Question

Which description is paired with its correct expression?

1. two less than the quotient of a number cubed and four, increased by eight; 2 - n³/4 + 8
2. six times the difference of five and a number squared; 6 (n²-5)
3. three more than the quotient of nine and a number cubed, decreased by two; 3 + 9/n³ - 2
4. twice the difference of a number squared and three; 2n²-3

Answer 1

The correct expression is 'two less than the quotient of a number cubed and four, increased by eight,' which translates mathematically to \(2 - \frac{n^3}{4} + 8\).

Step-by-step explanation:

The correct description paired with its expression is:

• two less than the quotient of a number cubed and four, increased by eight; \(2 - \frac{n^3}{4} + 8\).

This can be verified by evaluating the statement step by step. First, take the quotient of a number cubed \(n^3\) and four \(4\), which gives us \(\frac{n^3}{4}\). Then we need to subtract two from that quotient, leading us to \(\frac{n^3}{4} - 2\). Last, we increase that result by eight, which will give us the final expression: \(\frac{n^3}{4} - 2 + 8\) or simplified as \(2 - \frac{n^3}{4} + 8\).