Answered

IDNLearn.com: Your go-to resource for finding precise and accurate answers. Join our community to receive prompt and reliable responses to your questions from experienced professionals.

3. Which expression has a value of 3?

A. [tex]3\left(4^2-3^2\right)[/tex]
B. [tex]24-23 \cdot 3[/tex]
C. [tex]3^3-3^2[/tex]
D. [tex]\left(6^2-3\right)\left(9^2-70\right)[/tex]

4. Which phrase is a description of [tex]2m + 7[/tex]?

A. 7 more than 2 times [tex]m[/tex]
B. 2 more than 7 times [tex]m[/tex]
C. 2 times the sum of 7 and [tex]m[/tex]
D. 7 times the sum of 2 and [tex]m[/tex]

Sagot :

GinnyAnsweridn
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).
We appreciate your contributions to this forum. Don't forget to check back for the latest answers. Keep asking, answering, and sharing useful information. Your questions find clarity at IDNLearn.com. Thanks for stopping by, and come back for more dependable solutions.