answer:Since the graphs of the linear functions y = ax + 2 and y = 3x - b are symmetric about the line y = x, it follows that a = frac{1}{3}. Therefore, the equation of the linear function y = ax + 2 becomes y = frac{1}{3}x + 2. Letting x = -6, we get y = 0. Since the point (-6, 0) is symmetric about the line y = x to the point (0, -6), the linear function y = 3x - b must pass through (0, -6). Therefore, b = 6. Hence, the correct option is boxed{text{B}}.

answer:To factorize the given expression y^{3}-16y, we look for common factors and patterns that resemble well-known algebraic identities. Recognizing that 16y can be written as y cdot 16 and seeing the potential for a difference of squares, we proceed as follows: 1. First, factor out the common factor y: [y^{3}-16y = y(y^{2}-16)] 2. Notice that y^{2}-16 is a difference of squares, which can be factored as (y+4)(y-4): [y(y^{2}-16) = y(y+4)(y-4)] Thus, the factorization of the original expression y^{3}-16y is boxed{y(y+4)(y-4)}.

answer:Willie starts with 36.0 stickers and Emily gives him 7.0 more. To find out how many stickers Willie ends with, you add the number of stickers he starts with to the number of stickers Emily gives him: 36.0 (Willie's starting stickers) + 7.0 (stickers given by Emily) = 43.0 stickers So, Willie ends with boxed{43.0} stickers.

answer:1. **Identify the coefficients**: For the equation x^2 - 9x + 14 = 0, the coefficients are a = 1, b = -9, and c = 14. 2. **Apply Vieta's formulas**: - Sum of the roots, r_1 + r_2 = -frac{b}{a} = -frac{-9}{1} = 9. - Product of the roots, r_1r_2 = frac{c}{a} = frac{14}{1} = 14. 3. **Check additional condition**: The problem states that the sum of the roots equals the product of the roots. This condition is satisfied because both r_1 + r_2 = 9 and r_1r_2 = 14. 4. **Calculate the square of the difference of the roots**: - (r_1 - r_2)^2 = (r_1 + r_2)^2 - 4r_1r_2 = 9^2 - 4 times 14 = 81 - 56 = 25. 5. **Find the difference of the roots**: - r_1 - r_2 = sqrt{25} = 5. 6. **Conclusion**: The difference of the roots of the quadratic equation x^2 - 9x + 14 = 0 is 5. The final answer is boxed{textbf{(C)} 5}