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Illusion [34]
3 years ago
12

Will mark brainliest. Please answer:

Mathematics
1 answer:
wlad13 [49]3 years ago
4 0

Answer:

1. (-1,-6)

2. (6,2)

Step-by-step explanation:

Graph each inequality. Test a point in each and shade appropriately. The darkest shaded part is a solution to the set. If the points lie within this region, they are solutions. Please note they cannot land in on of the lighter shade regions or on the lines unless equal to. This means only points on the red line in the darker shaded regions are solutions.

1. (-1,-6)

2. (6,2)

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Find the distance between the following points using the Pythagorean theorem: (-5, 4) and (8, -3)
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First, draw a diagram to visualize the situation:

As we can see, the difference between the x-coordinates of the points is the length of one leg of a right triangle, and the difference between the y-coordinates is the length of the other leg.

Then, for the given points (-5,4) and (8,-3), the distance given by the Pythagorean Theorem is:

\begin{gathered} d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2} \\  \\ =\sqrt{(8--5)^2+(-3-4)^2} \\  \\ =\sqrt{(13)^2+(-7)^2} \\  \\ =\sqrt{169+49} \\  \\ =\sqrt{218} \\  \\ \approx14.7648... \end{gathered}

Therefore, the distance between the points (-5,4) and (8,-3) is: √218.

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