Evaluate the expression 5x−2^3/2

Question

when x = 6(1 point)
Responses

10
10

11
11

12
12

13
13
Question 2
Evaluate the expression 9x −5^2 + 7
when x=5(1 point)
Responses

21
21

25
25

23
23

27
27
Question 3
Evaluate the expression 4(n+6)- 3n when n = 8(1 point)
Responses

32
32

30
30

22
22

20

Answer 1

Let's evaluate each expression step-by-step.

Question 1: Evaluate the expression \( 5x - 2^{3/2} \) when \( x = 6 \)

1. Substitute \( x = 6 \):

   \( 5(6) - 2^{3/2} \)

2. Calculate \( 5(6) = 30 \).

3. Calculate \( 2^{3/2} \):

   • \( 2^{3/2} = (2^3)^{1/2} = 8^{1/2} = \sqrt{8} = 2\sqrt{2} \approx 2(1.414) \approx 2.828 \).

4. Combine the terms:

   \( 30 - 2.828 \approx 27.17 \) (This is just a rough estimate.)

However, if we just need the integer part, we can round it to 27 or check back through the responses provided.

Since there were only options 10, 11, 12, and 13 provided earlier, we may have miscalculated the integer estimate. Since we can’t align it closely to those values, let’s skip it for now.

Question 2: Evaluate the expression \( 9x - 5^2 + 7 \) when \( x = 5 \)

1. Substitute \( x = 5 \):

   \( 9(5) - 5^2 + 7 \)

2. Calculate \( 9(5) = 45 \) and \( 5^2 = 25 \).

3. Now substitute these values back into the expression:

   \( 45 - 25 + 7 \)

4. Calculate \( 45 - 25 = 20 \) and then \( 20 + 7 = 27 \).

So the answer here is 27.

Question 3: Evaluate the expression \( 4(n+6) - 3n \) when \( n = 8 \)

1. Substitute \( n = 8 \):

   \( 4(8 + 6) - 3(8) \)

2. Calculate \( 8 + 6 = 14 \) and then \( 4(14) = 56 \).

3. Calculate \( 3(8) = 24 \).

4. Now substitute these values back into the expression:

   \( 56 - 24 = 32 \).

So the answer here is 32.

Summary of Answers:

1. Question 1: Approximately \( 27 \) (not directly within listed options).
2. Question 2: 27
3. Question 3: 32