The system of inequalities that represents the given criteria are 3x² > y and y² + 6 > x.
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Let the first number be x and the second number be y.
We are told that three times the square of a number is greater than a second number. Thus; 3x² > y
Now, The square of the second number increased by 6 is greater than the first number. Thus;
y² + 6 > x
Thus, the system of inequalities that represents the given criteria are 3x² > y and y² + 6 > x.
where;
x is first number and y is second number.
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Answer:
A
Explanation:
Let's solve the equation to be written as y in terms of x by adding y to and subtracting 12 from both sides:
3x - y = 12
3x - 12 = y
Now, replace y in the other expression that we want to find (
) with this expression 3x - 12:


Now, we also know that 8 = 2³, so substitute 2³ for 8 in the expression:


Remember that when dividing powers with the same base (in this case, the common base is 2), the result will be a single power whose exponent is the difference of the other two powers. Here, then we have:

Thus, the answer is A.