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Basile [38]
3 years ago
7

What is the discriminant of 9х2 + 2 = 10x?

Mathematics
1 answer:
vredina [299]3 years ago
5 0

\bf 9x^2+2=10x\implies 9x^2-10x+2=0 \\\\[-0.35em] ~\dotfill\\\\ \qquad \qquad \qquad \textit{discriminant of a quadratic} \\\\\\ \stackrel{\stackrel{a}{\downarrow }}{9}x^2\stackrel{\stackrel{b}{\downarrow }}{-10}x\stackrel{\stackrel{c}{\downarrow }}{+2}=0 ~~~~~~~~ \stackrel{discriminant}{b^2-4ac}= \begin{cases} 0&\textit{one solution}\\ positive&\textit{two solutions}~~\checkmark\\ negative&\textit{no solution} \end{cases} \\\\\\ (-10)^2-4(9)(2)\implies 100-72\implies 28

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Answer:

In 4 months the cost of both gyms will be the same.

Step-by-step explanation:

At first we need to model the function to calculate the cost of the 2 gyms.

Slope-intercept equation of linear function

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where

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Let linear function to calculate total cost of gym be:

c(n)=mn+b

where

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n\rightarrow number of months

b\rightarrow start-up fee (y-intercept)

For Gym 1

m=20 , b=12

c(n)=20n+12

For Gym 2

m=22 , b=4

c(n)=22n+4

In order to find the number of months the cost of both gyms will be the same, we need to equate both functions and solve for number of months (n)

20n+12=22n+4

\\\textrm{Subtracting 22n from both sides}\\20n-22n+12=22n-22n+4\\-2n+12=4\\\textrm{Subtracting 12 from both sides}\\-2n+12-12=4-12\\-2n=-8\\\textrm{Dividing both sides by -2}\\\frac{-2}{-2}n=\frac{-8}{-2}\\n=4\textrm{ months}

So,

In 4 months the cost of both gyms will be the same.

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