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- https://math.libretexts.org/Bookshelves/Algebra/Elementary_Algebra_1e_(OpenStax)/07%3A_Factoring
- https://math.libretexts.org/Bookshelves/Algebra/Elementary_Algebra_1e_(OpenStax)/09%3A_Roots_and_Radicals/9.08%3A_Rational_Exponents/9.8E%3A_Exercises\(\frac{r^{\frac{5}{2}}·r^{−\frac{1}{2}}}{r^{−\frac{3}{2}}}\) \(\frac{a^{\frac{3}{4}}·a^{−\frac{1}{4}}}{a^{−\frac{10}{4}}}\) Simplify \(242^{\frac{1}{2}}\) to find the length of each side of his patio...\(\frac{r^{\frac{5}{2}}·r^{−\frac{1}{2}}}{r^{−\frac{3}{2}}}\) \(\frac{a^{\frac{3}{4}}·a^{−\frac{1}{4}}}{a^{−\frac{10}{4}}}\) Simplify \(242^{\frac{1}{2}}\) to find the length of each side of his patio.Round to the nearest tenth of a foot. Simplify \(\frac{12^{\frac{1}{2}}}{16^{\frac{1}{2}}}\) to find how many seconds it took for the decoration to reach the ground. Simplify \(\frac{1024^{\frac{1}{2}}}{16^{\frac{1}{2}}}\) to find how many seconds it took for the flare to reach the water.
- https://math.libretexts.org/Bookshelves/Algebra/Elementary_Algebra_1e_(OpenStax)/08%3A_Rational_Expressions_and_Equations
- https://math.libretexts.org/Bookshelves/Algebra/Intermediate_Algebra_1e_(OpenStax)/09%3A_Quadratic_Equations_and_Functions/903%3A_Solve_Quadratic_Equations_by_Completing_the_Square/9.3E%3A_ExercisesIn the following exercises, complete the square to make a perfect square trinomial. ExerciseS 5 - 28: Solve Quadratic Equations of the Form \(x^{2}+b x+c=0\) by Completing the Square ExerciseS 29 - 40...In the following exercises, complete the square to make a perfect square trinomial. ExerciseS 5 - 28: Solve Quadratic Equations of the Form \(x^{2}+b x+c=0\) by Completing the Square ExerciseS 29 - 40: Solve Quadratic Equations of the Form \(a x^{2}+b x+c=0\) by Completing the Square Solve the equation \(x^{2}+10 x=-25\) Solve the equation \(y^{2}+8y=48\) by completing the square and explain all your steps.
- https://math.libretexts.org/Bookshelves/Algebra/Intermediate_Algebra_1e_(OpenStax)/12%3A_Sequences_Series_and_Binomial_Theorem/12.01%3A_Prelude_to_Sequences_Series_and_Binomial_TheoremSometimes known as cryptographers, these people develop complex patterns in computer codes that block access to would-be thieves as well as write codes to intercept and decode information from them so...Sometimes known as cryptographers, these people develop complex patterns in computer codes that block access to would-be thieves as well as write codes to intercept and decode information from them so that they may be identified. In this chapter, you will explore basic sequences and series related to those used by computer programmers to prevent cyber crime.
- https://math.libretexts.org/Bookshelves/Algebra/Intermediate_Algebra_1e_(OpenStax)/08%3A_Roots_and_Radicals/8.05%3A_Add_Subtract_and_Multiply_Radical_ExpressionsAdding radical expressions with the same index and the same radicand is just like adding like terms. We call radicals with the same index and the same radicand like radicals to remind us they work the...Adding radical expressions with the same index and the same radicand is just like adding like terms. We call radicals with the same index and the same radicand like radicals to remind us they work the same as like terms.
- https://math.libretexts.org/Bookshelves/Algebra/Intermediate_Algebra_1e_(OpenStax)/07%3A_Rational_Expressions_and_Functions/7.06%3ASolve_Applications_with_Rational_EquationsNotice in the last example that when we cleared the fractions by multiplying by the LCD, the result is the same as if we had cross-multiplied. To solve applications with proportions, we will follow ou...Notice in the last example that when we cleared the fractions by multiplying by the LCD, the result is the same as if we had cross-multiplied. To solve applications with proportions, we will follow our usual strategy for solving applications But when we set up the proportion, we must make sure to have the units correct—the units in the numerators must match each other and the units in the denominators must also match each other.
- https://math.libretexts.org/Bookshelves/Algebra/Intermediate_Algebra_1e_(OpenStax)/11%3A_Conics/11.05%3A_HyperbolasIn the figure, we placed the hyperbola so the foci \(((−c,0),(c,0))\) are on the \(x\)-axis and the center is the origin. Sketch the rectangle that goes through the points \(3\) units to the left/righ...In the figure, we placed the hyperbola so the foci \(((−c,0),(c,0))\) are on the \(x\)-axis and the center is the origin. Sketch the rectangle that goes through the points \(3\) units to the left/right of the center and \(4\) units above and below the center. Sketch the rectangle that goes through the points \(3\) units to the left/right of the center and \(2\) units above and below the center. The midpoint of the segment joining the foci is called the center of the hyperbola.
- https://math.libretexts.org/Bookshelves/Algebra/Elementary_Algebra_1e_(OpenStax)/06%3A_Polynomials
- https://math.libretexts.org/Bookshelves/Algebra/Intermediate_Algebra_1e_(OpenStax)/03%3A_Graphs_and_Functions/3.06%3A_Relations_and_Functions/3.6E%3A_ExercisesThe function \(N(t)=85+20t\) represents the relation between the number of unwatched shows, N, and the time, t, measured in weeks. The daily cost to the printing company to print a book is modeled by ...The function \(N(t)=85+20t\) represents the relation between the number of unwatched shows, N, and the time, t, measured in weeks. The daily cost to the printing company to print a book is modeled by the function \(C(x)=3.25x+1500\) where C is the total daily cost and x is the number of books printed. The daily cost to the manufacturing company is modeled by the function \(C(x)=7.25x+2500\) where \(C(x)\) is the total daily cost and x is the number of items manufactured.
- https://math.libretexts.org/Bookshelves/Algebra/Intermediate_Algebra_1e_(OpenStax)/03%3A_Graphs_and_Functions/3.02%3A_Graph_Linear_Equations_in_Two_Variables/3.2E%3A_ExercisesIn the following exercises, plot each point in a rectangular coordinate system and identify the quadrant in which the point is located. Explain how you would choose three x-values to make a table to g...In the following exercises, plot each point in a rectangular coordinate system and identify the quadrant in which the point is located. Explain how you would choose three x-values to make a table to graph the line \(y=15x−2\). Do you prefer to use the method of plotting points or the method using the intercepts to graph the equation \(4x+y=−4\)? Do you prefer to use the method of plotting points or the method using the intercepts to graph the equation \(y=23x−2\)?
