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2 years ago

When 47 is added to a number the result is 37 less than 7 times the number.

Mathematics

1 answer:

svetoff [14.1K]2 years ago

5 0

X - the number

$x+47=7x-37 \\
x-7x=-37-47 \\
-6x=-84 \\
x=\frac{-84}{-6} \\
x=14$

The number is 14.

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Answer:

$\frac{\left(h+c\right)cr^2}{h\left(r^2-c^2\right)}$

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$\frac{\frac{1}{c}+\frac{1}{h}}{\frac{1}{c^2}-\frac{1}{r^2}}$

Combine $\frac{1}{c} + \frac{1}{h}$

$\frac{\frac{h+c}{ch}}{\frac{1}{c^2}-\frac{1}{r^2}}$

Combine the bottom, too.

$=\frac{\frac{h+c}{ch}}{\frac{r^2-c^2}{c^2r^2}}$

Apply the fraction rule

$=\frac{\left(h+c\right)c^2r^2}{ch\left(r^2-c^2\right)}$

Cancel

$=\frac{\left(h+c\right)cr^2}{h\left(r^2-c^2\right)}$

Therefore, $\frac{\left(\frac{1}{c}+\frac{1}{h}\right)}{\left(\frac{1}{\left(c^2\right)}-\frac{1}{\left(r^2\right)}\right)}:\quad \frac{\left(h+c\right)cr^2}{h\left(r^2-c^2\right)}$

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