What is the quotient of 43,482 ÷ 12?
1 answer:
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Answer:
Step-by-step explanation:
Given: ; find x and y.
Let's start with finding x first. Let's distribute the left side of the equation.
Let's move everything we can to the left side of the equation. Some things will cancel out.
Now, let's move the term that includes to the left side of the equation. Everything else should be moved to the right.
Let's get rid of the negative sign in front of by dividing both sides by -1.
To get completely isolated, divide both sides by
.
Simplify.
Let's solve for y. We will start with the distributed and simplified equation to make it easier.
Now, let's move the term that includes to the left side of the equation. Everything else should be moved to the right.
Again, let's get rid of the negative sign in front of the by dividing both sides by -1.
To isolate y, divide both sides by z.
Simplify.
Input is the same as the x-term and output is the same as the y-term.
For example, take a look at the image provided with thee table.
Looking at the first box of our table, notice that if we subtract 5 from 1, we get -4 and if we subtract 5 from 2 we get -3 and if we subtract 5 from 3, we get -2. Notice that in each case, we're subtracting 5 from the input to get the output.
I attached a table so you can practice if you'd like to. All you have to do is subtract 5 from each input and you will end up with the output. The first few are done for you. I also provided an answer key in the next image so you can check your work.
The last one might be a little trick. In the input, we have n which is a variable that represents any number. If we want to find the nth term, we simply subtract 5. So we have n - 5.
First image is practice if you'd like and the second is the key.
If you don't want to do it, no worries.
Answer:
The nth term rule of the quadratic sequence is .
Step-by-step explanation:
We are given the following quadratic sequence below;
4, 15, 30, 49, 72, 99, 130,...
As we know that the formula for the nth term of the quadratic sequence is given by =
Firstly, we will find the difference between the term of the given sequence;
1st difference of the given sequence;
(2nd term - 1st term), (3rd term - 2nd term), (4th term - 3rd term), (5th term - 4th term), (6th term - 5th term), (7th term - 6th term)
= (15 - 4), (30 - 15), (49 - 30), (72 - 49), (99 - 72), (130 - 99),....
= (11, 15, 19, 23, 27, 31,.....)
Now, we will find the second difference of the given sequence, i.e;
= (15 - 11), (19 - 15), (23 - 19), (27 - 23), (31 - 27),....
= (4, 4, 4, 4, 4)
Since the differences are same now, so to find the value of a we have to divide the value of second difference by 2, i.e;
The value of a = = 2
SO, the first term of the nth term rule equation is =
.
Now, in the term , put the value of n = 1, 2, 3, 4 and 5 and then form the sequence, i.e;
If n = 1, then =
= 2
If n = 2, then =
= 8
If n = 3, then =
= 18
If n = 4, then =
= 32
If n = 5, then =
= 50
SO, the sequence formed is (2, 8, 18, 32, 50).
Now, find the difference of this sequence and the original quadratic sequence, i.e;
= (4 - 2), (15 - 8), (30 - 18), (49 - 32), (72 - 50)
= (2, 7, 12, 17, 22)
Now, as we can see that the above sequence resembles the general form of (5n - 3) because:
If we put n = 1, then (5n - 3) = 5 - 3 = 2
If we put n = 2, then (5n - 3) = 10 - 3 = 7 and so on....
From this, we concluded that the value of b and c are 5 and (-3) respectively.
Hence, the nth term rule for the given quadratic sequence is .