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Oksi-84 [34.3K]
3 years ago
14

Divide. Express the quotient in simplest form.

Mathematics
1 answer:
Scorpion4ik [409]3 years ago
3 0
( \frac{x^2 - x -12}{2x} ) ÷ ( \frac{x^2 - 2x - 8}{4x^2} )

= ( \frac{x^2 - x -12}{2x} ) × ( \frac{4x^2}{x^2 - 2x - 8} )

= \frac{x(x^2 - x -12)}{x^2 - 2x - 8}

= \frac{x(x^2 -4x +3x -12)}{x^2 -4x +2x -8}

= \frac{x[x(x - 4) +3(x - 4)]}{x(x - 4) +2(x - 4)}

= \frac{x(x-4)(x+3)}{(x-4)(x+2)}

= \frac{x(x+3)}{(x+2)}
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Claire is a manager at a toy packaging company. The company packs 80 boxes of toys every hour for the first 3 hours of the day.
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Answer:

See the attached figure.

Step-by-step explanation:

Modeling each part as a function.

Let x is hours of the working day

The company packs 80 boxes of toys every hour for the first 3 hours of the day. ⇒ y₁ = 80 x , x ∈ [0,3]

At the end of the 3 hours The company packs = 80 * 3 = 240

They stop packaging for the next 2 hours in order to carry out a training session. ⇒ y₂ = 240 , x ∈ [3,5]

Then, for the next 4 hours, they pack 20 boxes of toys every hour

y₃ = 20x + c , x ∈ [5,9]

To find c, y₂ = y₃ at x =5

∴ 240 = 20 * 5 + c

∴ c = 240 - 20 * 5 =240 - 100 = 140

∴ y₃ = 20x + 140 , x ∈ [5,9]

So,

y₁ = 80 x , x ∈ [0,3]

y₂ = 240 , x ∈ [3,5]

y₃ = 20x + 140 , x ∈ [5,9]

The graph models the piecewise function for the given situation is as shown in the attached figure.

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Answer:

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Step-by-step explanation:

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