Hank brought a fish tank
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<h2>Answer:</h2>
Dotted linear inequality shaded below passes through (0, 4) & (4,3). Dotted parabolic inequality shaded above passes through points (negative 6,4), (negative 4, 0) & (negative 2, 4).
<h2>Step-by-step explanation:</h2>Hello! Let me help you to find the correct option to this problem. First of all, we have the following system of inequalities:
To solve this, let's write the following equations:
<h3>FIRST:</h3>This is a linear function written in slope-intercept form as . So, the slope
and the y-intercept is
. Since in the inequality we have the symbol < then the graph of the line must be dotted. To get the shaded region, let's take a point, say,
and let's test whether the region is above or below the graph. So:
Since the expression is true, then the region is the one including point , that is, it's shaded below.
This is a parabola that opens upward and whose vertex is . Since in the inequality we have the symbol > then the graph of the parabola must be dotted. Let's take the same point
to test whether the region is above or below the graph. So:
Since the expression is false, then the region is the one that doesn't include point , that is, it's shaded above
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<h3>On the other hand, testing points (0, 4) and (4,3) on the linear function:</h3>So the line passes through these two points.
<h3 /><h3>Now, testing points (negative 6,4), (negative 4, 0) & (negative 2, 4) on the parabola:</h3><h3 />So the line passes through these three points.
Finally, the shaded region is shown below.
