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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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Kryger [21]
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¹/₅ = b

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4 0
3 years ago
Find the mean and mode for this set of data.<br>5, 6, 8, 3, 5, 7, 4, 11, 5, 7​
dangina [55]

Answer:the mean is 6.1 the mode is 5 and 7.

Step-by-step explanation: the mean is 6.1 because the number add up to 61 and there are 10 numbers 61/10=6.1

The mode is 5 and 7 because they occur most frequently

3 0
3 years ago
What is the absolute value of -90?
Alexandra [31]

Answer: 90

Step-by-step explanation:

3 0
3 years ago
Read 2 more answers
write the equation of a line that passes through the points (5, -7) and is perpendicular to the line -2x + 6y = -4
VashaNatasha [74]

Answer:

y= -3x + 8

Step-by-step explanation:

Put -2x + 6y = -4 into slope-interceltp form

Take the negative reciprocal of the slope.

Use this reciprocal in point-slope form

and you have,

= y= -3x + 8

<em>(EDITED)</em> Steps:

2x+6y = -4

6y=2x - 4

y= 1/3x + 2/3

if two lines are perpendicular,

m1 * m2 + -1

1/3 * m2 = -1

m2 = -3

the line perpendicular to this line is

y = -3x + k ; k ∈ R

the line passes through the point (5,-7)

so,

-7 = -3. (5) +k

-7 = -15 + k

k = 8

∴the equation of a line that passes through the point (5,-7) and is perpendicular to the line -2x+6y=-4 is

y= -3x + 8

Hope this helps, have a nice day/night! :D

6 0
2 years ago
Ahmed wrote the two expressions below.
Vsevolod [243]
Put an equal sign between the two expressions, and solve for x
3 0
3 years ago
Read 2 more answers
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