Question

Which of the following values for m makes the inequality m−−√+17<24
true?(1 point)
Responses

64
64

50
50

49
49

48
48
Rema

Answer 1

To solve the inequality \(\sqrt{m} + 17 < 24\), we can start by isolating the square root:

1. Subtract 17 from both sides:
\[
\sqrt{m} < 24 - 17
\]
\[
\sqrt{m} < 7
\]

2. Square both sides to eliminate the square root:
\[
m < 7^2
\]
\[
m < 49
\]

Now we need to check which of the given values for \(m\) satisfies this inequality:

- For \(m = 64\): \(64 < 49\) is **false**.
- For \(m = 50\): \(50 < 49\) is **false**.
- For \(m = 49\): \(49 < 49\) is **false**.
- For \(m = 48\): \(48 < 49\) is **true**.

Thus, the value of \(m\) that makes the inequality true is **48**.