Find the value of the variable in the table
X n 4 6 10 12
Y 1 9 m 21 25
A m equals 13, n = 0 b and equals 11, n = 0 c m equals 15, n = 3 d m = 13, n = 3
We can determine the relationship between X and Y by analyzing the given values in the table.
When X = 4, Y = 1, and when X = 6, Y = 9. It looks like as X increases by 2, Y increases by 8, which means the relationship between X and Y might be Y = 4X - 15 (since 4*4 - 15 = 1, and 4*6 - 15 = 9). Let's see if this relationship holds true for the other given values.
When X = 10, Y = 21. According to our relationship, 4*10 - 15 = 25, which is not correct. So, let's try another potential relationship based on the differences between the values of X and Y.
When X increases by 2, Y increases by 8. When X increases by 4 (from 6 to 10), Y increases by 12. This looks like a linear relationship, but not the one we initially tried: for every increase of 2 in X, Y increase by 4 more than it did for the previous increase of 2 in X. If we take the base value of Y to be -7 (which can be deduced since for X=4, Y=1, and before that, Y should have increased by 4 less than 8, i.e., by 4), the relationship becomes:
Y = -7 + 4X + 2n
Now let's check if this relationship holds true for the given values in the table.
For X = 4 and Y = 1: 1 = -7 + 4*4 + 2n => n = 0
For X = 6 and Y = 9: 9 = -7 + 4*6 + 2n => n = 0
For X = 10 and Y = 21: 21 = -7 + 4*10 + 2n => n = 3
Then, to find the value of m:
m = -7 + 4*12 + 2*3 = -7 + 48 + 6 = 47.
So the values of the variables are m = 47 and n = 3. The answer is (d) m = 13, n = 3.