Attachment Below- help would be appreciated! :)
1 answer:
Answer:
A, B, C, E, and F
To solve this problem, you should make sure to find the equation first. Start by doing rise/run with your two given points on the graph. From the point (-1,1) you rise 4 and then run 16 over to the point (3,2). That gives us a slope of 4/16 which can then be simplified to 1/4. That means that letter F tells us the equation of the line is y= 1/4x + 5/4.
From there you want to check your points, (3,2) and (-1,1). The first number is always x and the second number is always y. So you plug the point numbers into the equation we just found to see if they work. In the photos I inserted are how to do this step.
Once you have checked your points and you know for sure they're solutions, that gave you letters A and B. Since the point (1, 3/2) is also given in one of the answers we should check that point as well. (Also done in one of the photos) Since the point came out correctly that gives us letter C and also tells us there is more than 2 solutions. This means that letter E is also correct.
Hope this helped!
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Answer:
[-3, ∞)
Step-by-step explanation:
There are many ways to find the range but I will use the method I find the easiest.
First, find the derivative of the function.
f(x) = x² - 10x + 22
f'(x) = 2x - 10
Once you find the derivative, set the derivative equal to 0.
2x - 10 = 0
Solve for x.
2x = 10
x = 5
Great, you have the x value but we need the y value. To find it, plug the x value of 5 back into the original equation.
f(x) = x² - 10x + 22
f(5) = 5² - 10(5) + 22
= 25 - 50 +22
= -3
Since the function is that of a parabola, the value of x is the vertex and the y values continue going up to ∞.
This means the range is : [-3, ∞)
Another easy way is just graphing the function and then looking at the range. (I attached a graph of the function below).
Hope this helped!
The value of K for which f(x) is a valid probability density function is 1/4.
<h3>How to solve for the value of K</h3>open the equation
2K + 2K = 1
4K = 1
divide through by 4
K = 1/4
Read more on probability density function here
#SPJ4