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anygoal [31]
3 years ago
8

A juice company decides to test 5 different brands of juice. The different brands have been labeled A, B, C, D, and E. The compa

ny decides to compare each brand with the other brands by pairing together different brands. How many different pairs will result by selecting two different brands at a time
Mathematics
2 answers:
posledela3 years ago
8 0
<span>9765625 I used the calculator.</span><span />
lina2011 [118]3 years ago
7 0
Considering that the first brand cannot combine with itself, each brand can combine with 4 others. So if there are 5 brands, there would be 20 possible combinations (5x4=20).
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The function f(x)f(x) is a quartic function and the zeros of f(x)f(x) are -6−6, -5−5, -2−2 and 11. Assume the leading coefficien
Luden [163]
<h2>Answer: </h2>

\boxed{f(x) = 11x^4 + 22x^3 - 1001x^2 - 5632x - 7260}

<h2>Explanation: </h2>

A quartic function is a function given by the the following equation in standard form:

f(x)=a_{4}x^4+a_{3}x^3+a_{2}x^2+a_{1}x+a_{0} \\ \\ \\ Where: \\ \\ a_{4},a_{3},a_{2},a_{1},a_{0} \ \text{are constant} \\ \\ \text{and} \ a_{4} \ \text{is the leading coefficient}

From the statement we must assume the leading coefficient of f(x) is 11, so:

a_{4}=11

The zeros are:

x=-6 \\ \\ x=-5 \\ \\ x=-2 \\ \\ x=11

So, we can write:

f(x)=11(x-(-6))(x-(-5))(x-(-2))(x-11) \\ \\ \\ So: \\ \\ \mathrm{Rule}:-\left(-a\right)=a \\ \\ \\ Then: \\ \\ f(x)=11\left(x+6\right)\left(x+5\right)\left(x+2\right)\left(x-11\right)

Expand:\left(x+6\right)\left(x+5\right):\ x^2+11x+30: \ \text{Distributive Property} \\ \\ \\ Then: \\ \\ f(x)=11\left(x^2+11x+30\right)\left(x+2\right)\left(x-11\right) \\ \\ \\ Expand:\left(x^2+11x+30\right)\left(x+2\right):\ x^3+13x^2+52x+60:  \ \text{Distributive Property} \\ \\ \\ Then: \\ \\ f(x)=11\left(x^3+13x^2+52x+60\right)\left(x-11\right)

Expand: \left(x^3+13x^2+52x+60\right)\left(x-11\right):\ x^4+2x^3-91x^2-512x-660 \\  (Distributive \ property)

Finally:

f(x) = 11(x^4 + 2x^3 - 91x^2 - 512x - 660) \\ \\ \boxed{f(x) = 11x^4 + 22x^3 - 1001x^2 - 5632x - 7260}

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Oksana_A [137]
8.

16 eyes total / 2 eyes per potion = 8 potions
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lilavasa [31]
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hammer [34]

Answer:

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Step-by-step explanation:

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