Answer:
Step-by-step explanation:
You have to put this into vertex form in order to find the time it was at its highest. To do this you have to complete the square. First rule is to set the equation equal to 0, then move the constant over to the other side of the equals sign. Let's do that:
The next rule is that the leading coefficient HAS to be a positive 1, and right now ours is a -5. So we have to factor out the -5, leaving us:
The next step is to take half the linear term, square it, and add it to both sides. Our linear term is a -4; half of that is -2, and squaring -2 gives you a 4. So adding in the 4 to the parenthesis on the left is a given; however, don't forget about the -5 hanging out in front as a multiplier. We didn't just add in a 4, we added in -5 times 4 which is -20. Putting all that together:
The reason we do this is apparent on the left side. We create a perfect square binomial of the form
Notice that I also added the 2 negatives on the right at the same time. Now the last step is to move the -135 back over with the other guys and set it equal to y again:
Now it's in the form
where (h, k) are the vertex, or the highest point of the parabola: (2, 135). This means that at 2 seconds the object was at its highest point in its path of 135 m.
This is the answer in point form a d equation
Let the boxes be Box 1, Box 2, Box 3.
consider the 3 white balls. They can be all of them in one box:
(3, 0, 0) (3 in Box 1, 0 in box 2 and 0 in box 0)
(0, 3, 0)
(0, 0, 3)
We can have 2 in one box, and 1 in one of the remaining boxes:
(2, 0, 1)
(2, 1, 0)
(0, 2, 1)
(1, 2, 0)
(0, 1, 2)
(1, 0, 2)
and there is only one way: (1, 1, 1) to place one white ball in each box
In total there are: 3+6+1=10 ways to place the white balls. Similarly there are 10 ways to place the black ones.
Since every placement of the white balls can be combined with any placement of the black balls, there are 10*10=100 ways to place the 3white balls and the 3 black bals in the boxes.
Answer: 100
This is a problem of Difference-of-squares. We know that for a difference of squares
the factorization is given by:
To learn this you need to remember that a <em>difference</em> means <em>subtraction.</em> So applying those concepts we can solve this problem step by step.
Applying distributive property:
Applying distributive property again:
Simplifying:
<em>The correct answer is C</em>
