🧮 algebra

1. **State the problem:** Simplify the expression $$\frac{2\frac{1}{2}}{1-\left(\frac{1}{2}\right)^2}$$. 2. **Convert mixed number to improper fraction:**

1. **State the problem:** Simplify the expression $$\frac{-\frac{1}{3}-\left(-3\right)}{1+\left(-\frac{1}{3}\right)\left(-3\right)}$$. 2. **Recall the formula:** This expression re

1. **State the problem:** We need to analyze the function $$f(x) = (x - 1)^3 (x + 2)^2$$. 2. **Formula and rules:** This is a polynomial function expressed as a product of powers o

1. **Enunciado do problema:** Calcular o erro relativo da estimativa por interpolação linear para $x=2,7$ usando os dados da tabela e compará-lo com o valor exato $y=0,993251$.

1. O problema pede para fazer uma interpolação polinomial usando os pontos dados $(-1,1)$, $(1,1)$ e $(3,-7)$ e avaliar o polinômio em $x=0$. 2. Usaremos o método de interpolação p

1. O problema pede para encontrar o valor de $y$ quando $x=0$ usando interpolação polinomial com os pontos dados: $(-1,1)$, $(1,1)$ e $(3,-7)$. 2. Usaremos o polinômio interpolador

1. Vamos considerar o sistema linear dado: $$\begin{cases} x_1 + 8x_2 + 2x_3 = 10 \\ 15x_1 + x_2 + 2x_3 = 13 \\ x_1 + x_2 + 3x_3 = -4 \end{cases}$$

1. O problema pede a solução do sistema de equações: $$\begin{cases} 3x_1 + 5x_2 = 13 \\ 2x_1 + x_2 = 6 \end{cases}$$

1. El problema pide hallar el dominio y rango de cada función dada. 2. Recordemos que el dominio de una función es el conjunto de valores de $x$ para los cuales la función está def

1. **State the problem:** Solve the equation $-3y = 33$ for $y$. 2. **Formula and rules:** To solve for $y$, divide both sides of the equation by $-3$.

1. **State the problem:** Solve for $x$ in the equation $3 \cdot (-2.5) = x$. 2. **Formula and rules:** Multiplication of a positive number by a negative number results in a negati

1. The problem is to write the inequality represented by the graph. 2. The graph shows a solid dot at $-2$ and a line extending to the right up to $4$ and beyond, indicating all nu

1. The problem is to write the inequality represented by the graph. 2. The graph shows a solid dot at 0 and shading extending to the right, indicating all values greater than or eq

1. **State the problem:** Simplify the expression $$4^{\frac{3}{4}} \times \sqrt{\left(\frac{6}{5}\right)^{15} \times \left(\frac{6}{5}\right)^9}$$. 2. **Recall the rules:**

1. **State the problem:** Solve the equation $$\frac{x+2}{3} - \frac{1}{2} = 2$$. 2. **Formula and rules:** To solve equations with fractions, find a common denominator to eliminat

1. **State the problem:** Solve the equation $$\frac{2x}{5} + \frac{x}{10} = 3$$ for $x$. 2. **Formula and rules:** To solve equations with fractions, find a common denominator to

1. **State the problem:** Solve the equation $$\frac{x}{3} - \frac{x}{6} = 4$$. 2. **Formula and rules:** To solve equations with fractions, find a common denominator to combine te

1. **Planteamiento del problema:** Se administra 50 mg de un medicamento y la cantidad restante disminuye a la tercera parte cada 5 horas.

1. **State the problem:** Solve the equation $$\frac{x}{2} + \frac{x}{3} = 10$$ for $x$. 2. **Formula and rules:** To solve equations with fractions, find a common denominator to c

1. **State the problem:** Solve the equation $$\frac{x}{5} - \frac{2}{3} = 1$$. 2. **Formula and rules:** To solve for $x$, we need to isolate $x$ on one side. We will first add $\

1. **State the problem:** Solve the equation $$\frac{x}{4} + \frac{3}{2} = 5$$ for $x$. 2. **Identify the formula and rules:** To solve for $x$, we need to isolate $x$ on one side