1. **State the problem:** We are given the expression $0.2y^2 + 0.32y + 0.96$ and want to rewrite it in the form $a(5y^2 + 8y + 24)$, where $a$ is a constant. 2. **Identify the formula:** We want to factor out a constant $a$ such that: $$0.2y^2 + 0.32y + 0.96 = a(5y^2 + 8y + 24)$$ 3. **Compare coefficients:** To find $a$, compare the coefficients of corresponding terms: - For $y^2$: $0.2 = a imes 5$ - For $y$: $0.32 = a imes 8$ - For the constant term: $0.96 = a imes 24$ 4. **Solve for $a$ using the first coefficient:** $$a = \frac{0.2}{5}$$ 5. **Simplify the fraction:** $$a = \frac{0.2}{5} = \frac{\cancel{0.2}}{\cancel{5}} = 0.04$$ 6. **Verify with other coefficients:** - Check $y$ term: $a \times 8 = 0.04 \times 8 = 0.32$ (matches) - Check constant term: $a \times 24 = 0.04 \times 24 = 0.96$ (matches) 7. **Conclusion:** The value of $a$ is $0.04$. **Final answer:** $$a = 0.04$$