If x = 10, what is the value of z in the equation z = (x³ / 5) - 12?

To find the value of z in the equation ( z = \left(\frac{x^3}{5}\right) - 12 ) when ( x = 10 ), start by substituting 10 into the equation for ( x ).

First, calculate ( x^3 ):

[

10^3 = 1000

]

Next, divide ( 1000 ) by ( 5 ):

[

\frac{1000}{5} = 200

]

Now, subtract ( 12 ) from ( 200 ):

[

200 - 12 = 188

]

Therefore, when ( x = 10 ), the value of ( z ) is ( 188 ). This corresponds to the correct answer, which reflects the calculations performed using the provided formula and input value. If the students carefully execute each step of substitution and arithmetic, they can confidently arrive at the correct answer.