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Margarita [4]
3 years ago
14

Right triangle XYZ has legs of length XY = 12 and YZ = 6. Point D is chosen at random within the triangle XYZ. What is the proba

bility that the area of triangle XYD is at most 12?
Mathematics
2 answers:
Llana [10]3 years ago
8 0

The "successful" region has half the size of the whole triangle, so by similar triangles, the probability that the area of triangle XYD is at most 12 is 1/4.

Brilliant_brown [7]3 years ago
7 0

Answer:

5/9

Step-by-step explanation:

If you draw the triangle out on a grid papar and draw a line across the 2 marker point from XY up of the YZ side, you will see that the line from that marker point across to the hypotenuse is actually 8. Then you find the area of the little triangle with legs 8 and 4 (since 6-2 is 4), and the area is 16. After that, find the total area of the big triangle, which is 12x6/2=36. Since we want to know the area of the quadrilateral at the bottom of the big triangle seperated by the 2 marker point, we subtract 16 from 36, which equals to 20. 20/36=5/9. And that is my final answer. I tested it and it is correct. I hope this helps.

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<h2>Hello!</h2>

The answer is:

The quadratic function that fits the given picture is:

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<h2>Why?</h2>

We can solve the problem and find the correct function that fits the curve below by finding which function intercepts the y-axis at -5 (we can see it from the picture), also, we need to look for a function that represents a parabola opening upwards. We need to remember that when a parabola is opening upwards, its quadratic term coefficient is negative.

So, we can see that from the given functions, the only function that represents a parabola opening upwards and its y-intercept is located at y equal to -5 is the second option:

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We have that :

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We can see that the quadratic term (a) is negative, and the quadratic function intercepts the y-axis at y equal to -5.

Hence, the answer is:

The quadratic function that fits the given picture is:

y=-3x^{2}+13x-5

Have a nice day!

Note: I have attached a picture for better understanding.

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