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Novay_Z [31]
3 years ago
11

What is the inverse of the function below? f(x) = 2^x + 6

Mathematics
2 answers:
erik [133]3 years ago
7 0

Answer:

f^-1 (x) = log 2 (x-6)

Step-by-step explanation:

Helen [10]3 years ago
6 0

The inverse of this function would be f(x) = \frac{Log(x - 6)}{Log2}.



You can find the value of any inverse function by switching the f(x) and the x value. Then you can solve for the new f(x) value. The end result will be your new inverse function. The step-by-step process is below.



f(x) = 2^{x} - 6 ----> Switch f(x) and x



x = 2^{f(x)} - 6 ----> Add 6 to both sides



x + 6 = 2^{f(x)} -----> Take the logarithm of both sides in order to get the f(x) out of the exponent



Log(x + 6) = f(x)Log2 ----> Now divide both sides by Log2



\frac{Log(x + 6)}{Log2} = f(x) ----> And switch the order for formatting purposes.



f(x) = \frac{Log(x + 6)}{Log2}



And that would be your new inverse function.

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{\bf \red {\huge{answer : }}}

The money increased from 600 pounds to 621 pounds.

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\pink {\sf{hence , \frac{21}{621} \times 100 }}

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Therefore , the dog's weight increased by 3 79/207%

4 0
3 years ago
Surface area of a 4m and 4m and 4m cube
jeka94

Answer: 96 m²

Step-by-step explanation: Surface area is the sum of the areas of all of the faces of a 3-dimensional figure.

So to find the surface area of a cube, it's important to understand that each face of a cube has the same area so we can simply find the area of one face of a cube and multiply by the number of faces which is 6.

To find the area of one face of a cube, we can use the formula for the area of a square which is S².

Since the length of a side is 4 meters, we have (4 m)² or 4 meters x 4 meters which is 16 m².

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6 0
3 years ago
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An arts academy requires there to be 5 teachers for every 95 students and 4 tutors for every 40 students how many students does
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Answer:

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To find the amount of students per teacher and per tutor you have to divide

95 students /5 teachers

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40 students /4 tutors

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2 years ago
What multiplies together to get 10 but adds together to get -11
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3 years ago
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Complete this table to show the sample space for each roll in the game
leva [86]

I'm assuming you only need help with part B. If that's the case, then all we do is add up the values outside of the table to get the inner cell results. For example, in row 1, column 1, we have 1's outside. They add to 1+1 = 2. So we'll have 2 in the first row and first column of the table. The other cells are computed in this way. In figure 1 (see attached image), I show the intermediate step of adding. Then in figure 2, I actually add up the values and show the final result of what the table will look like when all said and done. Take note of the color coding to help see how the values match up for each inner cell of the table. The color coding is optional.

------------------------------------------------------------------------------------------------------------

Edit: 

Part C -- Part 1) Probability of rolling double sixes


There are five copies of "6" in the table (see figure 2 of the attached image) out of 36 total possibilities. How did I get 36? It's the result of multiplying 6*6. This is because there are 6 faces per die. As the table shows, there are 6 rows and 6 columns giving 36 cells total.


So we divide the number of times "6" shows up (5 times) out of the number of total possibilities (36 total) to get: 5/36 = 0.1389 = 13.89%


Answer as a fraction: 5/36

Answer as a decimal: 0.1389

Answer as a percent: 13.89%

The decimal and percent forms are approximate

---------------------------------------------


Part C -- Part 2) Probability of rolling doubles


To roll doubles, all we need to do is roll the same number twice on each die. In other words, we have "twin values" so to speak. Back in part 1 above, we dealt with just '6's showing up twice. There are other doubles as well


The doubles possibilities are: 

1 and 1

2 and 2

3 and 3

4 and 4

5 and 5

6 and 6


Each combo listed above only shows up once. So we have 6 instances where we have doubles (one instance per side of the die). This is out of 36 total


Divide the values mentioned: 6/36 = 1/6 = 0.1667 = 16.67%


Answer as a fraction: 1/6

Answer as a decimal: 0.1667

<span>Answer as a percent: 16.67%</span>

The decimal and percent forms are approximate

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3 years ago
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