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Look at the system of inequalities. $\newline$ $y \leq -3x + 9$ $\newline$ $x \geq 0$ $\newline$ $y \geq 0$ $\newline$ The solution set is the triangular region where all the inequalities are true. $\newline$ What are the vertices of that triangular region? $\newline$ (,) $\newline$ (,) $\newline$ (,)

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Find the focus or directrix of a parabola

Full solution

Q. Look at the system of inequalities.

\newline

y \leq -3x + 9

\newline

x \geq 0

\newline

y \geq 0

\newline

The solution set is the triangular region where all the inequalities are true.

\newline

What are the vertices of that triangular region?

\newline

(____,____)

\newline

(____,____)

\newline

(____,____)

Find Intersection with X-Axis: First, let's find the intersection of $y = -3x + 9$ and the x-axis ( $y = 0$ ). $\newline$ Set $y = 0$ in the equation $y = -3x + 9$ and solve for $x$ . $\newline$ $0 = -3x + 9$ $\newline$ $3x = 9$ $\newline$ $x = 3$ $\newline$ So, the intersection with the x-axis is at $(3, 0)$ .
Find Intersection with Y-Axis: Next, find the intersection of $y = -3x + 9$ and the y-axis ( $x = 0$ ). $\newline$ Set $x = 0$ in the equation $y = -3x + 9$ and solve for $y$ . $\newline$ $y = -3(0) + 9$ $\newline$ $y = 9$ $\newline$ So, the intersection with the y-axis is at $(0, 9)$ .
Find Origin as Third Vertex: The third vertex is the intersection of the x-axis $y = 0$ and the y-axis $x = 0$ . This is simply the origin, which is $(0, 0)$ .

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x

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y

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