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3 years ago

The ravens won three more games than they lost.they played 96 games.how much games did they win?

1 answer:

4 0

$x-the \ number \ of \ games \ won \ \\\\ y-the \ number \ of \ games \ lost \\\\ x= y+3 \\\\ x+y=96 \\\\ 3+y+y=96 \\\\ 3+2y=96 \\\\2y=96-3\\\\2y=93 \\\\ \boxed{y=\frac{93}{2}=46.5\approx46\ games \ lost} \\\\ x=3+46 \\\\ \boxed{x=49 \ games \ win}$

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Step-by-step explanation:

A rational function is

$\frac{p(x)}{q(x)}$

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If p is a asymptote, or hole at that value, then we will use

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Step 1: We have asymptote as 0 and -1 so our denomiator will include

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So our denomator so far is

$\frac{p(x)}{x(x + 1)}$

Step 2: Find Holes.

Since 12 is the value of the hole,

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This will be both on the numerator and denomator so qe have

$\frac{(x - 12)}{x(x + 1)(x - 12)}$

Step 3: Put the x intercepts in the numerator.

Since 5 and -7 is the intercepts,

$\frac{(x - 12)(x - 5)(x + 7)}{x(x + 1)(x - 12)}$

Step 4: Horinzontal Asymptotes,

Multiply the numerator and denomiator out fully,

$\frac{ {x}^{3} - 10 {x}^{2} - 59x + 420 }{ {x}^{3} - 12 {x}^{2} + x - 12}$

Take a L

look at the coefficients,

Notice they have the same degree,3, this means if we divide the leading coefficents, we will get our horinzonral asymptote.

Multiply the numerator by 4.

$\frac{4(x - 12)(x - 5)(x - 7)}{x(x + 1)(x - 12)}$

Above is the function,

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3 years ago