Question

Which description is paired with its correct expression?

a) Seven less than the quotient of two and a number squared, increased by six:
A) 7 - (2^2) + 6
b) Nine times the difference of a number cubed and three:
B) 9(n^3 - 3)
c) Eight more than the quotient of a number squared and four, decreased by seven:
C) 8(n^2/4) - 7
d) Twice the difference of a number cubed and eight
D) 2(n^3 - 8)

Answer 1

The correct pairings of descriptions with expressions are b) Nine times the difference of a number cubed and three: B) 9(n^3 - 3), c) Eight more than the quotient of a number squared and four, decreased by seven: C) 8(n^2/4) - 7, and d) Twice the difference of a number cubed and eight: D) 2(n^3 - 8).

Step-by-step explanation:

To determine which description is paired with its correct expression, let's analyze each one:

1. Seven less than the quotient of two and a number squared, increased by six: The correct expression would be 7 less than (the quotient of two and a number squared), then increased by six. This could be represented as (n^2/2) + 6 - 7, which is not present among the options.
2. Nine times the difference of a number cubed and three: This matches expression B perfectly, which is 9(n^3 - 3).
3. Eight more than the quotient of a number squared and four, decreased by seven: The expression would be the quotient of a number squared and four, increased by eight, then decreased by seven. This matches expression C, which is 8(n^2/4) - 7.
4. Twice the difference of a number cubed and eight: The corresponding expression would be twice the difference between a number cubed and eight, which matches expression D, 2(n^3 - 8).

Therefore, the descriptions paired with their correct expressions are:

• b) Nine times the difference of a number cubed and three: B) 9(n^3 - 3)
• c) Eight more than the quotient of a number squared and four, decreased by seven: C) 8(n^2/4) - 7
• d) Twice the difference of a number cubed and eight: D) 2(n^3 - 8)