Solving Quadratic Equations
... Recall, when we tried to solve x² + 6x + 5 = 0 (Task 3, #3d), we couldn’t solve by taking square roots. We now can set this equation up so that we will be able to eventually take the square roots of both sides and solve for the variable. 10. Let’s use the chart below to solve: x² + 6x + 5 = 0 by com ...
... Recall, when we tried to solve x² + 6x + 5 = 0 (Task 3, #3d), we couldn’t solve by taking square roots. We now can set this equation up so that we will be able to eventually take the square roots of both sides and solve for the variable. 10. Let’s use the chart below to solve: x² + 6x + 5 = 0 by com ...
Connecting Variation, Slope, and First Differences
... A relation can be expressed in four ways (the text refers to this as the rule of four): using words (the description of the situation) using numbers (a table of values) using a diagram or graph using an equation Recall that the equations of a line has the form y = mx + b, where m represents ...
... A relation can be expressed in four ways (the text refers to this as the rule of four): using words (the description of the situation) using numbers (a table of values) using a diagram or graph using an equation Recall that the equations of a line has the form y = mx + b, where m represents ...
Trigonometry and Pre
... Trigonometry/Precalculus Prerequisite Skills Review The following exercises will give you an opportunity to refresh your prior knowledge and skills from Algebra and Geometry and Advanced Algebra, in preparation for Trig/Pre-calculus. For the following problems, write out your steps or show how you a ...
... Trigonometry/Precalculus Prerequisite Skills Review The following exercises will give you an opportunity to refresh your prior knowledge and skills from Algebra and Geometry and Advanced Algebra, in preparation for Trig/Pre-calculus. For the following problems, write out your steps or show how you a ...
Equation
In mathematics, an equation is an equality containing one or more variables. Solving the equation consists of determining which values of the variables make the equality true. In this situation, variables are also known as unknowns and the values which satisfy the equality are known as solutions. An equation differs from an identity in that an equation is not necessarily true for all possible values of the variable.There are many types of equations, and they are found in all areas of mathematics; the techniques used to examine them differ according to their type.Algebra studies two main families of equations: polynomial equations and, among them, linear equations. Polynomial equations have the form P(X) = 0, where P is a polynomial. Linear equations have the form a(x) + b = 0, where a is a linear function and b is a vector. To solve them, one uses algorithmic or geometric techniques, coming from linear algebra or mathematical analysis. Changing the domain of a function can change the problem considerably. Algebra also studies Diophantine equations where the coefficients and solutions are integers. The techniques used are different and come from number theory. These equations are difficult in general; one often searches just to find the existence or absence of a solution, and, if they exist, to count the number of solutions.Geometry uses equations to describe geometric figures. The objective is now different, as equations are used to describe geometric properties. In this context, there are two large families of equations, Cartesian equations and parametric equations.Differential equations are equations involving one or more functions and their derivatives. They are solved by finding an expression for the function that does not involve derivatives. Differential equations are used to model real-life processes in areas such as physics, chemistry, biology, and economics.The ""="" symbol was invented by Robert Recorde (1510–1558), who considered that nothing could be more equal than parallel straight lines with the same length.