If possible assume that

a+b = 2m, i.e. sum is a product of 2, hence even.

Since a is odd,

a=2k+1\\ for some integer k.

Subtract a from a+b to get

b = 2m+1-(2k+1)\\= 2m-2k\\=2(m-k)\\=2l

i.e. b is a multiple of some integer l by 2

i.e. b is even.

This contradicts our assumption that both a and b are odd

Hence proved that the sum of two odd integers is even.

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2 years ago
The expression 8x2 − 144x 864 is used to approximate a small town's population in thousands from 1998 to 2018, where x represent
Rzqust [24]

The expression that is most useful for finding the year where the population was at a minimum would be 8(x − 9)² + 216.

Given expression 8x² − 144x + 864 is used to approximate a small town's population in thousands from 1998 to 2018, where x represents the number of years since 1998.

<h3>What is a quadratic equation?</h3>

A quadratic equation is the second-order degree algebraic expression in a variable. the standard form of this expression is  ax² + bx + c = 0 where a. b are coefficients and x is the variable and c is a constant.

Given expression is 8x² − 144x + 864

Let y = 8x² − 144x + 864

also,  y - 864 = 8x² - 144x

by Extracting common factor 8 on the right side

y - 864 = 8(x² - 18x)

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on simplification

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The expression that is most useful for finding the year where the population was at a minimum would be 8(x − 9)² + 216.

Learn more about a quadratic equation here:

brainly.com/question/2263981

8 0
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A book was on sale for 40% off its original price. If
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Answer:

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So the original price of book will be $30

i hope it will help you!

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