Algebra Problems

Question

1.

The area is given in square feet. Find the length of a side of the square. Round your answer to the nearest hundredth of a foot.

2.

Simplify by combining like terms.

3.

State whether  is rational or irrational.

4.

Solve the following system by adding.

5.

Perform the indicated multiplication. Then simplify the radical expression. 

6.

Perform the indicated multiplication. Then simplify the radical expression. 

7.

Evaluate -, if possible.

8.

One number is 12 more than another. The sum of the smaller number and twice the larger number is 39. Find the larger number.

9.

Simplify by combining like terms.

10.

The forces (in pounds) on the arm of an industrial lift provide the equations.

1.4x + 1.8y = 50 2.7x - 1.2y = 10

Use the addition method to solve this system. Round your results to the nearest hundredth.

11.

Simplify .

12.

Solve the following system by adding.

-0.3x + 0.9y = -6.6 0.6x + 0.4y = -22

13.

State whether  is rational or irrational.

14.

A manufacturer has two machines that produce dog toys. On Wednesday, machine A operates for 4 hours and machine B operates for 5 hours and 175 dog toys are produced. On Thursday, machine A operates for 6 hours and machine B operates for 5 hours and 225 dog toys are produced. Use the following system:

4x + 5y = 175 6x + 5y = 225

where x is the number of dog toys produced by machine A in an hour and y is the number of dog toys produced by machine B in an hour. Solve the system graphically.

15.

Solve. 

16.

The time in seconds that it takes for an object to fall from rest is given by

in which s is the distance fallen (in feet). Find the time required for an object to fall from the ground from a building that is 1,400 feet high. Round your answer to the nearest hundredth of a second.

17.

A 82-ft rope is cut into two pieces so that one piece is 8 ft longer than the other. How long is each piece?

18.

Stan invested $13,000, part at 13% and part at 18%. If the total interest at the end of the year is $2,240, how much did he invest at 13%?

19.

Find the perimeter of the triangle shown in the figure. Write your answer in reduced radical form.

20.

Adult tickets for a play cost $17 and child tickets cost $12. If there were 32 people at a performance and the theater collected $474 from ticket sales, how many children attended the play?