If y varies directly as x, and y is 6 when x is 72, what is the value of y when x is 8?

For the case when x = 8, we have that y = 2/3.

Step-by-step explanation:

The idea that y varies directly as x, can be written in an equation as:

y = k*x, where k is an unknown constant (until now).

We know that y=6 when x=72, then, substituting these values in the above formula gives us the value of k:

6 = k*72, then: k = 6/72 = 1/12.

Now, we can rewrite our initial expression with the known value of k as:

y = (1/12)*x

For the case when x = 8, we have that:

y = (1/12)*8 = 8/12 = 2/3.

a, b, c, d are correct.

step-by-step explanation:

we have g(x) = 3 and are required to find which option is a translation of g(x).

now, 'translation' is a transformation which means to shift the function in any direction and the general form of translation is g(x) + k, where k is any real number.

so, according to the options we see that all are correct as they satisfy the general form of translation.

also, it can be seen from the graph below that the function g(x) = 3 is shifted from its position in all the four options.