Answer: There are 495 possible different sets of answers the could contain exactly 8 correct answers of false.
Basically, we are looking for the number of different ways of selecting 8 objects out of a set of 12 objects. Our objects are answers of false and the set is the test.
This is a combination problem. The formula would be:
12! / (8! x 4!) = 495
Answer:
(-2,-36)
Step-by-step explanation:
![y=(x-4)(x+8)](https://tex.z-dn.net/?f=y%3D%28x-4%29%28x%2B8%29)
<u>1) Find the zeros of the parabola</u>
The zero-product property states that any value, when multiplied by 0 will equal 0. Therefore, to make y=0, either (x-4)=0 OR (x+8)=0.
Therefore, x=4 and x=-8.
<u>2) Find the x-coordinate of the vertex</u>
To do this, we take the average of our zeros.
![\frac{4+(-8)}{2} \\=\frac{-4}{2} \\=-2](https://tex.z-dn.net/?f=%5Cfrac%7B4%2B%28-8%29%7D%7B2%7D%20%5C%5C%3D%5Cfrac%7B-4%7D%7B2%7D%20%5C%5C%3D-2)
Therefore, the x-coordinate of the vertex is -2.
<u>3) Find the y-coordinate of the vertex</u>
Plug the x-coordinate back into the original equation
![y=(-2-4)(-2+8)\\y=(-6)(6)\\y=-36](https://tex.z-dn.net/?f=y%3D%28-2-4%29%28-2%2B8%29%5C%5Cy%3D%28-6%29%286%29%5C%5Cy%3D-36)
Therefore, the y-coordinate of the vertex is -36.
Therefore, the vertex of the parabola is (-2,-36).
I hope this helps!
Answer:
140?
Step-by-step explanation:
40 percent of 350 is 140 so I assume its 140.
Answer:
8.49
Step-by-step explanation:
there is a little formula related to the famous formula of Pythagoras.
it says that the height of a triangle is the square root of the product of both segments of the baseline (the segments the height splits the baseline into).
so, x is actuality the height of the triangle.
x = sqrt(3×24) = sqrt(72) = 8.49