Pre-algebra.. please help :/
1 answer:
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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:
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:
Finally, the system of inequalities would be:
And the final shaded region is the one shown in the second figure.
<h2>Learn more:</h2>Inequalities: brainly.com/question/2486051
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Answer:
- DE ≈ 9.49, EF ≈ 8.06, FD ≈ 14.87
- obtuse scalene triangle
Step-by-step explanation:
For finding side lengths, it is convenient to work with the differences of the coordinates.
DE = E(-1, -3) -D(8, -6) = (-9, 3)
EF = F(-2, 5) -E(-1, -3) = (-1, 8)
FD = D(8, -6) -F(-2, 5) = (10, -11)
Then the lengths are ...
DE = √((-9)² +3²) = √90 = 3√10 ≈ 9.49
EF = √((-1)² +8²) = √65 ≈ 8.06
FD = √(10² +(-11)²) = √221 ≈ 14.87
The lengths are all different and the largest angle is obviously more than 90°, so the triangle is an obtuse scalene triangle.
