Jon took out a loan at \(4\%\) simple interest and repaid it after \(5\) years. The total amount paid back was \(\$5760\), equal to the principal and interest. What was the principal?

A \(20\)-foot tall white oak tree grows at a rate of \(0.8\) feet per year. How long will it take for the tree to reach a height of \(32\) feet?

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?

Write the following numbers in the form \(a+bi\), and identify \(a\) and \(b\).

1. \(\sqrt{2}\)

2. \(\dfrac{1}{3}i\)

3. \(1+\sqrt{3}\)

What are the real and imaginary parts of the following complex numbers?

1. \(-2+3i\)

2. \(-i+4\)

3. \(-\sqrt{3}\)

Find the complex conjugates of the following numbers.

1. \(1+2i\)

2. \(-3i\)

3. \(2\)

Multiply \(-3+2i\) by its conjugate. What type of number results from the operation?

Use the definition of \(i\) to solve the equation \(x^2=-4\).

Find all solutions of the equation \(2x^2+2x+1=0\).

Solve the equation \(t^6-t^3=2\) for real values of \(t\).

Solve \(\dfrac{4}{3x}=\dfrac{2}{x}+\dfrac{2}{3}\) and check your solution.

Solve \(\dfrac{1}{x}=\dfrac{2}{x-2}+3\)

Solve \(\dfrac{1}{x-2}=\dfrac{6}{x+3}+\dfrac{12}{x^2+x-6}\)

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 Jennifer’s path on each leg of the trip is a straight line, and that there is no river current or wind speed.

Solve the following inequalities:

1. \(2x+\dfrac{5}{2}>3x-6\)

2. \(-4\leq 3x-2<7\)

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.

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

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

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

Solve the following equations:

1. \(\lvert 2x-3\rvert =7\)

2. \(\lvert x \rvert = -3\)

3. \(-\lvert 3x+1\rvert -3=-8\)

Solve the following inequalities and indicate the solution set on a number line.

1. \(\lvert 2x-3\rvert >7\)

2. \(\left\lvert -\dfrac{2}{3}x+4\right\rvert \leq 57\)

3. \(-4+\lvert 3-x\rvert >5\)

Graph the following on a number line and write each set using an absolute value inequality.

1. The set of all \(x\) whose distance from \(4\) is less than \(5\)

2. The set of all \(x\) whose distance from \(4\) is greater than \(5\)

A thermometer measures temperature with an uncertainty of \(0.25^\circ\text{F}\). If a person’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.