Find the first four terms of the sequence represented by the expression.
3n + 5
When n = 1: 3(1) + 5 = 8
When n = 2: 3(2) + 5 = 11
When n = 3: 3(3) + 5 = 14
When n = 4: 3(4) + 5 = 17
Therefore, the first four terms of the sequence represented by the expression 3n + 5 are 8, 11, 14, and 17.
which is a table of values for y=x -6
Here is a table of values for y = x - 6:
|x | y |
|- | - |
|0 | -6|
|1 | -5|
|2 | -4|
|3 | -3|
|4 | -2|
|5 | -1|
|6 | 0 |
|7 | 1 |
|8 | 2 |
|9 | 3 |
In this table, we can see that when x = 0, y = -6. As x increases by 1, y increases by 1. This is because the expression y = x - 6 represents a line with a slope of 1 and a y-intercept of -6.
i still dont get it
No problem, let me try to explain in simpler terms.
The equation y = x - 6 means that we take any value of x and subtract 6 from it to get the corresponding value of y. For example, if x is 3, then y would be 3 - 6 = -3.
To create a table of values, we choose several values of x and calculate the corresponding values of y. In the table I provided before, we chose x to be 0, 1, 2, 3, and so on, up to 9. We then subtracted 6 from each of these x values to get the corresponding y values.
For example, when x is 0, we have y = 0 - 6 = -6. Similarly, when x is 1, we have y = 1 - 6 = -5. When x is 2, we have y = 2 - 6 = -4, and so on.
In this way, we can create a table that shows the values of both x and y. We can then use this table to plot the points and draw a line that represents the equation y = x - 6. I hope this explanation is clearer for you!
what is function notation
Function notation is a way of writing a function using symbols and variables. It is used to describe a relation between two variables, where the value of one variable is determined by the value of the other variable.
Function notation uses the symbol "f" to represent a function, and an input or independent variable is represented by the symbol "x". The output or dependent variable is represented by "f(x)".
For example, if we have a function f(x) = 2x + 3, we can input different values of x and find the corresponding output. If we input x = 2, then f(2) = 2(2) + 3 = 7. If x = 4, then f(4) = 2(4) + 3 = 11.
In this way, function notation allows us to generalize a rule that relates x and y into a symbolically simpler expression. It is widely used in mathematics to model real-world situations and to solve problems by setting up equations representing a function.
Use the function rule f(x) = 3x - 2.
We can use the function rule f(x) = 3x - 2 to find the corresponding output for any input value of x.
For example, if x = 0, then f(0) = 3(0) - 2 = -2. This means that when x is 0, the output is -2.
Similarly, if x = 1, then f(1) = 3(1) - 2 = 1. This means that when x is 1, the output is 1.
We can also create a table of values for this function to help us see the pattern of the input and output values.
| x | f(x) |
|---|------|
| 0 | -2 |
| 1 | 1 |
| 2 | 4 |
| 3 | 7 |
| 4 | 10 |
In this table, we can see that as x increases by 1, the output value f(x) increases by 3. This is because the function rule tells us that for any value of x, the output is 3 times x minus 2.
can you simplify
Can you please provide me with the expression or equation you would like me to simplify? Then, I will be able to assist you.
can you make it easier to understand?
Of course! I'll do my best to explain things so they're easier to understand. Can you please provide me with the expression or equation you are having trouble with?
identify the source as arithmetic, geometric, or neither.
Explain your answer.
1.6, 0.8, 0.4, 0.2, ...
The given sequence is 1.6, 0.8, 0.4, 0.2, ..., and it is a geometric sequence.
A sequence is called a geometric sequence if there is a fixed ratio between consecutive terms. In other words, if you divide any term by the previous term, you get the same number every time.
In this sequence, if you divide any term by the previous term, you get:
0.8 ÷ 1.6 = 0.5
0.4 ÷ 0.8 = 0.5
0.2 ÷ 0.4 = 0.5
...
Since there is a fixed ratio of 0.5 between consecutive terms, this sequence is geometric.