Mathematics, 29.08.2019 08:00 jadieb63

For triangle xyw, the slope of wx is , the slope of xy is 0.56, and the slope of yw is .
which statement verifies that triangle wxy is a right triangle?
the slopes of wx and yw are opposite reciprocals.
the slopes of wx and xy are opposite reciprocals.
the slopes of xy and wx have opposite signs.
the slopes of xy and yw have the same signs.

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Answer from: cayden81

Given triangle XYW with vertices X(2, b), Y(-4, -2) and W(-2, 3), the slope of a straight line is given by
$m= \frac{y_2-y_1}{x_2-x_1}$

Thus, the slope of XY is given by
$\frac{-2-b}{-4-2} =0.56 \\ \\ -2-b=0.56(-6)=-3.36 \\ \\ b=-2+3.36=1.36$ ,

Thus the vertex of X is (2, 1.36)

Therefore, the slope of WX is given by
$\frac{1.36-3}{2-(-2)}= \frac{-1.64}{4} =-0.41$ ,

and the slope of YW is given by
$\frac{3-(-2)}{-2-(-4)}= \frac{3+2}{-2+4} = \frac{5}{2}=2.5$ .

For a right triangle, two of the sides intersect each other at 90 degrees (i.e. they are perpendicular to each other).

When two lines are perpendicular the product of the slopes of the the lines is -1. i.e. the slopes of two perpendicular lines are opposite reciprocal.

Two numbers are said to be opposite reciprocal when one of the number is the result of taking the reciprocal of the other number and then changing the sign.

Recall that the slope of WX is -0.41 and the slope of YW is 2.5, but 2.5 x (-0.41) ≈ -1.

Therefore, the statement that verifies that triangle WXY is a right triangle is "
The slopes of WX and YW are opposite reciprocals."

Answer from: Quest

the population of other specie of birds will decline or other specie of birds will find some alternate source of food to survive.

explanation:

according to the competitive exclusion principle, which is also known as gause's law, two specie living in the same niche and feeding on the same resource cannot co-exist stably.

as we have well studied the theory of natural selection which states that only those organisms survive which have better tendency to compete for food and adapt to the environmental conditions.

coming towards the question, what wi ll happen when one species outcompetes the other for the small fish , the other specie will not get enough food and will start to die or decline in population. eventually either other specie needs to find another alternative food source for itself or migrate at some other location where there is less competition otherwise it will just not exist anymore at that niche.

hope it !

Answer from: Quest

its the second choice.

step-by-step explanation:

the elements in the range will be 7 less than the elements in the domain.

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For triangle xyw, the slope of wx is , the slope of xy is 0.56, and the slope of yw is .
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