Chapter 1: Fundamentals

Solve the absolute value inequality. Express the answer using interval notation and graph the solution set.

$\left|\frac{x-2}{3}\right|<2$

Two-Intercept Form

(a)Show that if the x-and y-intercepts of a line are nonzero numbers a andb, then the equation of the line can be written in the form

$\frac{x}{a}+\frac{y}{b}=1$

This is called the two-intercept formof the equation of a line.

(b)Use part (a) to find an equation of the line whose x-intercept is 6 and whose y-intercept is $-8$.

Rationalize the denominator.

$\frac{1}{5-\sqrt{3}}$

Mary’s backyard vegetable garden measures 20 ft by 30 ft, so its area is $20\times 30=600{\mathrm{ft}}^2$. She decides to make it longer, as shown in the figure so that the area increases to $A=20(30+x)$. Which property of real numbers tells us that the new area can also be written $A=600+20x$?

Factor the expression by grouping terms

$x^3+4x^2+x+4$

Abbie paints twice as fast as Beth and three times as fast as Cathie. If it takes them $60\text{min}$to paint a living room with all three working together, how long would it take Abbie if she worked alone?

Find the number of real solutions of the equation$4x^2+5x+\frac{13}{8}=0$ by using discriminant.

Suppose that the equation $a{x}^2+bx+c=0$has real coefficients and complex roots. Why must the roots be complex conjugates of each other ? [Hint: Think about how you would find the roots using the Quadratic Formula.]

Write each number in decimal notation.

1. $3.19\times {10}^5$
2. $2.721\times {10}^8$
3. $2.670\times {10}^{-8}$
4. $9.999\times {10}^{-9}$