🧮 algebra
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Racionalizacion
1. El problema es practicar la racionalización de expresiones algebraicas que contienen raíces en el denominador.
2. La racionalización consiste en eliminar raíces del denominador
Sum Formulas
1. The problem asks to find the sum of all sums and provide formulas.
2. To clarify, the sum of a sequence of numbers can be found using different formulas depending on the type of
Asymptotes
1. **State the problem:** Find the rectangular and inclined asymptotes of the curve defined by the equation $ (x + y)^2 (x + 2y + 2) = (x + 9y - 2) $.
2. **Rewrite the equation:**
Expression Evaluation
1. **State the problem:** Calculate the value of the expression $(14-16.58)+5(15-16.58)+3(16-16.58)+2(17-16.58)+2(18-16.58)+(25-16.58)$.
2. **Rewrite the expression:** Note that co
Racionalizacion Algebra
1. El problema es practicar la racionalización en álgebra, que consiste en eliminar raíces del denominador de una fracción.
2. La fórmula básica para racionalizar un denominador co
Sistema Lineal
1. Planteamos el problema: Resolver el sistema de ecuaciones
$$\begin{cases} 3x - \frac{y - 3}{5} = 6 \\ 3y - \frac{x - 2}{7} = 9 \end{cases}$$
Simplify Rational
1. **Problem:** Simplify the expression $$\frac{x}{p(x)} - \frac{g(x)}{r(x)}$$ where $$p(x) = x - 4$$, $$g(x) = x^2 + 8$$, and $$r(x) = x^2 - 2x - 8$$.
2. **Formula and rules:** To
Simplify Rational
1. **Problem:** Simplify the expression $$\frac{x}{p(x)} - \frac{g(x)}{r(x)}$$ where $$p(x) = x - 4$$, $$g(x) = x^2 + 8$$, and $$r(x) = x^2 - 2x - 8$$.
2. **Formula and rules:** To
Simplify Rational
1. **Problem:** Simplify the expression $$\frac{x}{p(x)} - \frac{g(x)}{r(x)}$$ where $$p(x) = x - 4$$, $$g(x) = x^2 + 8$$, and $$r(x) = x^2 - 2x - 8$$.
2. **Formula and rules:** To
Simplify Expression
1. **State the problem:** Simplify the expression $-9z + z + 9 + 1$.
2. **Identify like terms:** Like terms are terms that contain the same variable raised to the same power. Here,
Simplify Expression
1. **State the problem:** Simplify the expression $6 + 6d + (-7) + -9d$.
2. **Identify like terms:** The terms $6$ and $-7$ are constants, and the terms $6d$ and $-9d$ are like ter
Simplify Expression
1. **State the problem:** Simplify the expression $-6b + 5 + 4b + (-7)$.
2. **Combine like terms:** Group the terms with $b$ and the constant terms separately.
Sequence Prediction
1. **Stating the problem:** We are given a sequence of numbers: 2.66, 2.05, 1.36, 5.29, 3.35, 1.21, 1.35, 1.42. We need to predict the next 5 digits in this sequence.
2. **Analyzin
Graphing Inequalities
1. **State the problem:** We need to graph the system of linear inequalities:
$$y \geq \frac{x}{3} - 1$$
Multiply Mixed
1. **State the problem:** Find the product of the mixed numbers $3 \frac{3}{5}$ and $2 \frac{2}{7}$.
2. **Convert mixed numbers to improper fractions:**
Linear Inequalities
1. **State the problem:** We need to graph the system of linear inequalities:
$$y \leq 3x - 4$$
Graphing Inequalities
1. **State the problem:** We need to graph the system of linear inequalities:
$$y \leq 3x - 4$$
Graphing Inequalities
1. **State the problem:** We need to graph the system of linear inequalities:
$$y \leq -2$$
Quadratic Function
1. **Problem Statement:**
Fill out the chart for the quadratic function and graph the function $y = -\frac{1}{4}x^2 - 3x - 8$ using a table of values.
Salary Increase
1. **Stating the problem:**
Chery, Eunice, and Farina currently earn 25000, 28000, and 23000 respectively. Their employer plans to increase their monthly salaries by 10% at the beg
Power Of 2
1. The problem is to evaluate the expression $2^8$.
2. The expression $2^8$ means 2 raised to the power of 8, which is multiplying 2 by itself 8 times.