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Lilit [14]
2 years ago
8

How would the sum of cubes formula be used to factor x3y3 + 343? Explain the process. Do not write the factorization.

Mathematics
2 answers:
Triss [41]2 years ago
4 0
The sum of cubes formula:
a³ + b³ = ( a + b ) ( a² - a b + b² )
x³ y³ = ( x y )³ and 343 = 7³
x³ y³ + 343 = ( x y )³ + 7³ = ( x y + 7 ) ( x² y² - 7 x y + 49 )
olga_2 [115]2 years ago
3 0

To factor, first identify the quantities that are being cubed. The first term is the cube of xy, and the constant is the cube of 7. Next, use the formula to write the factors. The first factor is the sum of xy and 7. The second factor has three terms: the square of xy, the negative of 7xy, and the square of 7.

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If 100% of a number is 15, what is 50% of the number?
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Answer:

Let n be the number

100% of a number is 15 is written as: 100% × n = 15

100% = 100 / 100 = 1

Hence

100% × n = n = 15

We now need to find 50% of the number

50% of 15 = (50 / 100) × 15 = 750 / 100 = 7.5

Step-by-step explanation:

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bogdanovich [222]

The system of equations of two unknowns is formulated and solved.

\large\displaystyle\text{$\begin{gathered}\sf \bf{ \left\{\begin{matrix} \ \ \ \dfrac{x}{y} = \dfrac{5}{7} \\ x^2+y^2 = 1184 \end{matrix}\right. \ \Longrightarrow \ x=\dfrac{5}{7}y  } \end{gathered}$}

\large\displaystyle\text{$\begin{gathered}\sf \bf{ \left (\dfrac{5}{7}y \right )^2+y^2=1184\ \Longrightarrow\ 25y^2+49y^2=58016 } \end{gathered}$}

                                                              \large\displaystyle\text{$\begin{gathered}\sf \bf{74y^{2}=58016} \end{gathered}$}\\\large\displaystyle\text{$\begin{gathered}\sf \bf{ \ \  \ \ \ \ y^{2}=784 } \end{gathered}$}\\\large\displaystyle\text{$\begin{gathered}\sf \bf{ \ \ \ \ \ y=\pm\sqrt{784}=\pm28  } \end{gathered}$}

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The fraction that satisfies the request is \bf{\dfrac{20}{28}} , since in \bf{\dfrac{-20}{-28}} the negative signs are canceled and the first fraction is obtained.

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