SOLUTIONS FOR PROBLEMS 1 - 30 1. Answer: 5 Evaluate – x – 3x
... Since the inequality is strictly greater than zero, neither of these are in the solution set. These two numbers divide the x axis into three sections: – ∞ < x < 2, 2 < x < 3, and 3 < x < ∞ Pick any "test" number for each section and substitute into the inequality: For – ∞ < x < 2, say x = 0. Substit ...
... Since the inequality is strictly greater than zero, neither of these are in the solution set. These two numbers divide the x axis into three sections: – ∞ < x < 2, 2 < x < 3, and 3 < x < ∞ Pick any "test" number for each section and substitute into the inequality: For – ∞ < x < 2, say x = 0. Substit ...
finm221F08smpKey.pdf
... Instructions: Show your work in the spaces provided below for full credit. Clearly identify answers and show supporting work to receive any credit. Give exact answers (e.g., π ) rather than inexact (e.g., 3.14); make obvious simpli cations, e.g., 0 rather than sin π . Point values are in parentheses ...
... Instructions: Show your work in the spaces provided below for full credit. Clearly identify answers and show supporting work to receive any credit. Give exact answers (e.g., π ) rather than inexact (e.g., 3.14); make obvious simpli cations, e.g., 0 rather than sin π . Point values are in parentheses ...
Section 1-3: Solving Inequalities
... A number line is used to show all the numbers that are solutions to x > 2. To show all of the numbers greater than 2 draw a number line with a 2 under it. An open circle above the 2 is used to show that 2 is not part of the solution as 2 is not greater than 2. Then all the numbers greater than 2 are ...
... A number line is used to show all the numbers that are solutions to x > 2. To show all of the numbers greater than 2 draw a number line with a 2 under it. An open circle above the 2 is used to show that 2 is not part of the solution as 2 is not greater than 2. Then all the numbers greater than 2 are ...
Finding the Inverse of a Matrix
... however, that inverse is unique. Example 2 shows how to use systems of equations to find the inverse of a matrix. ...
... however, that inverse is unique. Example 2 shows how to use systems of equations to find the inverse of a matrix. ...
Solve each inequality. Then graph the solution set on a number line
... To graph this inequality, draw an open circle at 18.75 and draw an arrow extending to the right. ...
... To graph this inequality, draw an open circle at 18.75 and draw an arrow extending to the right. ...
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.