Carmen is 5 1 ··4 years younger than Antoine. Katy is 11 1 ··2 years older than Carmen. To the nearest year, what is the difference in Antoine's age and Katy's age?

Let, age of Carmen, Antoine and Katy is C, A and K.

And it is given that :

               …1)

             ...2)

We need to find the difference in Antoine's age and Katy's age.

Subtracting equation 2) from 1), we get :

Therefore, Katy is years older than Antoine.

the discriminant is 64 + 4*1*12 = 112

this is prime.

step-by-step explanation:

option a is correct.

step-by-step explanation:

scale factor: it is used to find proportional measurements.

proportions means having the same ratio.

scale factor is the ratio of the model measurement to the actual measurement in a simplest form.

or we can say that the ratio of any two corresponding lengths in two similar geometric figures

if the scale factor is more than 1, then it is an enlargement,

if the scale factor less than 1, then it is a reduction.

given the two geometric figure:

by definition of proportions, we have