patterns and equations:
x: 0,3,__,10
y: __, 8, 12,15
To find the missing values in the pattern, let's examine the given x and y values.
For the x-values: 0, 3, __, 10
To find the pattern, we can observe that the difference between consecutive terms is increasing by 3: 3 - 0 = 3, and 10 - 3 = 7. So, the next difference in the sequence would be 7 + 3 = 10.
Therefore, the missing x-value is 3 + 10 = 13.
Now let's focus on the y-values: __, 8, 12, 15
To find the pattern, we can see that the difference between consecutive terms is not constant. Let's calculate the differences: 8 - __ = 4, 12 - 8 = 4, and 15 - 12 = 3.
Since the differences are not constant, we need to look for another pattern. By observing the differences between the differences, we find that they are constant. The differences of the differences are all 0. Therefore, we can conclude that the pattern is a quadratic equation.
To find the missing y-value, we can continue the pattern by adding the differences to the previous term:
15 + 3 = 18
So, the missing y-value is 18.
The completed pattern is:
x: 0, 3, 13, 10
y: 18, 8, 12, 15