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alexandr1967 [171]
3 years ago
5

Mario has a business selling muffins. Let x be the price of a muffin. Then, the profit P for Mario’s business is given by p(x)=-

100x2+350x-150 Choose the inequality that shows the business will make a positive profit.
Mathematics
2 answers:
Alex3 years ago
6 0

The first question's answer is:

0<-100x^2+350x-150

The second question "Look at the factorization shown below.

0 < –100x2 + 350x – 150

0 < –50(2x2 – 7x + 3)

0 < –50(2x – 1)(x – 3)

Select the range that Mario can choose from to price his muffins and make a positive profit.

The answer is:

$0.50 < x < $3.00

Rufina [12.5K]3 years ago
5 0
To make a positive profit p(x)>0 we need to make:
-100 x^{2} +350x-150 \ \textgreater \  0

Now we solve this for x:
-2 x^{2} +7x-3 \ \textgreater \ 0

We have:
a = -2
b = 7
c = -3

We will use formula for quadratic equation:
x_{1} =  \frac{-b+ \sqrt{ b^{2}-4ac } }{2a}  \\  \\  x_{2} =  \frac{-b- \sqrt{ b^{2}-4ac } }{2a}  \\  \\  x_{1} =  \frac{-7+ \sqrt{ 49-24 } }{-4} = \frac{-7+5 }{-4} = \frac{-2 }{-4} = \frac{1}{2}  \\  \\  x_{2} =  \frac{-7- \sqrt{ 49-24 } }{-4}  = \frac{-7-5 }{-4} = \frac{-12 }{-4} = 3

We got two solutions. One is fraction other is whole number. We will not consider fraction because the amount of muffins sold must be whole number. So our solution is:
x>3
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