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- https://math.libretexts.org/Bookshelves/Algebra/Advanced_AlgebraIntermediate Algebra is the second part of a two-part course in Algebra that builds on the basics learned in Elementary Algebra and introduces the more advanced topics required for further study of ap...Intermediate Algebra is the second part of a two-part course in Algebra that builds on the basics learned in Elementary Algebra and introduces the more advanced topics required for further study of applications found in most disciplines. Used as a standalone textbook, it offers plenty of review as well as something new to engage the student in each chapter. This textbook introduces functions early and stresses the geometry behind the algebra.
- https://math.libretexts.org/Bookshelves/Algebra/Advanced_Algebra/03%3A_Solving_Linear_Systems/3.0E%3A_3.E%3A_Solving_Linear_Systems\(\left\{ \begin{array} { l } { 4 x - y + 2 z = - 1 } \\ { x - 4 y + 3 z = 11 } \\ { 3 x + 5 y - 4 z = 1 } \end{array} \right.\) \(\left\{ \begin{array} { l } { x - 4 y + 6 z = 5 } \\ { 2 x + 5 y - z ...\(\left\{ \begin{array} { l } { 4 x - y + 2 z = - 1 } \\ { x - 4 y + 3 z = 11 } \\ { 3 x + 5 y - 4 z = 1 } \end{array} \right.\) \(\left\{ \begin{array} { l } { x - 4 y + 6 z = 5 } \\ { 2 x + 5 y - z = - 3 } \\ { 3 x - 4 y + z = 25 } \end{array} \right.\) Determine whether or not \((−3, 2, −5)\) is a solution to \(\left\{ \begin{array} { l } { x - y + 2 z = - 15 } \\ { 2 x - 3 y + z = - 17 } \\ { 3 x + 5 y - 2 z = 10 } \end{array} \right.\).
- https://math.libretexts.org/Bookshelves/Algebra/Advanced_Algebra/03%3A_Solving_Linear_Systems/3.02%3A_Solving_Linear_Systems_with_Two_VariablesIn this section, we review a completely algebraic technique for solving systems, the substitution method11. The idea is to solve one equation for one of the variables and substitute the result into th...In this section, we review a completely algebraic technique for solving systems, the substitution method11. The idea is to solve one equation for one of the variables and substitute the result into the other equation. After performing this substitution step, we are left with a single equation with one variable, which can be solved using algebra.
- https://math.libretexts.org/Bookshelves/Algebra/Advanced_Algebra/07%3A_Exponential_and_Logarithmic_Functions/00%3A_Front_Matter/02%3A_InfoPageThe LibreTexts libraries are Powered by NICE CXOne and are supported by the Department of Education Open Textbook Pilot Project, the UC Davis Office of the Provost, the UC Davis Library, the Californi...The LibreTexts libraries are Powered by NICE CXOne and are supported by the Department of Education Open Textbook Pilot Project, the UC Davis Office of the Provost, the UC Davis Library, the California State University Affordable Learning Solutions Program, and Merlot.
- https://math.libretexts.org/Bookshelves/Algebra/Advanced_Algebra/06%3A_Solving_Equations_and_Inequalities
- https://math.libretexts.org/Bookshelves/Algebra/Advanced_Algebra/01%3A_Algebra_Fundamentals/1.06%3A_Polynomials_and_Their_OperationsA polynomial is a special algebraic expression with terms that consist of real number coefficients and variable factors with whole number exponents.
- https://math.libretexts.org/Bookshelves/Algebra/Advanced_Algebra/03%3A_Solving_Linear_Systems/3.05%3A_Matrices_and_Gaussian_EliminationA linear system in upper triangular form can easily be solved using back substitution. The augmented coefficient matrix and Gaussian elimination can be used to streamline the process of solving linear...A linear system in upper triangular form can easily be solved using back substitution. The augmented coefficient matrix and Gaussian elimination can be used to streamline the process of solving linear systems.
- https://math.libretexts.org/Bookshelves/Algebra/Advanced_Algebra/08%3A_Conic_Sections/8.01%3A_Distance_Midpoint_and_the_ParabolaA conic section is a curve obtained from the intersection of a right circular cone and a plane. The conic sections are the parabola, circle, ellipse, and hyperbola.
- https://math.libretexts.org/Bookshelves/Algebra/Advanced_Algebra/08%3A_Conic_Sections/8.02%3A_CirclesA circle is the set of points in a plane that lie a fixed distance, called the radius, from any point, called the center. The diameter is the length of a line segment passing through the center whose ...A circle is the set of points in a plane that lie a fixed distance, called the radius, from any point, called the center. The diameter is the length of a line segment passing through the center whose endpoints are on the circle. In addition, a circle can be formed by the intersection of a cone and a plane that is perpendicular to the axis of the cone.
- https://math.libretexts.org/Bookshelves/Algebra/Advanced_Algebra/05%3A_Radical_Functions_and_Equations/5.03%3A_Adding_and_Subtracting_Radical_Expressions\(\begin{array} { l } { 5 \sqrt [ 3 ] { 3 x ^ { 4 } } + \sqrt [ 3 ] { 24 x ^ { 3 } } - \left( x \sqrt [ 3 ] { 24 x } + 4 \sqrt [ 3 ] { 3 x ^ { 3 } } \right) } \\ { = 5 \sqrt [ 3 ] { 3 x ^ { 4 } } + \s...\(\begin{array} { l } { 5 \sqrt [ 3 ] { 3 x ^ { 4 } } + \sqrt [ 3 ] { 24 x ^ { 3 } } - \left( x \sqrt [ 3 ] { 24 x } + 4 \sqrt [ 3 ] { 3 x ^ { 3 } } \right) } \\ { = 5 \sqrt [ 3 ] { 3 x ^ { 4 } } + \sqrt [ 3 ] { 24 x ^ { 3 } } - x \sqrt[3] { 24 x } - 4 \sqrt [ 3 ] { 3 x ^ { 3 } } } \\ { = 5 \sqrt [ 3 ] { 3 \cdot x \cdot x ^ { 3 } } + \sqrt [ 3 ] { 8 \cdot 3 \cdot x ^ { 3 } } - x \sqrt [ 3 ] { 8 \cdot 3 x } - 4 \sqrt [ 3 ] { 3 x ^ { 3 } } } \\ { = 5 x \sqrt [ 3 ] { 3 x } + 2 x \sqrt [ 3 ] { 3 } …
- https://math.libretexts.org/Bookshelves/Algebra/Advanced_Algebra/06%3A_Solving_Equations_and_Inequalities/605%3A_Solving_Quadratic_InequalitiesA quadratic inequality is a mathematical statement that relates a quadratic expression as either less than or greater than another. A solution to a quadratic inequality is a real number that will prod...A quadratic inequality is a mathematical statement that relates a quadratic expression as either less than or greater than another. A solution to a quadratic inequality is a real number that will produce a true statement when substituted for the variable.
