1. **Translate the word phrase into an algebraic expression:** The phrase is "Three times a number m, added to four times a second number n, divided by double a third number p." This translates to: $$\frac{3m + 4n}{2p}$$ --- 2. **Calculate the value of** $a^2(2b - c)$ **given** $a=4$, $b=-3$, $c=2$: First, substitute the values: $$4^2(2(-3) - 2)$$ Calculate inside the parentheses: $$2(-3) - 2 = -6 - 2 = -8$$ Calculate $4^2$: $$16$$ Multiply: $$16 \times (-8) = -128$$ --- 3. **Expand and simplify** $3(x + 2y) + 5x - (y + 7)$: Distribute: $$3x + 6y + 5x - y - 7$$ Combine like terms: $$3x + 5x = 8x$$ $$6y - y = 5y$$ So the simplified expression is: $$8x + 5y - 7$$ --- 4. **Write as a single fraction:** $\frac{2}{3}x + \frac{5}{4}x^2$ Find common denominator $12$: $$\frac{2}{3}x = \frac{8}{12}x$$ $$\frac{5}{4}x^2 = \frac{15}{12}x^2$$ Combine: $$\frac{8x + 15x^2}{12}$$ --- **Final answers:** A. $$\frac{3m + 4n}{2p}$$ B. $$-128$$ C. $$8x + 5y - 7$$ D. $$\frac{8x + 15x^2}{12}$$