Chapter 1: Fundamentals

Express the quantity without using absolute value

$\left|\mathrm{a}-\mathrm{b}\right|,\mathrm{wherea}<\mathrm{b}$

Simplify the fractional expression.

$\frac{2{\left(1+x\right)}^{\raisebox{1ex}{$1$}\!\left/ \!\raisebox{-1ex}{$2$}\right.}-x{\left(1+x\right)}^{-\raisebox{1ex}{$1$}\!\left/ \!\raisebox{-1ex}{$2$}\right.}}{x+1}$

Use a Special Factoring Formula to factor the expression

$8s^3-125t^3$

A box with a square base and no top is to be made from a square piece of cardboard by cutting 4-in. squares from each corner and folding up the sides, as shown in the figure. The box is to hold. How big a piece of cardboard is needed?

Mixtures The owner of a store sells raisins for$\mathrm{\backslash (}3.20$ per pound and nuts for$\mathrm{\backslash )}2.40$ per pound. He decides to mix the raisins and nuts and sell$50\text{lb}$ of the mixture for$\$2.72$ per pound. What quantities of raisins and nuts should he use?

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

$\left|3x+2\right|<4$

Using Slopes Verify the given geometric property.

Use slopes to show that$A\left(1,1\right),B\left(11,3\right),C\left(10,8\right)$ and $D\left(0,6\right)$are vertices of a rectangle.

An equation is given.

(a)Use a graphing calculator to graph the equation in the given viewing rectangle. (b) Find the x- and y-intercepts from the graph.

(c) Verify your answers to part (b) algebraically (from the equation).

$y=\sqrt[3]{1-x^2};\left[-5,5\right]\text{by}\left[-5,3\right]$

Express the quantity without using absolute value

$a+b+\left|a-b\right|,\mathrm{where}a<b$

A cylindrical can has a volume of and is tall. What is its diameter?