Question
Question 1
Evaluate the expression 5x−2^3/2
when x = 6(1 point)
Responses
10
10
11
11
12
12
13
13
Question 2
Evaluate the expression 4(n+6)- 3n when n = 8(1 point)
Responses
20
20
22
22
30
30
32
32
Question 3
Evaluate the expression 9x −5^2 + 7
when x=5(1 point)
Responses
27
27
25
25
23
23
21
Evaluate the expression 5x−2^3/2
when x = 6(1 point)
Responses
10
10
11
11
12
12
13
13
Question 2
Evaluate the expression 4(n+6)- 3n when n = 8(1 point)
Responses
20
20
22
22
30
30
32
32
Question 3
Evaluate the expression 9x −5^2 + 7
when x=5(1 point)
Responses
27
27
25
25
23
23
21
Answers
Answered by
GPT-4o mini
Let's evaluate each expression step by step.
**Question 1: Evaluate the expression 5x - 2^3/2 when x = 6**
1. Substitute x with 6:
\[
5(6) - 2^{3/2}
\]
2. Calculate \(5(6)\):
\[
30
\]
3. Calculate \(2^{3/2}\):
\[
2^{3/2} = (2^{3})^{1/2} = 8^{1/2} = \sqrt{8} = 2\sqrt{2} \approx 2 \times 1.414 \approx 2.828
\]
4. Thus, replace \(2^{3/2}\):
\[
30 - 2\sqrt{2} \approx 30 - 2.828 \approx 27.172
\]
Since none of the responses matches an evaluated answer in exact form and to match the original question format, it seems to imply:
- If considering just the integer response, the closest appropriate value to choose would be **10**, realizing there may have been a miscalculating on my part in understanding final results, but sticking to responses matches off integers but fail.
The question though suggests the responses might not have been clear.
---
**Question 2: Evaluate the expression 4(n + 6) - 3n when n = 8**
1. Substitute n with 8:
\[
4(8 + 6) - 3(8)
\]
2. Calculate \(8 + 6\):
\[
14
\]
3. Calculate \(4 \times 14\):
\[
56
\]
4. Calculate \(3 \times 8\):
\[
24
\]
5. Now, perform the operation:
\[
56 - 24 = 32
\]
So the final answer for question 2 is **32**.
---
**Question 3: Evaluate the expression 9x - 5^2 + 7 when x = 5**
1. Substitute x with 5:
\[
9(5) - 5^2 + 7
\]
2. Calculate \(9 \times 5\):
\[
45
\]
3. Calculate \(5^2\):
\[
25
\]
4. Now substitute:
\[
45 - 25 + 7
\]
5. Perform the subtraction and addition:
\[
45 - 25 = 20
\]
Then,
\[
20 + 7 = 27
\]
So the final answer for question 3 is **27**.
---
### Summary of Answers:
1. Question 1: **10**
2. Question 2: **32**
3. Question 3: **27**
**Question 1: Evaluate the expression 5x - 2^3/2 when x = 6**
1. Substitute x with 6:
\[
5(6) - 2^{3/2}
\]
2. Calculate \(5(6)\):
\[
30
\]
3. Calculate \(2^{3/2}\):
\[
2^{3/2} = (2^{3})^{1/2} = 8^{1/2} = \sqrt{8} = 2\sqrt{2} \approx 2 \times 1.414 \approx 2.828
\]
4. Thus, replace \(2^{3/2}\):
\[
30 - 2\sqrt{2} \approx 30 - 2.828 \approx 27.172
\]
Since none of the responses matches an evaluated answer in exact form and to match the original question format, it seems to imply:
- If considering just the integer response, the closest appropriate value to choose would be **10**, realizing there may have been a miscalculating on my part in understanding final results, but sticking to responses matches off integers but fail.
The question though suggests the responses might not have been clear.
---
**Question 2: Evaluate the expression 4(n + 6) - 3n when n = 8**
1. Substitute n with 8:
\[
4(8 + 6) - 3(8)
\]
2. Calculate \(8 + 6\):
\[
14
\]
3. Calculate \(4 \times 14\):
\[
56
\]
4. Calculate \(3 \times 8\):
\[
24
\]
5. Now, perform the operation:
\[
56 - 24 = 32
\]
So the final answer for question 2 is **32**.
---
**Question 3: Evaluate the expression 9x - 5^2 + 7 when x = 5**
1. Substitute x with 5:
\[
9(5) - 5^2 + 7
\]
2. Calculate \(9 \times 5\):
\[
45
\]
3. Calculate \(5^2\):
\[
25
\]
4. Now substitute:
\[
45 - 25 + 7
\]
5. Perform the subtraction and addition:
\[
45 - 25 = 20
\]
Then,
\[
20 + 7 = 27
\]
So the final answer for question 3 is **27**.
---
### Summary of Answers:
1. Question 1: **10**
2. Question 2: **32**
3. Question 3: **27**