College Algebra, 4th Edition

Cumulative Review Exercises Chapters P–6

1. Assuming that the distance between the points $(2,-3)$ and $(-1,y)$ is 5 units, find y.

In Problems 2–8, solve each equation or inequality.

2. ${\displaystyle \frac{4}{x-1}}-{\displaystyle \frac{3}{x+2}}={\displaystyle \frac{18}{(x+2)(x-1)}}$

3. $|2x-5|=3$

4. $4x^2=8x-13$

5. ${\left({\displaystyle \frac{3x-1}{x+5}}\right)}^2-3\left({\displaystyle \frac{3x-1}{x+5}}\right)-28=0$

6. ${\text{log}}_2\left|x\right|+{\text{log}}_2|x+6|=4$

7. ${\displaystyle \frac{x+2}{2x-1}}>0$

8. $x^2-7x+6\le 0$

9. Write all possible rational zeros of

    

   $$f(x)=4x^3+8x^2-11x+3.$$

10. Show that ${\displaystyle \frac{1}{2}}$ is a zero of multiplicity 2 of the function f in Exercise 9.

11. The horsepower required to propel a ship varies as the cube of the ship’s speed. If the horsepower required for a speed of 15 miles per hour is 10,125, find the horsepower required for a speed of 20 miles per hour.

12. A city covers an area of 400 square miles. At present, only 2% of its area is reserved for parks. In the unincorporated ...