Is this a relation: {(-2,1), (0,0), (0,1), (1,-2), (1,0), (1,3), (2,0)}? Explain why or why not.
tatiyna
It is a relation because any relation is simply a set of (x,y) values known as points or ordered pairs. There are no other qualifications needed to be a relation. We simply pair up any x and y value we want.
I think you meant to ask if it's a function or not. If so, then the answer is "no, it is not a function". Why not? Because the x value x = 0 produces more than one y output y = 1 and y = -2. Graph these points and you'll see them fail the vertical line test (ie its possible to draw a vertical line through more than one point on the graph). The same issue happens with (1,-2), (1,0) and (1,3) as well.
In summary:
Yes it is a relation
No it is not a function
The reasoning for each is stated above
Answers:
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Explanation:
7+6 = 13. Divide this over 5 to get 13/5 = 2 remainder 3. The quotient 2 is something we don't care about. <u>We only worry about the remainder</u>. Therefore 7+6 = 3 (mod 5)
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2+1 = 3 (mod 5) for similar reasoning as above. 3/5 = 0 remainder 3.
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20 = 9 (mod 11) since 20/11 = 1 remainder 9. Imagine you had 20 cookies and 11 friends. Each friend would get 1 whole cookie (quotient) and there could be 9 left over (remainder).
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35/11 = 3 remainder 2
Or you could use repeated subtraction like so to find the remainder
35-11 = 24
24-11 = 13
13-11 = 2
The last result (2) is smaller than 11, so we stop here and this is the remainder.
Therefore, 35 = 2 (mod 11)
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Here's another way to think of it. Consider you have $35 in your pocket. Let's say a store is selling trinkets for $11 each. We can pose these key questions:
- What is the most number of trinkets you can buy?
- If you buy that max amount, how much will you have left over?
The answer to the first question is 3 trinkets because 3*11 = 33 dollars is under the budget of $35. The amount left over is 35-33 = 2 dollars which is the remainder. It's not larger than 11, so we cannot buy any more trinkets at this point.
Answer:
im pretty sure its C
Step-by-step explanation:
Answer:
the original number is greater
Step-by-step explanation:
1. let 1x be your starting number
2. therefore, 0.5 * 1x = 0.5x ( amount after you decreased it by 50%)
3. then increase: 0.5x * 1.5 = 0.75x (amount after you increased it by 50%)
4. 0.75x < 1x (this means that the original number is larger than the one you decreased and then increased)
