What is the product of (6x3+3x)(x2+4)

1 answer:

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If you would like to know what is the product of (6 * x^3 + 3 * x) * (x^2 + 4), you can calculate this using the following steps:

(6 * x^3 + 3 * x) * (x^2 + 4) = 6 * x^3 * x^2 + 6 * 4 * x^3 + 3 * x * x^2 + 3 * 4 * x = 6 * x^5 + 24 * x^3 + 3 * x^3 + 12 * x = 6 * x^5 + 27 * x^3 + 12 * x

The correct result would be 6 * x^5 + 27 * x^3 + 12 * x.

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Write an equation for the following: y varies directly with x and z. Find K when x=2, y=12 and z=5.

olga_2 [115]

$\qquad \qquad \textit{direct joint variation} \\\\ \textit{\underline{y} varies directly with \underline{x} and \underline{z}}~\hspace{8.5em} \stackrel{\textit{constant of variation}}{y=\stackrel{\downarrow }{k}xz~\hfill } \\\\ \textit{\underline{y} varies directly with \underline{x}, }w^2\textit{ and }z^5~\hspace{6em} \stackrel{\textit{constant of variation}}{y=\stackrel{\downarrow }{k}xw^2z^5~\hfill } \\\\[-0.35em] ~\dotfill$

$y = kxz\qquad \textit{we know that} \begin{cases} x=2\\ y=12\\ z=5 \end{cases}\implies 12=k(2)(5) \\\\\\ \cfrac{12}{(2)(5)}=k\implies \cfrac{6}{5}=k~\hspace{10em}\boxed{y=\cfrac{6}{5}xz}$