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Alex73 [517]
3 years ago
15

Which of the following sets is NOT dlosed under addition?

Mathematics
2 answers:
sergij07 [2.7K]3 years ago
4 0

Answer:

Odd numbers.

Step-by-step explanation:

Closed under addition means you will able to take any two numbers from whatever set is mentioned and add them to get a number in that same set.

(If I say counting numbers, I'm still talking about the natural numbers.)

So let's look at the natural numbers {1,2,3,4,5,6,...}.

1+1=2

1+2=3

1+3=4

...

6+19=25

Let a and b be counting numbers.

a+b is still going to be a counting number.

You will always get a counting number when adding two counting numbers. So the counting numbers (also known as the natural numbers) is closed under addition.

Let's skip down to odd numbers because the other sets are similar to the first.

Let's add a pair of odd numbers.

3+5=8

8 is not odd so the odd numbers are not closed under addition because we will not always get an odd number. In fact, you will never get a odd number, but the thing is you just need one example to show it is not closed.

(2k+1)+(2a+1)

2(k+a)+2

2(k+a+1) is even so adding two odds will always give you an even.

weeeeeb [17]3 years ago
3 0
Odd numbers is your answer
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Read 2 more answers
Find the value of x and y to the nearest tenth
Readme [11.4K]
The value of 'x' is 24.2 and the value of 'y' is 46.5.

To solve this, we do the following steps.
<u>Step 1:</u> Divide 'y' into 2 parts, 'a' and 'b'. 'a' would be the lower leg of the 45°-45°-90° triangle, while 'b' is the lower leg of the 30°-60°-90° triangle.<em>
</em><u>Step 2:</u> Given the hypotenuse (34) of the 30°-60°-90° triangle, solve for 'b' using the cosine of 30°.
    cos30° = b/34 [adjacent over hypotenuse]
    b = 34cos30° [cross-multiply]
    b = 29.4
<u>Step 3:</u> Solve for the 90° leg (the side opposite the 30° angle) using the Pythagorean Theorem. We will name this leg "h" (cuz height).
     l² + l² = hyp²
     29.4² + h² = 34²
     h² = 1156 - 864.36
     √h² = √291.64
     h = 17.1
<u>Step 4:</u> Solve for 'x' by using the 45°-45°-90° triangle ratio (1:1:√2). √2 would be the hypotenuse of the 45°-45°-90° triangle, while 1 would be both congruent legs.     
  Side 'h' is one of the legs; side 'a' is the other. Since these legs are congruent, 'a' also measures 17.1. Now all we need to do is solve for 'x', which is our hypotenuse. To do this, we simply multiply the measure of side 'h' or 'a' by √2.
     x = 17.1 × √2
     x = 24.2
<u>Step 5:</u> Now that we got the value of 'x', solve for 'y' by adding the measures of sides 'a' and 'b' together.<em>
</em><u />     y = a + b
     y = 17.1 + 29.4
     y = 46.5

And there you have it! <em>Hope this helps.</em>
     <em>
</em>
5 0
3 years ago
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