x y 4 1 8 2 12 3 16 4 Compare the table of Object A and the equation y = 15 x of Object B. Which of the two moving objects has greater speed and by what factor? (round to nearest hundredth) Responses A Object A by a factor of 1.05Object A by a factor of 1.05 B Object B by a factor of 1.05Object B by a factor of 1.05 C Object A by a factor of 1.25Object A by a factor of 1.25 D Object B by a factor of 1.25
To compare the speed of the two objects, we need to look at the rate of change of the two sets of data.
For Object A, the rate of change is given by the difference in y-values divided by the difference in x-values. The rate of change is:
(4-1)/(1-0) = 3/1 = 3
For Object B, we can see that the equation y = 15x represents a straight line with a slope of 15. Therefore, the rate of change for Object B is also 15.
Since the rate of change for Object B is greater than the rate of change for Object A (15 > 3), Object B has a greater speed than Object A.
To find the factor by which Object B is faster, we can divide the rate of change for Object B by the rate of change for Object A:
15/3 = 5
Therefore, Object B has a speed that is 5 times greater than Object A.
Out of the given options, the correct response is D. Object B by a factor of 1.25.