Answer:
A) M(x) = 3/2x² - 6
Explanation:
Area of the figure
= Area of the triangle + Area of the rectangle
[tex] = (\frac{1}{2} \times b \times h) + (l \times b)[/tex]
[tex] = ( \frac{1}{2} \times x + 2 \times x) + (x + 2)(x - 3)[/tex]
[tex] = ( \frac{x {}^{2} + 2x }{2}) + (x(x - 3) + 2(x - 3))[/tex]
[tex] = (\frac{ {x}^{2} }{2} + \frac{2x}{2} ) + ( {x}^{2} - 3x + 2x - 6)[/tex]
[tex] = (\frac{ {x}^{2} }{2} + x) + ( {x}^{2} - x - 6)[/tex]
[tex] = \frac{ {x}^{2} }{2} + x + {x}^{2} - x - 6[/tex]
[tex] = ( \frac{ {x}^{2} }{2} + {x}^{2} ) + (x - x) - 6[/tex]
[tex] = ( \frac{ {x}^{2} }{2} + \frac{ {2x}^{2} }{2} ) - 6[/tex]
[tex] = \frac{ {3x}^{2} }{2} - 6[/tex]
[tex] = \frac{3}{2} {x}^{2} - 6[/tex]
