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The shaded area represents


Question

The shaded area represents

Options

A) x \(\leq\) 0, y \(\leq\) 0, 2y + 3x \(\leq\) 6

B) x \(\geq\) 0, y \(\geq\) 3, 3x + 2y \(\geq\) 6

C) x \(\geq\) 2, y \(\geq\) 0, 3x + 2y \(\leq\) 6

D) x \(\geq\) 0, y \(\geq\) 0, 3x + 2y \(\geq\) 6

The correct answer is A.

Explanation:

m = \(\frac{y_2 - y_1}{x_2 - x_2} = \frac{3 - 0}{0 - 2} = \frac{-3}{2}\)

= \(\frac{y - y_1}{x- x_1}\)

m = \(\frac{y - 3}{x}\) \(\geq\) \(\frac{-3}{2}\)

2(y - 3) \(\geq\) - 3x = 2y - 6 \(\geq\) - 3x

= 2y + 3x \(\leq\) 6 ; x \(\leq\) 0, y \(\leq\) 0


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Dicussion (1)

  • m = \(\frac{y_2 - y_1}{x_2 - x_2} = \frac{3 - 0}{0 - 2} = \frac{-3}{2}\)

    = \(\frac{y - y_1}{x- x_1}\)

    m = \(\frac{y - 3}{x}\) \(\geq\) \(\frac{-3}{2}\)

    2(y - 3) \(\geq\) - 3x = 2y - 6 \(\geq\) - 3x

    = 2y + 3x \(\leq\) 6 ; x \(\leq\) 0, y \(\leq\) 0

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