We start with

and wish to write it as

First, pull 2 out from the first two terms:

Let’s look at what is in parenthesis. In the final form this needs to be a perfect square. Right now we have

and we can obtain -10x by adding -5x and -5x. That is, we can build the following perfect square:

The “problem” with what we just did is that we added to what was given. Let’s put the expression together. We have

and when we multiply that out it does not give us what we started with. It gives us

So you see our expression is not right. It should have a -53 but instead has a -3. So to correct it we need to subtract another 50.
We do this as follows:

which gives us the final expression we seek:

If you multiply this out you will get the exact expression we were given. This means that:
a = 2
d = -5
e = -103
We are asked for the sum of a, d and e which is 2 + (-5) + (-103) = -106
Answer:
x=31/25
Step-by-step explanation:
3x+4/5=7-2x
Multiply through by 5
5(3x+4/5)=5(7-2x)
15x+4=35-10x
Collecting like terms
15x+10x=35-4
25x=31
x=31/25
Answer:
Step-by-step explanation:
Part A: 15
Part B: $125
The answer is -7
The arrows both point toward the left side, and sine there are seven spaces the arrows are going through, you subtract 7 spaces and get -7
Hope that helps.
Answer:
The population of bacteria can be expressed as a function of number of days.
Population =
where n is the number of days since the beginning.
Step-by-step explanation:
Number of bacteria on the first day=![\[5 * 2^{0} = 5\]](https://tex.z-dn.net/?f=%5C%5B5%20%2A%202%5E%7B0%7D%20%3D%205%5C%5D)
Number of bacteria on the second day = ![\[5 * 2^{1} = 10\]](https://tex.z-dn.net/?f=%5C%5B5%20%2A%202%5E%7B1%7D%20%3D%2010%5C%5D)
Number of bacteria on the third day = ![\[5*2^{2} = 20\]](https://tex.z-dn.net/?f=%5C%5B5%2A2%5E%7B2%7D%20%3D%2020%5C%5D)
Number of bacteria on the fourth day = ![\[5*2^{3} = 40\]](https://tex.z-dn.net/?f=%5C%5B5%2A2%5E%7B3%7D%20%3D%2040%5C%5D)
As we can see , the number of bacteria on any given day is a function of the number of days n.
This expression can be expressed generally as
where n is the number of days since the beginning.