Answer:
Note: this answer is kind of long so jump to picture to see a visual process.
In order to find the simplest radical form of a square root, you need prime factorize the number. In order to do this, you take a number and divide it by different prime numbers until all of its factors are now prime. We will use 24 as our example. 24 divided by 2 (which is prime) is 12. 12 divided by 2, is 6. 6 divided by 2 is 3. Therefor, our prime factorization of 24 is 2^3 * 3, which basically means 8 * 3. Then, take take out pairs of the same number and put on the OUTSIDE of the root. However, make sure that it is NEXT to the square root and not inside the mini hook that the square root makes. This means that that number is multiplying the square root of the number. Now, the only pair in this prime factorization is 2, so take two out of the prime factorization and that leaves us with square root 6 times 2, which is the answer.
Also, when taking out pairs, only take one number from the pair (in this case 2) and put it on the outside. If there is another pair, multiply that number by the other number. So if there was a pair of 3 and a pair of 2, take out 1 three and 1 two and multiply them and put on the outside.
Step-by-step explanation:
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First, let's find the slope of the line from the points given.
m = (4 - - 2) / (3 - 1)
m = 6 / 2
m = 3
Secondly, we know that a line perpendicular to the original must have a slope that is the opposite reciprocal of the original. For the given points, the opposite reciprocal slope would be -1/3.
Now, we can put all of the equations below into slope intercept form and find the ones that have a slope of -1/3.
Equation 1: Correct
y = -1/3x - 5
Equation 2: Incorrect
y = 3x - 3
Equation 3: Incorrect
y - 2 = 3(x + 1)
y - 2 = 3x + 1
y = 3x + 2
Equation 4: Correct
x + 3y = 9
3y = -x + 9
y = -1/3x + 3
Equation 5: Incorrect
3x + y = -5
y = -3x - 5
Hope this helps!! :)
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.
3/50
Hope I helped!
Let me know if you need anything else!
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