The answer is 1210
PLEASE ANSWER FAST PLEASE!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! The point (1, −1) is on the terminal side of
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Answer:
<em>not</em> a rectangle
Step-by-step explanation:
There are several ways to determine whether the quadrilateral is a rectangle. Computing slope is one of the more time-consuming. We can already learn that the figure is not a rectangle by seeing if the midpoint of AC is the same as that of BD. (It is not.) A+C = (-5+4, 5+2) = (-1, 7). B+D = (1-2, 8-2) = (-1, 6). (A+C)/2 ≠ (B+D)/2, so the midpoints of the diagonals are different points.
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The slope of AB is ∆y/∆x, where the ∆y is the change in y-coordinates, and ∆x is the change in x-coordinates.
... AB slope = (8-5)/(1-(-5)) = 3/6 = 1/2
The slope of AD is computed in similar fashion.
... AD slope = (-2-5)/(-2-(-5)) = -7/3
The product of these slopes is (1/2)(-7/3) = -7/6 ≠ -1. Since the product is not -1, the segments AB and AD are not perpendicular to each other. Adjacent sides of a rectangle are perpendicular, so this figure is not a rectangle.
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Our preliminary work with the diagonals showed us the figure was not a parallelogram (hence not a rectangle). For our slope calculation, we "magically" chose two sides that were not perpendicular. In fact, this choice was by "trial and error". Side BC <em>is perpendicular</em> to AB, so we needed to choose a different side to find one that wasn't. A graph of the points is informative, but we didn't start with that.
The probability that at least 2 of the dinners selected are pasta dinners will be 0.8181...
<u><em>Explanation</em></u>
Pasta dinners = 7 , Chicken dinners = 6 and Seafood dinners = 2
The student selects 5 of the total 15 dinners. So, total possible ways for selecting 5 dinners
For selecting at least 2 of them as pasta dinners, the student can select 2, 3, 4 and 5 pasta dinners from total 7 pasta dinners.
So, the possible ways for selecting 2 pasta dinners
The possible ways for selecting 3 pasta dinners
The possible ways for selecting 4 pasta dinners
The possible ways for selecting 5 pasta dinners
Thus, the probability for selecting at least 2 pasta dinners