91Ó°ÊÓ

At what time after 4: 00 will the minute hand and the hour hand of a clock first be in the same position?

If two quantities vary directly, does this mean that one is "caused" by the other? Why or why not?

If \(y\) varies directly as \(x,\) does doubling \(x\) cause \(y\) to be doubled as well? Why or why not?

Perform the indicated operations and simplify. \(\frac{x^{2}}{3 x^{2}-5 x-2}-\frac{2 x}{3 x+1} \cdot \frac{1}{x-2}\)

Perform the indicated operations and simplify. $$\left[\frac{d^{2}-d}{d^{2}-6 d+8} \cdot \frac{d-2}{d^{2}+5 d}\right] \div \frac{5 d}{d^{2}-9 d+20}$$

The harmonic mean of two numbers \(a\) and \(b\) is a number \(M\) such that the reciprocal of \(M\) is the average of the reciprocals of \(a\) and \(b .\) Find a formula for the harmonic mean.