Sure, let's solve each part of the problem step-by-step.
### Part 3: Determine which expression has a value of 3
Let's evaluate each given expression step-by-step:
a. [tex]\(3(4^2 - 3^2)\)[/tex]
- Calculate [tex]\(4^2 = 16\)[/tex]
- Calculate [tex]\(3^2 = 9\)[/tex]
- Subtract: [tex]\(16 - 9 = 7\)[/tex]
- Multiply by 3: [tex]\(3 \times 7 = 21\)[/tex]
- Therefore, [tex]\(3(4^2 - 3^2) = 21\)[/tex]
b. [tex]\(24 - 23 \cdot 3\)[/tex]
- Multiply first: [tex]\(23 \cdot 3 = 69\)[/tex]
- Subtract: [tex]\(24 - 69 = -45\)[/tex]
- Therefore, [tex]\(24 - 23 \cdot 3 = -45\)[/tex]
c. [tex]\(3^3 - 3^2\)[/tex]
- Calculate [tex]\(3^3 = 27\)[/tex]
- Calculate [tex]\(3^2 = 9\)[/tex]
- Subtract: [tex]\(27 - 9 = 18\)[/tex]
- Therefore, [tex]\(3^3 - 3^2 = 18\)[/tex]
d. [tex]\((6^2 - 3)(9^2 - 70)\)[/tex]
- Calculate [tex]\(6^2 = 36\)[/tex]
- Calculate [tex]\(9^2 = 81\)[/tex]
- Subtract inside the parentheses: [tex]\(36 - 3 = 33\)[/tex]
- Subtract inside the parentheses: [tex]\(81 - 70 = 11\)[/tex]
- Multiply: [tex]\(33 \times 11 = 363\)[/tex]
- Therefore, [tex]\((6^2 - 3)(9^2 - 70) = 363\)[/tex]
None of these expressions evaluate to 3. Therefore, none of the given expressions in Part 3 has a value of 3.
### Part 4: Determine which phrase describes [tex]\(2m + 7\)[/tex]
Let's analyze each phrase to see which one correctly describes [tex]\(2m + 7\)[/tex]:
a. 7 more than 2 times [tex]\(m\)[/tex]:
- This phrase accurately describes [tex]\(2m + 7\)[/tex] because it means you take 2 times [tex]\(m\)[/tex] and then add 7.
b. 2 more than 7 times [tex]\(m\)[/tex]:
- This would be written as [tex]\(7m + 2\)[/tex], which is not [tex]\(2m + 7\)[/tex].
c. 2 times the sum of 7 and [tex]\(m\)[/tex]:
- This would be written as [tex]\(2(7 + m)\)[/tex], which simplifies to [tex]\(14 + 2m\)[/tex], not [tex]\(2m + 7\)[/tex].
d. 7 times the sum of 2 and [tex]\(m\)[/tex]:
- This would be written as [tex]\(7(2 + m)\)[/tex], which simplifies to [tex]\(14 + 7m\)[/tex], not [tex]\(2m + 7\)[/tex].
Therefore, the correct phrase that describes [tex]\(2m + 7\)[/tex] is:
a. 7 more than 2 times [tex]\(m\)[/tex].
So, the answers are:
For Part 3, none of the expressions have a value of 3.
For Part 4, the description of [tex]\(2m + 7\)[/tex] is "7 more than 2 times [tex]\(m\)[/tex]" which is option (a).
