The given equation relates the real numbers $b, c,$ and $d$, where $d > \dfrac{5}{9}c$:$b^2 + 5c = 9d$Which equation correctly expresses $b$ in terms of $c$ and $d$?

Answer: $b = \pm\sqrt{9d - 5c}$ (The specific option D from the test would be one form of this, typically the positive root or both roots if offered).

Explanation:1. Start with the given equation: $b^2 + 5c = 9d$

2. Isolate $b^2$: Subtract $5c$ from both sides of the equation: $b^2 = 9d - 5c$

3. Solve for $b$: To find $b$, take the square root of both sides. Remember that taking a square root can result in both a positive and a negative value. $b = \pm\sqrt{9d - 5c}$

The condition $d > \dfrac{5}{9}c$ ensures that $9d > 5c$, which means $9d - 5c > 0$. This guarantees that the term under the square root is positive, so $b$ is a real number.

4. Conclusion: The equation correctly expressing $b$ in terms of $c$ and $d$ is $b = \pm\sqrt{9d - 5c}$. (The multiple-choice option D would be one of these forms, e.g., $\sqrt{9d - 5c}$ or $-\sqrt{9d - 5c}$ or $\pm\sqrt{9d - 5c}$).