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Andrei [34K]
3 years ago
15

A rectangular baking pan is 12 inches long, 6 inches wide, and 2.5 inches tall. If 1 cubic inch of cake mix is approximately 0.5

5 ounces, how much cake mix can the pan hold?
Mathematics
1 answer:
ahrayia [7]3 years ago
7 0

Answer:

Amount of cake mix baking pan can hold is 99 ounces

Step-by-step explanation:

Here we have the size of the baking pan is given by the following relation

Volume of baking pan = Length × Width × Height

Volume of baking pan = 12 in. × 6 in. × 2.5 in. = 180 in.³

Mass of 1 cubic inch of cake mix = 0.55 ounces, therefore, the mass of cake mix that the 180 in.³ baking pan can hold is found as follows;

Amount of cake mix baking pan can hold = Volume of baking pan × Mass per cubic inch of cake mix

Amount of cake mix baking pan can hold = 180 in.³ × 0.55 ounce/in.³ = 99 ounces.

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Find all solutions to x³+3x² − 9x − 27 = 0 by factoring the equation.
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Step-by-step explanation:

To factor this cubic polynomial x^3+3x^2-9x-27 you must:

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x^3+3x^2-9x-27=\left(x^3+3x^2\right)+\left(-9x-27\right)

  • Factor out -9 from (-9x-27)

(-9x-27)=-9\left(x+3\right)

  • Factor out x^2 from (x^3+3x^2)

(x^3+3x^2)=x^2\left(x+3\right)

x^3+3x^2-9x-27=-9\left(x+3\right)+x^2\left(x+3\right)

  • Factor out common term x+3

-9\left(x+3\right)+x^2\left(x+3\right)=\left(x+3\right)\left(x^2-9\right)

x^3+3x^2-9x-27=\left(x+3\right)\left(x^2-9\right)

  • Factor x^2-9

x^2-9=\left(x+3\right)\left(x-3\right)

x^3+3x^2-9x-27= \left(x+3\right)\left(x+3\right)\left(x-3\right)

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  • Using the Zero Factor Theorem: = 0 if and only if = 0 or = 0

x+3=0, \quad{x=-3}\\x-3=0, \quad{x=3}

The solutions are

x=-3,\:x=3

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3 years ago
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