**Fall 2012Math 125Practice Final**

- Solve

- John bought a briefcase at a 30% discount sale for $75. What is the original price of the briefcase?

- A total of $4000 was invested, part of it at 5% interest and the remainder at 6%. If the total yearly interest amounted to $230, how much was invested at each rate? Use a system of linear equations to solve.

- A car leaves a town at 60 miles per hour. How long will it take a second car, traveling at 75 miles per hour, to catch the first car if it leaves 1 hour later?

- Solve for

- Solve

- Solve

- Solve. Express your answer in interval notation.

- Find the product

- Factor completely

- Factor

- Solve

- Solve

- Solve
- Solve

For 16- 20, perform the indicated operations, and express your answer in simplest form.

- Simplify the complex fraction

For 22 to24, solve the equation.

- A car travels 180 miles in the same time that a truck travels 120 miles. If the car’s speed is 20 miles per hour faster than the truck’s, find the car’s speed and the truck’s speed.
- John can paint the house in 3 hours. His friend Blake can paint the same house in 7 hours. How long will it take them to paint the house if they work together?
- Evaluate the numerical expression

For 12 and 13, simplify and express the final result using positive exponents.

- Express the radical in simplest radical form. Assume the variable represent positive real numbers
- Subtract
- Rationalize the denominator

For 33 and 34, solve the equation

- Simplify
- Simplify

For 37-38, write the expression using positive rational exponents.

- Simplify and express the final result using positive exponents

- perform the indicated operation and express the answer in simplest radical form

For 41 -46 perform the indicated operations and simplify

- Solve
- Solve by completing the square
- Solve
- Graph
- Find the slope and the y-intercept. Graph
- Graph the line that has the indicated slope and contains the indicated point
- Find the equation of the line that is perpendicular to the line and contains the point (3, -4). Express the equation in standard form.
- The Rent-Me Car Rental charges $35 per day plus $0.32 per mile to rent a car. Determine a linear function that can be used to calculate daily car rentals. Then use that function to determine the cost of renting a car for a day and driving 150 miles.
- On a 335- mile car trip, John averaged 5 miles per hour faster for the first 200 miles than he did for the last 135 miles. The entire trip took 7 hours. Find the rate for the first 200 miles.
- A pharmacist stocks a 10% solution of acid and a 22% solution of acid. How many liters of each should be mixed to produce 20 liters of an 18% solution of acid?
- Specify the domain

a)

b)

- If , find
- If and , determine
- If and , find
- Find the inverse of the given function
- If y varies directly as x, and if y=28 when x=5, find y when x=16

For 63 and 64, use the concepts of translation and/or reflection to describe how the curve can be obtained. What is the basic function? state each translation clearly.Graph

- Evaluate the expression
- Evaluate the expression
- Solve the equation without using your calculator
- Solve the equation
- Solve the equation
- Solve the equation
- Expand
- Suppose that $3000 is invested at 5% interest compounded quarterly. How much money has accumulated at the end of 10 years?

For 73 and 74, solve the equation without using your calculator

- The number of bacteria present in a certain culture after t hours is given by , where represents the initial number of bacteria. How long will it take 400 bacteria to increase to 2400 bacteria? Express your answer to the nearest tenth of an hour.Do we have exponential growth or decay? Justify your answer.

For 76 and 77, find the vertex of the parabola. State whether the parabola opens upward or downward. Do you have x-intercepts?y-intercept?

- Write the equation of the circle center and radius

For problems 79-82, name the graph of the equation. Explain your reasoning. Then graph.

- Solve the system using the method of your choice (you should know how to solve the system using all 3 methods)
- The perimeter of a rectangle is 90 inches. The length of the rectangle is 5 inches less than the width of the rectangle. Find the dimensions of the rectangle.
- Graph the solution set for the system
- Solve the system of equations

For 87-89, solve each system. Then Graph.

- Divide by