Final answer:
Using the provided formula y = 2x + 24 and substituting x with 6, we find that y equals 36. This means the child's height on their 6th birthday is 36 inches, which corresponds to option (a).
Step-by-step explanation:
To solve the mathematical problem completely and determine the child’s height on their 6th birthday, we use the formula provided, which is y = 2x + 24. In this equation, x represents the age of the child in years, and y stands for the child’s height in inches. We need to substitute the value of x with 6, since we are interested in the child’s height at age 6.
Substituting 6 into the equation, the calculation is as follows: y = 2(6) + 24, which simplifies to y = 12 + 24. Adding these two numbers gives us y = 36 inches. Therefore, the child's height on their 6th birthday is 36 inches, which corresponds to option (a).
To mention the correct option answer in the final answer, the child’s height on their 6th birthday, according to the given equation, is 36 inches, hence the correct answer to the question is option (a).