Respuesta :
Answer:
[tex] 36 = 2x^2 -7x +x^2 -9x +24[/tex]
[tex] 12= 3x^2 -16 x [/tex]
And we can rewrite this expression like this:
[tex] 3x^2 -16 x -12 =0[/tex]
And we can use the quadratic formual to solve this problem:
[tex] X =\frac{-b \pm \sqrt{b^2 -4ac}}{2a}[/tex]
With a = 3, b = -16 , c =-12. Replacing we got:
[tex] x = \frac{16 \pm \sqrt{(-16)^2 -4*(3)*(-12)}}{2*3}[/tex]
And the solutions for this case are:
[tex] x_1 = 6, x_2 =-\frac{2}{3}[/tex]
And then since we need to select the positive solution the final answer would be:
[tex] x = 6[/tex]
Step-by-step explanation:
For this case we have the following equations for the total area of the green space:
[tex] G = 2x^2 -7x[/tex]
[tex] M = x^2 -9x +24[/tex]
And the total area is given by 36 yd^2. And we know that:
[tex] R = 36 yd^2 = G+M[/tex]
Replacing the info given we got:
[tex] 36 = 2x^2 -7x +x^2 -9x +24[/tex]
[tex] 12= 3x^2 -16 x [/tex]
And we can rewrite this expression like this:
[tex] 3x^2 -16 x -12 =0[/tex]
And we can use the quadratic formual to solve this problem:
[tex] X =\frac{-b \pm \sqrt{b^2 -4ac}}{2a}[/tex]
With a = 3, b = -16 , c =-12. Replacing we got:
[tex] x = \frac{16 \pm \sqrt{(-16)^2 -4*(3)*(-12)}}{2*3}[/tex]
And the solutions for this case are:
[tex] x_1 = 6, x_2 =-\frac{2}{3}[/tex]
And then since we need to select the positive solution the final answer would be:
[tex] x = 6[/tex]
