Chapter 1: Fundamentals

Find the real solutions of the quadratic equation $\frac{x+5}{x-2}=\frac{5}{x+2}+\frac{28}{x^2-4}$.

A small-appliance manufacturer finds that if he produces xtoaster ovens in a month, his production cost is given by the equation

$y=6x+3000$

(where yis measured in dollars).

(a)Sketch a graph of this linear equation.

(b)What do the slope and y-intercept of the graph represent?

Find an equation of the circle that satisfies the given conditions.

Center$\left(-1,-4\right)$; radius 8

Factor the expression by grouping terms

$x^5+x^4+x+1$

Rationalize the denominator.

$\frac{2\left(x-y\right)}{\sqrt{x}-\sqrt{y}}$

Solve the inequality ${\mathbf{x}}^2\le \mathbf{1}$, express the solution using interval notation and graph the solution set on real number line.

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

$7|x+2|+5>4$

Solve the inequality. Express the solution using interval notation and graph the solution set on the real number line.

$\frac{x-4}{x^2-4}\le 0$

A phrase describing a set of real numbers is given. Express the phase as an inequality involving an absolute value.

All real numbers x less than 3 units from 0

The relationship between the Fahrenheit (F) and Celsius (C) temperature scales is given by the equation$F=\frac{9}{5}C+32.$

(a)Complete the table to compare the two scales at the given values.

(b)Find the temperature at which the scales agree.

[Hint:Suppose that is the temperature at which the scales agree. Set$F=a$ and $C=a$. Then solve fora.]