Question
Write the expression. Then, check all that apply.
a number cubed increased by four
A 2-column table with 4 rows. Column 1 is labeled Key Words with entries a number, cubed, increased by, four. Column 2 is labeled replace with entries n, exponent of 3, +, 4.
“A number cubed” is a power, where the base is the variable, n, and the exponent is 3.
“A number cubed” is a power where the base is 3 and the exponent is n.
“Increased by 4” means add 4.
“Increased by 4” means multiply by 4.
The expression is written as n3 + 4.
The expression is wriitten as 4n3
a number cubed increased by four
A 2-column table with 4 rows. Column 1 is labeled Key Words with entries a number, cubed, increased by, four. Column 2 is labeled replace with entries n, exponent of 3, +, 4.
“A number cubed” is a power, where the base is the variable, n, and the exponent is 3.
“A number cubed” is a power where the base is 3 and the exponent is n.
“Increased by 4” means add 4.
“Increased by 4” means multiply by 4.
The expression is written as n3 + 4.
The expression is wriitten as 4n3
Answers
GPT-4o mini
Let's analyze the phrases and their interpretations:
1. **"A number cubed"** - In this context, it means to take a variable (which we've identified as n) and raise it to the power of 3. Thus, it can be expressed as \( n^3 \).
2. **"Increased by 4"** - This phrase means to add 4 to whatever comes before it. Therefore, if we are taking "a number cubed," we add 4 to it, resulting in the expression \( n^3 + 4 \).
Now let's evaluate the statements:
- **"A number cubed" is a power, where the base is the variable, n, and the exponent is 3.** - This statement is **true**.
- **"A number cubed" is a power where the base is 3 and the exponent is n.** - This statement is **false**. The base is n, and the exponent is 3.
- **"Increased by 4" means add 4.** - This statement is **true**.
- **"Increased by 4" means multiply by 4.** - This statement is **false**. It means to add 4, not multiply.
- **The expression is written as n³ + 4.** - This statement is **true**. \( n^3 + 4 \) is the correct expression.
- **The expression is written as 4n³.** - This statement is **false**. The expression is not \( 4n^3 \); it is \( n^3 + 4 \).
In summary, the true statements are:
1. "A number cubed" is a power, where the base is the variable, n, and the exponent is 3.
2. "Increased by 4" means add 4.
3. The expression is written as \( n^3 + 4 \).
1. **"A number cubed"** - In this context, it means to take a variable (which we've identified as n) and raise it to the power of 3. Thus, it can be expressed as \( n^3 \).
2. **"Increased by 4"** - This phrase means to add 4 to whatever comes before it. Therefore, if we are taking "a number cubed," we add 4 to it, resulting in the expression \( n^3 + 4 \).
Now let's evaluate the statements:
- **"A number cubed" is a power, where the base is the variable, n, and the exponent is 3.** - This statement is **true**.
- **"A number cubed" is a power where the base is 3 and the exponent is n.** - This statement is **false**. The base is n, and the exponent is 3.
- **"Increased by 4" means add 4.** - This statement is **true**.
- **"Increased by 4" means multiply by 4.** - This statement is **false**. It means to add 4, not multiply.
- **The expression is written as n³ + 4.** - This statement is **true**. \( n^3 + 4 \) is the correct expression.
- **The expression is written as 4n³.** - This statement is **false**. The expression is not \( 4n^3 \); it is \( n^3 + 4 \).
In summary, the true statements are:
1. "A number cubed" is a power, where the base is the variable, n, and the exponent is 3.
2. "Increased by 4" means add 4.
3. The expression is written as \( n^3 + 4 \).