Answer: 6
Step-by-step explanation:
Answer:

Step-by-step explanation:
So we want to make x the subject of the formula:

First, distribute the left side:

Combine all the terms with x with it on one side. To do this, first subtract bx from both sides. The right side cancels:

Remove the -ab from the left. Add ab to both sides. The left side cancels:

Now, distribute out the x from the left side:

Divide both sides by (a-b). The left side cancels:

Therefore:

Answer:
The inverse of the function is
.
Step-by-step explanation:
The function provided is:

Let
.
Then the value of <em>x</em> is:

For the inverse of the function,
.
⇒ 
Compute the value of
as follows:
![f[f^{-1}(x)]=f[\frac{x-5}{3}]](https://tex.z-dn.net/?f=f%5Bf%5E%7B-1%7D%28x%29%5D%3Df%5B%5Cfrac%7Bx-5%7D%7B3%7D%5D)
![=3[\frac{x-5}{3}]+5\\\\=x-5+5\\\\=x](https://tex.z-dn.net/?f=%3D3%5B%5Cfrac%7Bx-5%7D%7B3%7D%5D%2B5%5C%5C%5C%5C%3Dx-5%2B5%5C%5C%5C%5C%3Dx)
Hence proved that
.
Compute the value of
as follows:
![f^{-1}[f(x)]=f^{-1}[3x+5]](https://tex.z-dn.net/?f=f%5E%7B-1%7D%5Bf%28x%29%5D%3Df%5E%7B-1%7D%5B3x%2B5%5D)

Hence proved that
.
Answer:
<em>The combined average of Altuve's weighted averages is 1 for 2 or 1/2</em>
Step-by-step explanation:
<u>Combined Average</u>
On Friday, Altuve had 3 out of 5 successes
On Saturday, Altuve had 2 out of 4 successes
On Friday, Altuve had 1 out of 3 successes
The total successes are 3+2+1=6
The total tries are 5+4+3=12
The combined average is:

Simplifying:

The combined average of Altuve's weighted averages is 1 for 2 or 1/2
Part 1: getting the area of the entrance
The entrance has a trapezoid shape.
Area of trapezoid can be calculated using the following rule:
Area of trapezoid = average base * height
The aveage base = (b1+b2)/2 = (8+16)/2 = 12 ft
height of trapezoid = 4 ft
Therefore:
area of entrance = 12*4 = 48 ft^2
Part 2: getting the area of the house:
area of house = area of back porch + area of side deck + area of play room + area of entrance
i- getting the area of the back porch:
The back porch is a square with side length = 6 ft
Therefore:
area of back porch = 6*6 = 36 ft^2
ii- getting the area of side deck:
The side deck is a rectangle whose length is 14 ft and width is 3 ft
Therefore:
area of side deck = 14*3 = 42 ft^2
iii- getting the area of play room:
The play room is a rectangle whose length is 14 ft and width is 16 ft
Therefore:
area of play room = 14*16 = 224 ft^2
iv- area of entrance is calculated in part 1 = 48 ft^2
Based on the above:
area of house = 36 + 42 + 224 + 48 = 350 ft^2
hope this helps :)