<span>We use the Pythagoras Theorem to derive a formula for finding the distance
between two points in 2- and 3- dimensional space.</span>
Let
P<span> = (x 1, y 1) </span>
Q<span> = (x 2, y 2) </span>
be two points on the Cartesian plane
<span>Then
from the Pythagoras Theorem we find that the distance between P and Q is</span>
PQ=((x2-x1)^2+(y2-y1)^2)^0.5
In a
similar way
it can
be proved that if
P<span> = (x 1, y 1, z1) and </span>
Q<span> = (x 2, y 2, z2) are two
points in the 3-dimensional space, </span>
<span>the
distance between P and Q is</span>
PQ=((x2-x1)^2+(y2-y1)^2+(z2-z1)^2)^0.5
<span>
</span>
See the graphs
<h2>
Explanation:</h2>
First Case:
Here we have the following function:

In order to graph this function, first let's take:

Step 1. Compress horizontally this function by 1/2, so it becomes:

Step 2. Stretch vertically this function, so it becomes:

Step 3. Shift the graph of the function three units down.

Second Case:
Applying a similar method, we get:
Step 1. Compress horizontally this function by 1/2, so it becomes:
Step 2. Stretch vertically this function, so it becomes:
Step 3. Shift the graph of the function tow units down.
Finally, the graphs are shown below.
<h2>Learn more:</h2>
Parabolas: brainly.com/question/11813702
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Answer:
6
Step-by-step explanation:
4.5/3 = 1.5
1.5 x 4 =6
As given Q is the midpoint of GH. SO it will divide GH in two equal parts. We can also say GQ is half of GH.
So we can write

As given GQ = 2x+3 , GH = 5x - 5




11 = x
So GQ = 2x+ 3 = 2*11 + 3 = 25
Answer: Subtract 3 from each side
Step-by-step explanation:
The goal of the problem is to isolate 3 on one side by itself. The only thing standing in our way is that pesky three. In order to get rid of it, and make y have the whole left side to themselves, we have to see what is three doing in the equation. Well, it is a positive three and it is being added to y. So, we want to do the opposite of what it is. Since it is a positive three, we are going to subtract three on both sides. It will zero itself out on the left side and move on over to the right side, giving y the entire left side of the equation.