The term "closed" in math means that if you take two items from a set, do some operation, then you'll always get another value in the same set (sometimes you may get the same value as used before). For example, adding two whole numbers leads to another whole number. We therefore say "the set of whole numbers is closed under addition". This applies to integers as well because integers are positive and negative whole numbers. So we can say that integers are closed under addition.
Integers are not closed under division. Take two integers like 2 an 5 and divide: 2/5 = 0.4 which is not an integer. Integers don't have decimal parts.
The set of whole numbers is {0,1,2,3,...} and we can subtract the two values 1 and 2 to get 1-2 = -1. The order matters here. Subtracting a larger value from a smaller leads to a negative. The value -1 is not in the set of whole numbers. So we can say that whole numbers is not closed under subtraction
Finally, the set of irrational numbers is closed under addition. Adding any two irrational numbers leads to another irrational number. For instance, pi+sqrt(2) = 3.142 + 1.414 = 4.556; I'm using rounded decimals as approximate values. An irrational number is one where we cannot write it as a fraction of integers. Contrast that with a rational number in which we can write it as a fraction of integers. Example: 10 = 10/1 is a rational number.
Answer:
3 units
Step-by-step explanation:
So if we want to know how high the spring board is, this will need to be the time at which the diver is still at the top of the board, in this case t = 0 seconds.
So we will need to find h(0)
- h(0) = 5(0)² + 10(0) + 3 = 0 + 0 + 3 = 3
Answer:
n squared + 3n + 1
Step-by-step explanation:
5,11,19,29
Firstly look at the difference between each number. The first difference is 6 then 8 then 10 etc. After that you look at your created sequence - 6,8,10 etc. The difference is 2 each time. Then applying rules, you have to do the constant difference divided by 2 to get a coefficient of n squared. So in this case it's n squared because 2/2 = 1 so you don't have to place a 1 in front of the n squared. After you create a sequence from the n squared. That would be 1,4,9 etc. Then you need to see how to get from the sequence: 1,4,9 etc to your original sequence: 5,11,19 etc. So if you calculate it you will get 4,7,10 because firstly 5-1 = 4 then 11-4 = 7 etc. The sequence 4,7,10 is a linear sequence so the constant difference is 3 each time. So to get a nth term of a linear sequence you will start off as 3n then you will substitute 1 then 2 then 3 into the 3n. Therefore that would be 3,6 etc. So if you take the first substituted term, that would be 3 as said before then you will have to see how to get from the 3 to 4 so that is just adding 1. So the nth term of this linear sequence is 3n + 1. Check if it works at the end. So the overall nth term of the quadratic sequence is n squared as said before + 3n + 1.
so basically what i was thinking of was they sold them in the spring
Answer: x = 5
/2 , 4 , -2
Step-by-step explanation: