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lutik1710 [3]
3 years ago
6

Prove that if n is an even integer, then n + 1 is odd. Give a proof by contraposition of this theorem.

Mathematics
1 answer:
S_A_V [24]3 years ago
7 0

Answer:

Proved below

Step-by-step explanation:

If we assume that n + 1 even when n is even, it means that;

n + 1 = 2x

Where x is an integer

Then;

n = 2x - 1

This means that n is odd because 2x - 1 is odd.

But we know that n is even, thus, our assumption is wrong.

Therefore, n + 1 is odd when n is even.

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Two angles in a triangle add up to 98 degrees . What is the size of the third angle ?
ira [324]
First you must know that the sum of the interior angles of a triangle are 180.  Once you know that, you just simply add 98+x=180 (you can use an variable as you see fit, doesn't need to be x). And then you simply solve for x by dividing 98 on both sides leaving you with 82.
8 0
3 years ago
Sneha went to a field trip in a botanical garden. She came across many plants but was attracted by rose plants and started to co
padilas [110]

Answer:

ok so there is 20 rows and 45 in each this is a basic multiplication problem

20*45=900

Hope This Helps!!!

6 0
4 years ago
Read 2 more answers
Adam is 159 centimeters tall and casts a shadow 105 centimeters in height. If Cara is 140 centimeters tall, how many centimeters
vodomira [7]

Answer:

The answer to your question is 12.55 cm

Step-by-step explanation:

Data

Adam                                  Cara

height = 159 cm                  height = 140 cm

shadow = 105 cm                shadow = x

Process

1.- To solve this problem use the Thales' theorem

         Cara's shadow / Cara's height = Adam's shadow / Adam's height

- Substitution

                                     x / 140 = 105 / 159

-Solve for x

                                     x = 105 (140) / 159

-Simplification

                                     x = 14700 / 159

                                     x = 92.45 cm

Cara's shadow is 92.45 cm long.

2.- If both shadows are in line, then Cara must walk forward

                105 - 92.45 cm

                12.55 cm

             

4 0
3 years ago
Evaluate 2xy<br> when x=−14<br> and y=3<br> .<br> The value of the expression is =
kondor19780726 [428]

9514 1404 393

Answer:

  -84

Step-by-step explanation:

Put the values where the variables are and do the arithmetic.

  2xy = 2(-14)(3) = -84

5 0
3 years ago
A plant costs £6.80.Julie has £30.00 how many plants can she buy?​
irinina [24]

Answer:

Julie can buy 4 plants

Step-by-step explanation:

A plant costs £6.80 and Julie has £30.

In order to find out how many plants she can buy with £30, we need to see how much times £6.80 can go into £30. In other words, we need to divide £30 by £6.80 so we get the number times it can go into £30. That will be the number of plants.

£30 ÷ £6.80 = 4.41176470588

Julie can't get 0.41176470588 of a plant so we have to round it to 4. She can buy 4 plants.

She has a bit of money left over (you can tell by the decimal number), but that isn't enough to buy another plant. So she buys 4 and has £2.80 left.

£6.80 x 4 = £27.20

4 0
4 years ago
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