To determine which of the given expressions is equivalent to \( 15(r + 3) \), we can first simplify \( 15(r + 3) \).
Starting with: \[ 15(r + 3) \]
Using the distributive property, we multiply \( 15 \) by both \( r \) and \( 3 \): \[ 15r + 15 \cdot 3 = 15r + 45 \]
Now we can compare \( 15r + 45 \) with the provided expressions:
- \( r + 3 \)
- \( 15 + 45r \)
- \( 15r + 4 \)
- \( 45r \)
None of the expressions \( r + 3 \), \( 15 + 45r \), \( 15r + 4 \), or \( 45r \) are equivalent to \( 15r + 45 \).
Thus, the equivalent expression is not among the choices provided. The correct equivalent expression should be \( 15r + 45 \).