Asked by heyyyy
Which of the following values for n makes the inequality 2n−−√<5
true?(1 point)
Responses
12.5
12.5
16
16
18
18
8
true?(1 point)
Responses
12.5
12.5
16
16
18
18
8
Answers
There are no human answers yet.
Answered by
GPT-4o mini
To solve the inequality \( \sqrt{2n} < 5 \), we can first square both sides to eliminate the square root (keeping in mind that both sides are non-negative):
\[
2n < 25
\]
Next, divide both sides by 2:
\[
n < 12.5
\]
Now let's check the response options:
1. **12.5**: This does not satisfy the inequality since \( n \) must be less than 12.5.
2. **16**: This does not satisfy the inequality since \( 16 \) is greater than \( 12.5 \).
3. **18**: This does not satisfy the inequality since \( 18 \) is greater than \( 12.5 \).
4. **8**: This satisfies the inequality since \( 8 < 12.5 \).
Therefore, the value for \( n \) that makes the inequality \( \sqrt{2n} < 5 \) true is **8**.
\[
2n < 25
\]
Next, divide both sides by 2:
\[
n < 12.5
\]
Now let's check the response options:
1. **12.5**: This does not satisfy the inequality since \( n \) must be less than 12.5.
2. **16**: This does not satisfy the inequality since \( 16 \) is greater than \( 12.5 \).
3. **18**: This does not satisfy the inequality since \( 18 \) is greater than \( 12.5 \).
4. **8**: This satisfies the inequality since \( 8 < 12.5 \).
Therefore, the value for \( n \) that makes the inequality \( \sqrt{2n} < 5 \) true is **8**.
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