Help me with this question.. stuck with it..
1 answer:
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The answer is:
The explanation is shown below:
1- You have the following expression given in the exercise:
2- When you multiply signs, you obtain:
3. Now, you must add like terms, as following:
4. Therefore, you have that the expression simplified is:
Answer:
Step-by-step explanation:
Your final answer is the standard form of a parabola. Since your equation has an x-squared term in it and not a y-squared term, your form will be
To get it into this form we will solve the quadratic for y and then set it equal to 0 so we can complete the square on it. Solving for y then setting y equal to 0:
so
We only need to complete the square on the x-terms, so we will move the constant back over to the other side of the equals sign:
The rule for completing the square is that the leading coefficient HAS to be a 1. Ours is 1/8, so we have to factor it out. When we do that we are left with:
To complete the square on the left, we take half the linear term, square it, and add it onto both sides. Our linear term is 2 (the number stuck to the x-term). Half of 2 is 1, and 1 squared is 1. So we add it into the parenthesis on the left. BUT we cannot discount the 1/8 sitting out front there. It is a multiplier. So what we actually added on the left is 1/8(1). That looks like this:
Now we will write the left side into its perfect square binomial (which was the whole reason for doing this!) and simplify the right at the same time:
Now we will set the whole thing back to equal y:
That's one form. But you need it in vertex form, so we add 3 to both sides:
and then multiply both sides by 8:
If you need to break it down further to include what your p value is, then:
Either that one or the one right above it should work.
Answer:
a = 5.
Step-by-step explanation:
The graph here is a probability density graph. What will represent on the graph?
is the area
- between the graph and the x-axis,
- to the left of
.
The area under the graph between 0 and 9 is a trapezoid. Consider the trapezoid in three slices from left to right:
- A right triangle of area
,
- A rectangle of area
, and
- Another right triangle of area
.
The area of the leftmost triangle plus that of the rectangle is exactly 0.6. In other words, the area to the left of between the graph and the x-axis is
.
.
.
As a side note shall be the only answer to this question since the area under the graph to the left of
can only increase or stay constant but not decrease as the value of
increases.