Write a linear equation based on given information. Through (5,-5) and (4,0)
1 answer:
For this case we have that by definition, the equation of the line of the slope-intersection form is given by:
Where:
m: It is the slope of the line
b: It is the cut point with the y axis
We have the following points:
We find the slope:
Thus, the equation is of the form:
We substitute a point and find b:
Finally, the equation is:
Answer:
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Answer:
Step-by-step explanation:
First off, I'm assuming that when you said "directrices" you mean the oblique asymptotes, since hyperbolas do not have directrices they have oblique asymptotes.
If we plot the asymptotes and the foci, we see that where the asymptotes cross is at the origin. This means that the center of the hyperbola is (0, 0), which is important to know.
After we plot the foci, we see that they are one the y-axis, which is a vertical axis, which means that the hyperbola opens up and down instead of sideways. Knowing those 2 characteristics, we can determine that the equation we are trying to fill in has the standard form
We know h and k from the center, now we need to find a and b. Those values can be found from the asymptotes. The asymptotes have the standard form
y = ±
Filling in our asymptotes as they were given to us:
y = ± where a is 2 and b is 1. Now we can write the formula for the hyperbola!:
which of course simplifies to
Answer:
The appropriate alternative hypothesis if he wanted to substantiate his suspicion would be
Step-by-step explanation:
At the null hypothesis, we test that the mean is equal to a certain value.
At the alternate hypothesis, we test that the mean is different, less than or more than the mean value tested at the null hypothesis.
The historical U.S. mean unemployment insurance benefit was reported to be $238 per week.
This means that the null hypothesis is:
A researcher in the state of Virginia anticipated that sample data would show evidence that the mean weekly unemployment insurance benefit in Virginia was above the national level.
This means that the alternate hypothesis is: