answer:Let the two positive integers be x and y. Juan's mistake was to subtract instead of adding, so his equation is x-y=2. Maria's mistake was to multiply instead of adding, so her equation is xy=120. We can solve Juan's equation for x to get x=2+y. Substituting this into Maria's equation, we have (2+y)y=120. Expanding and rearranging, we get y^2+2y-120=0. Factoring the quadratic, we have (y+12)(y-10)=0. So, the possible values of y are -12 and 10. Since y must be positive, we have y=10. Substituting this back into x=2+y, we get x=2+10=12. Therefore, the correct answer is x+y=12+10=boxed{22}. The answer is: 22

answer:The slope of a line is defined as the change in y divided by the change in x. Since point A is at (0, 0), the y-coordinate of point B is the change in y. The x-coordinate of point B is the change in x. Since the slope of segment AB is frac{2}{3}, we have frac{text{change in } y}{text{change in } x} = frac{2}{3}. We are given that the y-coordinate of point B is 4, so the change in y is 4 - 0 = 4. We can substitute these values into the slope equation to find the change in x: frac{4}{text{change in } x} = frac{2}{3}. Cross-multiplying gives us 3 cdot 4 = 2 cdot text{change in } x, or 12 = 2 cdot text{change in } x. Dividing by 2 gives us text{change in } x = 6. Since the x-coordinate of point A is 0, the x-coordinate of point B is 0 + 6 = 6. The sum of the x- and y-coordinates of point B is 6 + 4 = boxed{10}.The answer is: 10

answer:We can find the x-intercepts by setting y equal to zero and solving for x. Setting (x-5)(x^2+5x+6)=0, we have two cases to consider: Case 1: x-5=0 In this case, we have x=5, which is one x-intercept. Case 2: x^2+5x+6=0 We can factor the quadratic as (x+2)(x+3)=0, which gives us two additional x-intercepts, x=-2 and x=-3. Therefore, there are a total of boxed{3} different x-intercepts on the graph of y=(x-5)(x^2+5x+6). The answer is: 3

answer:Lydia planted the tree when she was 4 years old and it takes 7 years for the tree to bear fruit, so the tree will bear fruit when Lydia is 4 + 7 = 11 years old. Since Lydia is currently 9 years old, she will be 11 years old when she gets to eat an apple from her tree for the first time. 11 The answer is: 11