Answer:
Blank 1 is Pythagorean Theorem, 2 is sides, 3 is right, 4 is legs, and 5 is the hypotenuse.
Step-by-step explanation:
We will have the following:
First, we write the both equations: the line and the circle:
This can be seeing as follows:
Now, we determine the point where the line intersects the circle in the first quadrant, so first, we determine the positive part of the circle, that is:
Now, we equal this expression and the line:
From this, we take the positive value, since it the only one that makes sense under the parameters required, now we find the value of y:
So, the solution is at the point:
This can be seeing as follows:
Question:
Solution:
The solution to a system of linear equations is where the graphs of each linear equation intersect. In this case, we can see that the lines intersect at the point:
(-3,2)
thus, the correct answer is (-3,2).
Answers:
- Exponential and increasing
- Exponential and decreasing
- Linear and decreasing
- Linear and increasing
- Exponential and increasing
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Explanation:
Problems 1, 2, and 5 are exponential functions of the form where b is the base of the exponent and 'a' is the starting term (when x=0).
If 0 < b < 1, then the exponential function decreases or decays. Perhaps a classic example would be to study how a certain element decays into something else. The exponential curve goes downhill when moving to the right.
If b > 1, then we have exponential growth or increase. Population models could be one example; though keep in mind that there is a carrying capacity at some point. The exponential curve goes uphill when moving to the right.
In problems 1 and 5, we have b = 2 and b = 1.1 respectively. We can see b > 1 leads to exponential growth. I recommend making either a graph or table of values to see what's going on.
Meanwhile, problem 2 has b = 0.8 to represent exponential decay of 20%. It loses 20% of its value each time x increases by 1.
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Problems 3 and 4 are linear functions of the form y = mx+b
m = slope
b = y intercept
This b value is not to be confused with the previously mentioned b value used with exponential functions. They're two different things. Unfortunately letters tend to get reused.
If m is positive, then the linear function is said to be increasing. The line goes uphill when moving to the right.
On the other hand if m is negative, then we go downhill while moving to the right. This line is decreasing.
Problem 3 has a negative slope, so it is decreasing. Problem 4 has a positive slope which is increasing.
Answer: 4 units! Just took the test!
Step-by-step explanation: