Intermediate Algebra 2e

# Key Terms

break-even point
The point at which the revenue equals the costs is the break-even point; $C(x)=R(x).C(x)=R(x).$
coincident lines
Coincident lines have the same slope and same y-intercept.
complementary angles
Two angles are complementary if the sum of the measures of their angles is 90 degrees.
consistent and inconsistent systems
Consistent system of equations is a system of equations with at least one solution; inconsistent system of equations is a system of equations with no solution.
cost function
The cost function is the cost to manufacture each unit times $xx$, the number of units manufactured, plus the fixed costs; C(x) = (cost per unit)x + fixed costs.
determinant
Each square matrix has a real number associated with it called its determinant.
matrix
A matrix is a rectangular array of numbers arranged in rows and columns.
minor of an entry in a $3×33×3$ determinant
The minor of an entry in a $3×33×3$ determinant is the $2×22×2$ determinant found by eliminating the row and column in the $3×33×3$ determinant that contains the entry.
revenue
The revenue is the selling price of each unit times x, the number of units sold; R(x) = (selling price per unit)x.
row-echelon form
A matrix is in row-echelon form when to the left of the vertical line, each entry on the diagonal is a 1 and all entries below the diagonal are zeros.
solutions of a system of equations
Solutions of a system of equations are the values of the variables that make all the equations true; solution is represented by an ordered pair $(x,y).(x,y).$
solutions of a system of linear equations with three variables
The solutions of a system of equations are the values of the variables that make all the equations true; a solution is represented by an ordered triple $(x,y,z).(x,y,z).$
square matrix
A square matrix is a matrix with the same number of rows and columns.
supplementary angles
Two angles are supplementary if the sum of the measures of their angles is 180 degrees.
system of linear equations
When two or more linear equations are grouped together, they form a system of linear equations.
system of linear inequalities
Two or more linear inequalities grouped together form a system of linear inequalities.