Answer:
see below
Step-by-step explanation:
10^33/2
Rewriting the numerator as 10 * 10 ^ 32
10 * 10 ^32
--------------------
2
10/2 = 5
5 * 10 ^32
Therefore
10^33/2=5*10^32
Answer:
4 packs of invitations and 2 packs of napkins.
Step-by-step explanation:
The answer is m=5 and m=-2. There is no extraneous solution for this equation.
<span>The definition of quadratic function is given by:
</span>
![(1) \ f(x)=ax^{2}+bx+c \\ \\ where \ a, b, c \ are \ real \ values](https://tex.z-dn.net/?f=%281%29%20%5C%20f%28x%29%3Dax%5E%7B2%7D%2Bbx%2Bc%20%5C%5C%20%5C%5C%20where%20%5C%20a%2C%20b%2C%20c%20%5C%20are%20%5C%20real%20%5C%20values)
<span>
So the problem asks for two conditions:
<em>1. Write the quadratic function in factored form.
</em>
<em>2. The vertex has an x-coordinate of 3.</em>
Then the equation (1) must be written as follows:
</span>
![f(x)=(x-m)(x-n) \\ \\ where \ m \ and \ n \ are \ the \ roots](https://tex.z-dn.net/?f=f%28x%29%3D%28x-m%29%28x-n%29%20%5C%5C%20%5C%5C%20where%20%5C%20m%20%5C%20and%20%5C%20n%20%5C%20are%20%5C%20the%20%5C%20roots)
<span>
To satisfy the two conditions:
So we are free to choose the value of one root, say:
![m=1](https://tex.z-dn.net/?f=m%3D1)
Thus:
Finally,
the answer is:
![f(x)=(x-1)(x-5)](https://tex.z-dn.net/?f=f%28x%29%3D%28x-1%29%28x-5%29)
The graph of this function is shown in the figure below.</span>