1. Problem 8: Find the initial speed of a car that skids 108 feet using the formula $v = \sqrt{35 \times \text{skid length}}$. 2. Substitute the skid length 108 feet into the formula: $$v = \sqrt{35 \times 108}$$ 3. Calculate the product inside the square root: $$35 \times 108 = 3780$$ 4. So, $$v = \sqrt{3780}$$ 5. Factor 3780 to simplify the square root: $$3780 = 36 \times 105$$ 6. Use the property $\sqrt{a \times b} = \sqrt{a} \times \sqrt{b}$: $$v = \sqrt{36} \times \sqrt{105} = 6 \sqrt{105}$$ 7. Therefore, the estimated initial speed is $6 \sqrt{105}$ miles per hour. --- 8. Problem 9: Solve for $x$ in the equation $6y = 5x - 1$. 9. Add 1 to both sides: $$6y + 1 = 5x$$ 10. Divide both sides by 5: $$x = \frac{6y + 1}{5}$$ 11. This matches option D. Final answers: - Problem 8: $6 \sqrt{105}$ - Problem 9: $x = \frac{6y + 1}{5}$