Question

Y=-0.5x²+2x и y=0.5x

Answer 1

-0.5x^2+2x=0.5x

-0.5x^2+1.5x=0

x(-0.5x+1.5) =0

x=0 или -0.5x+1.5=0

x=3

Answer 2

The given equations are:

1. y = -0.5x² + 2x
2. y = 0.5x

To find the points of intersection between these two equations, we can set them equal to each other:

-0.5x² + 2x = 0.5x

Let's solve this equation:

Adding 0.5x to both sides: -0.5x² + 2x - 0.5x = 0

Combining like terms: -0.5x² + 1.5x = 0

Now, let's factor out an x:

x(-0.5x + 1.5) = 0

Setting each factor equal to zero:

x = 0 (Equation 1) -0.5x + 1.5 = 0

Adding 0.5x to both sides: 1.5 = 0.5x

Dividing both sides by 0.5: 3 = x (Equation 2)

Now, substitute the values of x back into the equations to find the corresponding y-values:

For x = 0 (Equation 1): y = -0.5(0)² + 2(0) = 0

For x = 3 (Equation 2): y = 0.5(3) = 1.5

Therefore, the points of intersection between the two equations are (0, 0) and (3, 1.5).