The data (1, 5), (3, 16), (5, 35), (7, 67), (9, 110) could be modeled as a linear relationship if (2 points)
x is transformed to x2
y is transformed to y2
x is transformed to x3
y is transformed to y3
A, just took the quiz and it was right
A. x is transformed to x^2 is correct
To determine if the given data could be modeled as a linear relationship, we can examine the transformations applied to the variables x and y.
1. x is transformed to x^2:
If we square the x-values of the data points, we get (1^2, 5^2), (3^2, 16^2), (5^2, 35^2), (7^2, 67^2), and (9^2, 110^2), which simplifies to (1, 25), (9, 256), (25, 1225), (49, 4489), and (81, 12100), respectively. We can notice that the relationship between x^2 and y does not appear to be linear.
2. y is transformed to y^2:
If we square the y-values of the data points, we get (1, 5^2), (3, 16^2), (5, 35^2), (7, 67^2), and (9, 110^2), which simplifies to (1, 25), (3, 256), (5, 1225), (7, 4489), and (9, 12100), respectively. Again, the relationship between x and y^2 does not seem to be linear.
3. x is transformed to x^3:
If we raise the x-values to the power of 3, we get (1^3, 5), (3^3, 16), (5^3, 35), (7^3, 67), and (9^3, 110), which simplifies to (1, 5), (27, 16), (125, 35), (343, 67), and (729, 110), respectively. We can observe that the relationship between x^3 and y is not linear.
4. y is transformed to y^3:
If we raise the y-values to the power of 3, we get (1, 5^3), (3, 16^3), (5, 35^3), (7, 67^3), and (9, 110^3), which simplifies to (1, 125), (3, 4096), (5, 42875), (7, 315823), and (9, 1331000), respectively. Once again, the relationship between x and y^3 does not appear to be linear.
Based on these transformations, none of the given options (x^2, y^2, x^3, y^3) would result in a linear relationship.