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2 answers:
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The company picnic cost $ 1300 for 80 employees
<em><u>Solution:</u></em>
Given that cost of a company picnic varies directly as the number of employees attending the picnic
Let "c" be the company picnic cost
Let "n" be the number of employees attending the picnic
Therefore,
Where "k" is the constant of proportionality
c = kn ---------- eqn 1
<em><u>Given that company picnic costs $487.50 for 30 employees</u></em>
Therefore substitute c = 487.50 and n = 30
<em><u>How much does a company picnic cost for 80 employees?</u></em>
Substitute n = 80 and k = 16.25 in eqn 1
Thus $ 1300 is the cost for 80 employees
Answer:
When we have a quadratic equation:
a*x^2 + b*x + c = 0
There is something called the determinant, and this is:
D = b^2 - 4*a*c
If D < 0, then the we will have complex solutions.
In our case, we have
5*x^2 - 10*x + c = 0
Then the determinant is:
D = (-10)^2 - 4*5*c = 100 - 4*5*c
And we want this to be smaller than zero, then let's find the value of c such that the determinant is exactly zero:
D = 0 = 100 - 4*5*c
4*5*c = 100
20*c = 100
c = 100/20 = 5
As c is multiplicating the negative term in the equation, if c increases, then we will have that D < 0.
This means that c must be larger than 5 if we want to have complex solutions,
c > 5.
I can not represent this in your number line, but this would be represented with a white dot in the five, that extends infinitely to the right, something like the image below:
