Chapter 1: Fundamentals

Use a Special Factoring Formula to factor the expression

$x^2+12x+36$

Let a, b, and c be real numbers such that $\mathbf{a}\mathbf{>}\mathbf{0}$ ,$\mathbf{b}\mathbf{<}\mathbf{0}$and role="math" $\mathbf{c}\mathbf{<}\mathbf{0}$. Find the sign of each expression.

$\mathbf{\left(}\mathbf{a}\mathbf{\right)}\mathbf{-}\mathbf{a}$

$\mathbf{\left(}\mathbf{b}\mathbf{\right)}\mathbf{bc}$

$\mathbf{\left(}\mathbf{c}\mathbf{\right)}\mathbf{a}\mathbf{-}\mathbf{b}$

$\mathbf{\left(}\mathbf{d}\mathbf{\right)}\mathbf{ab}\mathbf{+}\mathbf{ac}$

Distance and Time A woman cycles$\text{8\hspace{0.33em}mi}/\text{h}$ faster than she runs. Every morning she cycles and runs $\text{2}\frac{1}{2}\text{mi}$, for total of one hour exercise. How fast does she run?

Find the center and radius of the circle, and sketch its graph.

$x^2+y^2=9$

Recall that the symbol $\overline{z}$represents the complex conjugate of z. If $z=a+bi\text{and}w=c+di$, show that each statement is true.

$z\cdot \overline{z}\text{isarealnumber.}$

Find the number of real solutions of the equation $x^2+2.20x+1.21=0$by using discriminant.

A spherical tank has a capacity of 750 gallons. Using the fact that one gallon is about $0.1337{\mathrm{ft}}^3$, find the radius of the tank.

Write each number in scientific notation.

1. $69,300,000$
2. $7,200,000,000,000$
3. $0.000028536$
4. $0.0001213$

Use a Special Factoring Formula to factor the expression

$16z^2-24z+9$

A city lot has the shape of a right triangle whose hypotenuse is longer than one of the other sides. The perimeter of the lot is $392\mathrm{ft}$. How long is each side of the lot?