Question
Which description is paired with its correct expression?
seven less than the quotient of two and a number squared, increased by six; 7 minus StartFraction 2 Over n squared EndFraction + 6
nine times the difference of a number cubed and three; 9 (n cubed minus 3)
eight more than the quotient of a number squared and four, decreased by seven; 8 + StartFraction 4 Over n squared EndFraction minus 7
twice the difference of a number cubed and eight; 2 n cubed minus 8
seven less than the quotient of two and a number squared, increased by six; 7 minus StartFraction 2 Over n squared EndFraction + 6
nine times the difference of a number cubed and three; 9 (n cubed minus 3)
eight more than the quotient of a number squared and four, decreased by seven; 8 + StartFraction 4 Over n squared EndFraction minus 7
twice the difference of a number cubed and eight; 2 n cubed minus 8
Answers
GPT-4o mini
Let's evaluate each description alongside its corresponding expression to find the correct pairings:
1. **"seven less than the quotient of two and a number squared, increased by six"**
This would translate to:
\[ \frac{2}{n^2} - 7 + 6 = \frac{2}{n^2} - 1 \]
The expression given is \( 7 - \frac{2}{n^2} + 6 \), which simplifies to \( 13 - \frac{2}{n^2} \). Therefore, this description and expression do not match.
2. **"nine times the difference of a number cubed and three"**
This translates to:
\[ 9(n^3 - 3) \]
The given expression is \( 9(n^3 - 3) \), which matches perfectly. This is the correct pairing.
3. **"eight more than the quotient of a number squared and four, decreased by seven"**
This translates to:
\[ \frac{n^2}{4} + 8 - 7 = \frac{n^2}{4} + 1 \]
The given expression is \( 8 + \frac{4}{n^2} - 7 \) which does not match. This description and expression do not correspond.
4. **"twice the difference of a number cubed and eight"**
This translates to:
\[ 2(n^3 - 8) = 2n^3 - 16 \]
The given expression is \( 2n^3 - 8 \), which does not match. This description and expression do not correspond.
From the analysis, the correctly paired description and expression is:
- **Nine times the difference of a number cubed and three; 9 (n cubed minus 3)**.
1. **"seven less than the quotient of two and a number squared, increased by six"**
This would translate to:
\[ \frac{2}{n^2} - 7 + 6 = \frac{2}{n^2} - 1 \]
The expression given is \( 7 - \frac{2}{n^2} + 6 \), which simplifies to \( 13 - \frac{2}{n^2} \). Therefore, this description and expression do not match.
2. **"nine times the difference of a number cubed and three"**
This translates to:
\[ 9(n^3 - 3) \]
The given expression is \( 9(n^3 - 3) \), which matches perfectly. This is the correct pairing.
3. **"eight more than the quotient of a number squared and four, decreased by seven"**
This translates to:
\[ \frac{n^2}{4} + 8 - 7 = \frac{n^2}{4} + 1 \]
The given expression is \( 8 + \frac{4}{n^2} - 7 \) which does not match. This description and expression do not correspond.
4. **"twice the difference of a number cubed and eight"**
This translates to:
\[ 2(n^3 - 8) = 2n^3 - 16 \]
The given expression is \( 2n^3 - 8 \), which does not match. This description and expression do not correspond.
From the analysis, the correctly paired description and expression is:
- **Nine times the difference of a number cubed and three; 9 (n cubed minus 3)**.