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Math Topics

College Algebra

Equations and Inequalities

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Linear Equations and Applications

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Quadratic Equations and Applications

The height of a ball after being thrown vertically upward from a point \(80\) feet above the ground with a velocity of \(40\) feet per second is given by \(h=-16t^2+40t+80\), where \(t\) is the time in seconds since the ball was thrown and \(h\) is in feet.

When will the ball be \(50\) feet above the ground?

When will the ball reach the ground?

For what values of \(t\) does this problem make sense (from a physical sense)?

The mobility rate (the percentage of people who changed residence) for the years 2000-2016 can be modeled by the equation \(y=0.0072t^2+0.0766t+11.318\), where \(t\) is the number of years since 2000. In what year between 2000 and 2016 was the mobility rate \(12\) percent?

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Complex Numbers and Quadratic Equations

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Other Types of Equations

A theatre club arranged for a chartered bus trip to a play at a cost of \(\$350\). To lower costs, \(10\) nonmembers were invited to join the trip. The bus fare per person then decreased by \(\$4\). How many theatre club members were going on the trip?

Jennifer is standing on one side of a river that is \(3\) kilometers wide. Her bus is located on the opposite side of the river. Jennifer plans to cross the river by rowboat and then jog the rest of the way to reach the bus, which is \(10\) kilometers along the river from point \(B\) directly across the river from her current location (point \(A\)). If she can row \(5\) kilometers per hour and jog \(7\) kilometers per hour, at which point on the other side of the river should she dock her boat so that it will take her a total of exactly two hours to reach the bus? Assume that JenniferÃ¢â‚¬â„¢s path on each leg of the trip is a straight line, and that there is no river current or wind speed.

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Linear Inequalities

T-Mobile offers two prepaid plans for their mobile phone customers.

Plan A charges \(\$3.00\) per month plus \(10\) cents per text message, whether sent or received.

Plan B charges a flat rate of \(\$45\) per month for unlimited text messages.

Express the monthly cost for Plan A in terms of the number of text messages.

Express the monthly cost for plan B in terms of the number of text messages.

How many text messages would you have to send or receive per month for Plan B to be cheaper than Plan A.

To operate a gourmet coffee booth in a shopping mall, it costs \(\$500\) (the fixed cost) plus \(\$6\) for each pound of coffee bought at wholesale price. The coffee is then sold to customers for \(\$10\) per pound.

Find an expression for the operating cost of selling \(q\) pounds of coffee.

Find an expression for the revenue earned by selling \(q\) pounds of coffee.

Find the break-even point.

How many pounds of coffee must be sold for the revenue to be greater than the total cost?

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Equations and Inequalities Involving Absolute Value

A thermometer measures temperature with an uncertainty of \(0.25^\circ\text{F}\). If a personÃ¢â‚¬â„¢s body temperature is measured at \(98.3^\circ\text{F}\), use absolute value notation to write an inequality for the range of possible body temperatures.