[tex](1) \ x>0 \\ \\ (2) \ y>0 \\ \\ (3) \ y<-x+6[/tex]
Explanation:
A right triangle is a special triangle that has a right angle. In this case, we have to write a system of inequalities that defines a shaded region that looks like a right triangle. First of all, let's say that at the origin the triangle will have a right angle. To do so, we'd need to set:
[tex]x>0 \\ \\ y>0[/tex]
So the shaded region in this first part will be the First Quadrant as indicated in the first figure below. So if the opposite side lies on the x-axis the adjacent side will lie on the y-axis or if the adjacent side lies on the x-axis the opposite side will lie on the y-axis. Everything is ok up to this point. We just need to define the hypotenuse, so we'd need to define a line. In order to have a right triangle, we need a line with negative slope and positive y-intercept shaded under the line. So, this inequality could be:
[tex]y<-x+6[/tex]
Finally, the system of inequalities would be:
[tex](1) \ x>0 \\ \\ (2) \ y>0 \\ \\ (3) \ y<-x+6[/tex]
And the final shaded region is the one shown in the second figure.
Learn more:
Inequalities: https://brainly.com/question/2486051
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