Answer:
-5
Step-by-step explanation:
the lowest ratio of 6 is 2 so 7 less then 2 is -5
44 students would choose computer games because 20+14+24=54 students in total 44 + 14=54
Answers:
- Exponential and increasing
- Exponential and decreasing
- Linear and decreasing
- Linear and increasing
- Exponential and increasing
=========================================================
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.
---------------------
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.
Replacing x with x-2 moves the graph 2 units to the right.
Replacing b(x) with b(x)-3 moves the graph 3 units down.
The transformation
h(x) = b(x -2) -3
moves the graph of b(x) 2 units to the right and 3 units down.
Answer:
approximately 12.04 units
Step-by-step explanation:
We'll use the Pythagorean Theorem to solve this problem.
There are two points here. The horizontal distance between them is 8 units and the vertical distance is 9.
According to the Pythagorean Theorem (or the Distance Formula), the distance between the two points is
d = √(8^2 + 9^2) = √(64 + 81) = √145 units, or approximately 12.04 units.