If I have the option to have a PB and J sandwich or ham sandwich; chips, fruit, pretzels, or string cheese; and oreos or chocolate chip cookies, how many different lunches are possible?

16

Step-by-step explanation:

PB and J, Chips, Oreos

PB and J, fruit, Oreos

PB and J, pretzels, Oreos

PB and J, String cheese, Oreos

PB and J, Chips, Chocolate chip

PB and J, Fruit, Chocolate chip

PB and J, pretzels, Chocolate chip

PB and J, string cheese, Chocolate chip

Ham, Chips, Oreos

Ham, fruit, Oreos

Ham, pretzels, Oreos

Ham, String cheese, Oreos

Ham, Chips, Chocolate chip

Ham, Fruit, Chocolate chip

Ham, pretzels, Chocolate chip

Ham, string cheese, Chocolate chip

answer: b. f(x) = (x + 2)^3 (x^2 - 7x + 3)^4

step-by-step explanation:

polynomials always have as many roots as their order. this is a 4th order polynomial- hence 4 roots!

complex roots of polynomials always come in pairs. the quadratic equation has the "+/-" in that will alwaysgenerate m+ni amd m-ni, so 7-2i must be a root of this polynomial equation.

the order of the numerator and denominator are both 2. so the horizontal asymptote is y=a2/b2 =7

verticle asymptotes are the forbidden x-values. f(x) becomes undefined at x=-3 because this value will cause a zero denominator.

a graph of r(x) will have vertical asymptotes at ±1 because these values will make the denominator zero. so the domain of the function cannot include ±1.

you 're wlecome! : )

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