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marysya [2.9K]
4 years ago
8

a hairstylist schedules 1/4 hour to trim a customers hair and 1/6 hour to style the customers hair. the hairstylist plans to wor

k 3 1/3 hours each day for 5 days each week. how many appointments can the hairstylist schedule each week if each customer must be trimmed and styled? (show work)
Mathematics
1 answer:
spin [16.1K]4 years ago
4 0
So a trim lasts 1/4*60=15 minutes and a style lasts 1/6*60=10 minutes.
If we add these together, 15+10=25 minutes that is how long each customer takes.
In one day she works for 3 1/3*60=200 minutes in total, so can fit in 200/25=8 appointments per day.
So in 5 days she can have 8*5=40 total appointments each week.
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Answer:

The solutions are x=\frac{3)+\sqrt{153} }{-12}, x=\frac{3)-\sqrt{153} }{-12}

If you need to have them in a decimal form rounded to 3 decimals, the answers would be x=-1.281, x=0.781

Step-by-step explanation:

We are given the equation 6-6x^2-3x=0

The first thing that can be done is to rearrange the terms so that they are in descending order of power. This makes it easier to work with

This gives us -6x^2-3x+6=0

To find the solutions to this equation, we can use the quadratic formula, which will tell us that the solutions are equal to \frac{-b+\sqrt{b^2-4ac} }{2a} ,\frac{-b-\sqrt{b^2-4ac} }{2a}

From our equation, we can gather that a=-6, b=-3, c=6

Now that we have our variables, we can plug them into the quadratic formula to get our solutions.

\frac{-(-3)+\sqrt{(-3)^2-4(-6)(6)} }{2(-6)}\\\\\frac{3)+\sqrt{9+144} }{-12}\\\\\frac{3)+\sqrt{153} }{-12}

And now for our second equation

\frac{-(-3)-\sqrt{(-3)^2-4(-6)(6)} }{2(-6)}\\\\\frac{3)-\sqrt{9+144} }{-12}\\\\\frac{3)-\sqrt{153} }{-12}

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