Question 1

A rectangular park is 4 miles long and 2 miles wide. What is the length of the pedestrian route that runs diagonally across the park? Give your answer in exact radical form.

Accepted Answer

$$\sqrt{8}$$ miles

Question 2

The area of a rectangular patio is 180 square feet. Its width is 8 feet longer than its length. What are the dimensions of the patio?

Accepted Answer

Length: $$10 ft$$, Width: $$18 ft$$

Question 3

Given the tuition model $$y = 18.34x^2$ + 512.9x + 9314$$, where $$x = 0$$ corresponds to the year 2000, what is the approximate cost in the year 2000?

Accepted Answer

$$9314$$

Question 4

Using the tuition model $$y = 18.34x^2$ + 512.9x + 9314$$, what is the approximate cost in the year 2009?

Accepted Answer

$$11702.06$$

Question 5

Based on the tuition model $$y = 18.34x^2$ + 512.9x + 9314$$, in what year was the cost $$11702$$?

Accepted Answer

2009

Question 6

Solve the radical equation $$x - 3 = 2. $$What is the solution set?

Accepted Answer

$$x = 5$$

Question 7

Solve the radical equation $$2x + 1 = 5. $$What is the solution set?

Accepted Answer

$$x = 2$$

Question 8

Solve the equation $$x^2 - 2x = x$. What is the solution set?

Accepted Answer

$$x = 0$$ 	ext{ or } x = 2$

Question 9

Solve the equation $$x + 7 = x + 1. $$What is the solution set?

Accepted Answer

No solution

Question 10

When solving radical equations, why is it important to check for extraneous solutions?

Accepted Answer

Because squaring both sides can introduce solutions that do not satisfy the original equation.

Question 11

Solve the rational equation $$\frac{1}{x} = \frac{1}{5} + \frac{3}{2x}. $$What is the solution set?

Accepted Answer

$$x = 10$$

Question 12

Solve the rational equation $$\frac{8}{x+3} = \frac{5}{x-2}. $$What is the solution set?

Accepted Answer

$$x = 7$$

Question 13

Solve the rational equation $$\frac{3}{x+ x-2} + \frac{8}{x} = \frac{13}{16}. $$What is the solution set?

Accepted Answer

$$x = 16$$

Question 14

Solve the rational equation $$\frac{4}{x+3} - 2 = \frac{5x-9}{x+3}. $$What is the solution set?

Accepted Answer

$$x = 1$$

Question 15

Which of the following is the correct process for solving a radical equation such as $$\sqrt{x+2} = 5$$?

Accepted Answer

Isolate the radical, square both sides, solve for $$x$$, and check for extraneous solutions.

Question 16

A chemical storage tank is rectangular and has a length that is 5 meters more than its width. If the area is $$60$$ square meters, what are the dimensions of the tank?

Accepted Answer

Width: $$6 m$$, Length: $$11 m$$

Question 17

A medical researcher models the spread of a virus with the quadratic equation $$N = 2t^2$ + 3t + 10$$, where $$N is $$the number of cases and $$t is $$the number of days since the outbreak began. How many cases are there on day 5?

Accepted Answer

$$65$$

Question 18

A rectangular garden has a perimeter of $$36$$ meters. Its length is twice its width. What are the dimensions of the garden?

Accepted Answer

Width: $$6 m$$, Length: $$12 m$$

Question 19

A student solves the equation $$\sqrt{x-1} = 3$$ and finds $$x = 10. $$What should the student do next?

Accepted Answer

Check the solution by substituting $$x = 10$$ back into the original equation.

College Algebra Study Guide: Quadratic, Radical, and Rational Equations

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