The length of a rectangle is 3 less than twice its width.

The length of a rectangle is 3 less than twice its width. If the area of the rectangle is 65 square inches, find the dimensions of the rectangle.

Graphing a Piecewise Function

Graph the piecewise function: f(x) = {x+1 if x less than or equal to -2 {-1 if x>-2

Solving functions

Given f(x)= 4x squared - 3x + 2 and g(x)= 3x - 2, find each of the following. simplify the expression if possible. a. f(-5) b. f(x+h) - f(x)/ h c. (f o g)(x)

Graphs : Equations of Lines through a Point

Suppose point P has coordinates (1/2 , 2/3) a. What is the equation of the vertical line through P? b. What is the equation of the horizontal line through P?

Graphing a relation

GRAPH THE RELATION x=|y+3| - 2

Solve the Equation

(x-4)/2-(3x+1)/3=(4y+5)/6

Mathematical Induction : How Would You Explain this to a Fellow Student?

How would you write an explanation of the idea behind mathematical induction for a fellow student?

Finite Fields : Field Extensions

Please see the attached file for the fully formatted problem. Show the existence of an extension of Fq of order l for any prime l.

Exponential & Logarithmic Functions Word Problem

NUMBER OF FARMS. The number N of farms in the United States has declined continually since 1950. In 1950 there were 5,647,800 farms, and in 1995 that number had decreased to 2,071,520. Assuming that the number of farms decreased according to the exponential model: A). Find the value of k, and write an exponential function ...continues

Irreducible Polynomial : Splitting Field

Let K be obtained as a field Q(alpha) where alpha is a root of P(x) = x3 −3. Find an irreducible polynomial which defines the splitting field of P(x).