need to solve the equation 150=-6x2+100x-180. you can subtract 150 from both sides and use the quadratic formula to find x=4.53 and 12.13. this means that if the store sells soccer balls for 4.53$ or 12.13$ it will earn a daily profit of 150$
The given question lacks the essential part for answering the question, however, the missing information is as follows:
=> Soccer ball profit
y=-6x^2 + 100x – 180
The correct price of each soccer ball would be:
Given:
Soccer ball profit
y=-6x^2 + 100x – 180
Profit required = 150
Formula:
The quadratic formula for the quadratic equation is -
[tex]x=\dfrac{-b\pm \sqrt{b^2-4ac}}{2a}[/tex]
Solution:
In this case, the daily profit is required $150
then Y = 150 in the equation then,
150 = -6x^2 + 100x – 180
Taking 150 to L.H.S. and fliping the sign:
0 = 6x2+100x-180-150
0 = 6x2+100x+330
Solving the new quadratic equation:
[tex]x=\dfrac{-(-100)\pm \sqrt{(-100)^2-4(6)(330)}}{2(6)}\\x=\dfrac{100\pm \sqrt{10000-7920}}{12}\\x=\dfrac{100\pm \sqrt{2080}}{12}[/tex]
Simplifying the radical:
[tex]x=\dfrac{100\pm 4\sqrt{130}}{12}\\x=\dfrac{4(25\pm \sqrt{130})}{12}\\x=\dfrac{25\pm \sqrt{130}}{3}[/tex]
which becomes
x = 4.532
x = 12.134
Thus, the correct price of each soccer ball would be:
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