Notes

 

Questions

\(\textbf{1)}\) y varies directly with x. When x=3, y=10. What is y when x is 12?

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The answer is y=40 when x=12.

 

\(\textbf{2)}\) y varies directly with x. When x=5, y=15. What is y when x is 3?

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The answer is y=9 when x=3.

 

\(\textbf{3)}\) y varies directly with x. When x=5, y=2. What is y when x is 10?

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The answer is y=4 when x=10.

Show Work

\(\,\,\,\,\,\,y=kx\)
\(\,\,\,\,\,\,2=k5\)
\(\,\,\,\,\,\,\frac{2}{5}=k\)
\(\,\,\,\,\,\,.4=k\)
\(\,\,\,\,\,\,y=.4x\)
\(\,\,\,\,\,\,y=.4(10)\)
\(\,\,\,\,\,\,y=4\)
\(\,\,\,\,\,\,\)The answer is y=4 when x=10.

 

\(\textbf{4)}\) m varies inversely with n. When n=3, m=10. What is m when n is 6?

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The answer is m=5 when n=6

 

\(\textbf{5)}\) m varies jointly with n and z. When n=3 and z=4, m=18. What is m when n is 6 and z is 8?

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The answer is m=72 when n=6 and z=8

 

\(\textbf{6)}\) m varies directly with the square of n and inversely with w. When w=4 and n=2, m=5. What is m when w=8 and n=4?

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The answer is m=10 when w=8 and n=4

 

See Related Pages\(\)

\(\bullet\text{ Ratios and Proportions}\)
\(\,\,\,\,\,\,\,\,\displaystyle\frac{4}{3}=\frac{d-4}{12}…\)

\(\bullet\text{ Rational Expressions- Multiplying and Dividing}\)
\(\,\,\,\,\,\,\,\,\displaystyle\frac{x^2+3x-4}{(x+4)(x+5)}\cdot \displaystyle\frac{x+5}{x-1}…\)

\(\bullet\text{ Rational Expressions- Adding and Subtracting}\)
\(\,\,\,\,\,\,\,\,\displaystyle\frac{x-5}{x+3}+\frac{x+2}{x^2+5x+6}…\)

\(\bullet\text{ Direct, Inverse, and Joint Variation}\)
\(\,\,\,\,\,\,\,\,\) \(…\)

\(\bullet\text{ Complex Fractions}\)
\(\,\,\,\,\,\,\,\,\displaystyle\frac{\frac{x}{5}+\frac{1}{3}}{\frac{1}{5}-\frac{1}{6}}…\)

\(\bullet\text{ Partial Fraction Decomposition}\)
\(\,\,\,\,\,\,\,\,\displaystyle\frac{8x+10}{x^2+2x}=\displaystyle\frac{5}{x} + \frac{3}{x+2}…\)