the function m = 25

Question

x+50
gives the saline concentrate of a solution in milliliters when x milliliters of water is mixed with 50 milliliters of a 50% saline solution.
what are the constraints on the variable m in the function

the value of m is restricted to ''blank'' numbers
the constraint on the variable m is written as ''blank''

answer the blank spots with the correct answer.

Answer 1

To analyze the function \( m = \frac{25}{x + 50} \), we need to determine the constraints on the variable \( m \).

1. Identifying the domain of \( x \):

   • \( x \) represents the amount of water in milliliters. Since volume cannot be negative, \( x \) should be greater than or equal to 0: \[ x \geq 0 \]

2. Behavior of the function:

   • As \( x \) increases, \( x + 50 \) also increases, which means \( m \) decreases.
   • When \( x = 0 \): \[ m = \frac{25}{0 + 50} = \frac{25}{50} = 0.5 \]
   • As \( x \) approaches infinity, the term \( x + 50 \) increases without bound, which means \( m \) approaches 0: \[ \lim_{x \to \infty} m = 0 \]

3. Conclusion on the variable \( m \):

   • The values of \( m \) are restricted between \( 0 \) and \( 0.5 \).

Given this analysis, we can fill in the blanks:

• The value of \( m \) is restricted to non-negative numbers (since \( m \) cannot be negative).
• The constraint on the variable \( m \) is written as \( 0 < m \leq 0.5 \).

Thus, the final answers are:

• The value of \( m \) is restricted to non-negative numbers.
• The constraint on the variable \( m \) is written as \( 0 < m \leq 0.5 \).