91Ó°ÊÓ

Write an equation that describes each variation. \(F\) varies directly with \(m\) and inversely with \(d ; F=32\) when \(m=20\) and \(d=8\).

Involve fractions. Clear the fractions by first multiplying by the least common denominator, and then solve the resulting linear equation. $$p+\frac{p}{4}=\frac{5}{2}$$

Solve the radical equation for the given variable. $$\sqrt{x^{2}-2 x-5}=x+1$$

Refer to the following: The ratio of the speed of an object to the speed of sound determines the Mach number. Aircraft traveling at a subsonic speed (less than the speed of sound) have a Mach number less than \(1 .\) In other words, the speed of an aircraft is directly proportional to its Mach number. Aircraft traveling at a supersonic speed (greater than the speed of sound) have a Mach number greater than \(1 .\) The speed of sound at sea level is approximately 760 mph. The U.S. Air Force's newest fighter aircraft is the F-22A Raptor, which is capable of Mach 1.5. How fast can a F-22A Raptor fly at sea level?

Solve each polynomial inequality and express the solution set in interval notation. $$x^{3}+4 x \leq 4 x^{2}$$

Write an equation of the line in slope-intercept form, if possible, given the slope and a point that lies on. Slope: \(m=-1\) (3,-4)

Write an equation of the line in slope-intercept form, if possible, given the slope and a point that lies on. Slope: \(m=-\frac{1}{7}\) (-5,3)

A Cessna 175 can average 130 mph. If a trip takes 2 hours one way and the return takes 1 hour and 15 minutes, find the wind speed, assuming it is constant.

A jogger and a walker cover the same distance. The jogger finishes in 40 minutes. The walker takes an hour. How fast is each exerciser moving if the jogger runs 2 mph faster than the walker?

Solve using the quadratic formula. $$\frac{1}{4} x^{2}-\frac{2}{3} x-\frac{1}{3}=0$$