Question

In a game of cornhole, Sasha tossed a bean bag and it landed at the edge of the hole. The hole can be represented by the equation x^2+ y^2= 5, and the path of the bean bag canbe represented by y = -0.5x^2 -1.5x + 4. To which points could she have tossed her bean bag?(-1,-2) or (-2, 1)(1.-2) or (2,1)(-1,2) or (-2,-1)(1, 2) or (2, -1)

Answer 1

To find where Sasha tossed her bean bag, we must solve the system with equations representing the circle and the parabola's path. By substituting the parabola equation into the circle's and solving for x and y, we can find the intersection points.

Step-by-step explanation:

In order to find the points where Sasha could have tossed her bean bag, we need to solve the system of equations given by the circle x² + y² = 5 and the parabola y = -0.5x² - 1.5x + 4. We substitute the expression for y from the parabola's equation into the circle's equation:

1. 
   
3. x² + (-0.5x² - 1.5x + 4)² = 5
4. 
   
6. Solve the resulting equation for x.
7. 
   
9. Substitute the found x-values back into the parabola's equation to find the corresponding y-values.

After calculating, we can determine the intersection points that represent where the bean bag could have landed at the edge of the hole. The correct points will satisfy both equations.