unknown

Examples of unknown in the following topics:

• Equations and Inequalities

  • Equations often express relationships between given quantities—the knowns—and quantities yet to be determined—the unknowns.
  • The process of expressing the unknowns in terms of the knowns is called solving the equation.
  • In an equation with a single unknown, a value of that unknown for which the equation is true is called a solution or root of the equation.
  • In a set of simultaneous equations, or system of equations, multiple equations are given with multiple unknowns.
  • A solution to the system is an assignment of values to all the unknowns so that all of the equations are true.

• Introduction to Variables

  • Variables are used in mathematics to denote arbitrary or unknown numbers.
  • The last one, $x$, represents the solution of the equation, which is unknown and must be solved for.
  • A number on its own (without an unknown variable) is called a constant; in this case, $d$ represents a constant.
  • Therefore, a term may simply be a constant or a variable, or it may include both a coefficient and an unknown variable.
  • In this case, $b$ is an unknown variable, not a parameter of the equation.

• Solving Equations: Addition and Multiplication Properties of Equality

  • Equations often express relationships between given quantities ("knowns") and quantities yet to be determined ("unknowns").
  • The process of expressing an equation's unknowns in terms of its knowns is called solving the equation.
  • In an equation with a single unknown, a value of that unknown for which the equation is true is called a solution or root of the equation.
  • Let $x$ equal the unknown value: the number of hours of labor.
  • To solve for the unknown, first undo the addition operation (using the subtraction property) by subtracting $339 from both sides of the equation:

• The Law of Sines

  • The law of sines can be used to find unknown angles and sides in any triangle.
  • To find an unknown side, we need to know the corresponding angle and a known ratio.
  • The last unknown side is $b$, and we will follow a similar process for this.
  • The angle $\beta$ and the side-lengths $b$ and $c$ are unknown.

• Linear and Quadratic Equations

  • The process of expressing the unknowns in terms of the knowns is called solving the equation.
  • In an equation with a single unknown, a value of that unknown for which the equation is true is called a solution or root of the equation.
  • In a set simultaneous equations, or system of equations, multiple equations are given with multiple unknowns.
  • A solution to the system is an assignment of values to all the unknowns so that all of the equations are true.
  • where $x$ represents a variable or an unknown, and $a$, $b$, and $c$ are constants with $a \neq 0$.

• Applications and Mathematical Models

  • Systems of equations are problems that have multiple unknowns and multiple observations, and can be used in many practical applications.
  • A system of equations is a way to evaluate multiple unknown quantities.
  • You will need observations of these quantities in order to properly solve for the unknowns.
  • Your unknowns are the other two balls, c and h.
  • In this example, the unknowns are the two masses and the observations are the balances.

• Rational Equations

  • A rational equation sets two rational expressions equal to each other and involves unknown values that make the equation true.
  • This suggests a strategy: Find a common denominator, set the numerators equal to each other, and solve for any unknowns.
  • Several real-life situations can be modeled using equations that set two fractions, or ratios, to be equal to each other—for example, finding unknown dimensions of certain shapes.

• Equations in Two Variables

  • Equations with two unknowns represent a relationship between two variables and have a series of solutions.
  • Equations with two unknowns represent a relationship between two variables.

• Solving Systems of Equations Using Matrix Inverses

  • We have seen, in the chapter on simultaneous equations, how to solve two equations with two unknowns.
  • But suppose we have three equations with three unknowns?

• What is an Equation?

  • When an equation contains a variable such as $x$, this variable is considered an unknown value.
  • However, it becomes useful to have a process for finding solutions for unknowns as problems become more complex.