answer:The vertex of the parabola y = x^2 + a^2 is (0,a^2). Substituting this into the equation of the line, we get a^2 = 0 + a + a, which simplifies to a^2 = 2a. Rearranging, we have a^2 - 2a = 0, which factors as a(a-2) = 0. Therefore, the two possible values of a are a = 0 and a = 2. Thus, there are boxed{2} values of a for which the line passes through the vertex of the parabola. The answer is: 2

answer:Cubing both sides of the equation, we get 3 - x = -frac{27}{8}. Then, adding x to both sides, we find x = 3 + frac{27}{8} = frac{51}{8}. Therefore, the only solution to the equation is x = boxed{frac{51}{8}}. The answer is: frac{51}{8}

answer:Substituting the given values, we have 2 times 2 - 3 times 1. Evaluating the expression, we get 4 - 3 = boxed{1}. The answer is: 1

answer:To find the y-intercept, we set x = 0 and solve for y. Thus, 3(0) + 5y = 20, so 5y = 20 and y = 4. The y-intercept point is therefore boxed{(0,4)}. The answer is: (0,4)