🧮 algebra

1. **State the problem:** The number of bacteria cells doubles every 10 minutes, starting with 1 cell. We want to find the number of cells after 1 hour. 2. **Identify the formula:*

1. Planteamos el problema: Resolver el sistema de ecuaciones: $$\begin{cases} x - 2y - 6 = 0 \\ \frac{x - y}{2} + x = 4 \end{cases}$$

1. **State the problem:** We are given a system of two equations: $$x - 2y - 6 = 0$$

1. **State the problem:** Solve the system of equations by graphing: $$\begin{cases} y = 2x - 1 \\ y = -x + 5 \end{cases}$$

1. **State the problem:** We are given two linear equations:

1. El problema es factorizar el polinomio $$x^3 - 2x^2 - 5x + 6$$. 2. Para factorizar un polinomio cúbico, primero buscamos raíces racionales posibles usando el teorema del factor:

1. El problema es factorizar el polinomio $$x^3 - 2x^2 - 5x + 6$$ y determinar cuál de las opciones dadas es correcta. 2. Para factorizar un polinomio cúbico, primero buscamos raíc

1. **State the problem:** Simplify the expression $24 \div 6 + 4 \times (3 + 6)$.\n\n2. **Recall order of operations (PEMDAS/BODMAS):** Parentheses first, then multiplication and d

1. **State the problem:** Simplify the expression $b^{3/5} \cdot b^{4/2}$ assuming all variables are positive. 2. **Recall the rule for multiplying powers with the same base:**

1. We are asked to simplify the expression $7 \log_4 \left(4^{2x+5}\right) - 10 \log (x+5)$. 2. Recall the logarithm power rule: $\log_b (a^c) = c \log_b a$. Also, $\log_b b = 1$.

1. **Problem Statement:** We are asked to find the lowest common denominator (LCD) for pairs of denominators and then compare fractions by converting them to equivalent fractions w

1. **State the problem:** Simplify the expression $37(-10) - 4(2 \times 4) - 77$. 2. **Recall the order of operations:** Perform multiplication and division before addition and sub

1. Reduce $\frac{36}{63}$ to lowest terms. Step 1: Find the greatest common divisor (GCD) of 36 and 63.

1. **State the problem:** Simplify the expression $j^{-13} \cdot j^{4} \cdot j^{6}$. 2. **Recall the rule for multiplying powers with the same base:**

1. El problema es simplificar visualmente una expresión matemática para que sea más fácil de entender. 2. Para simplificar una expresión, primero identificamos términos semejantes

1. Solve the inequality $$\frac{1}{x+2} \leq \frac{2}{3x+1}$$ algebraically. 2. First, bring all terms to one side to form a single inequality:

1. Solve for $x$ in the equation $5x - 15y = 20$. Step 1: Start with the equation:

1. **State the problem:** Simplify the expression $$\left( \frac{4x^5 y}{16xy^4} \right)^3$$. 2. **Write the formula and rules:** When simplifying powers of fractions, use $$\left(

1. **Planteamiento del problema:** Se nos dan dos polinomios: $$P(x) = \frac{3}{2}x^3 + 2x^2 + \frac{1}{2}x + 1$$

1. **State the problem:** Solve the quadratic equation $$6w^2 - 26w + 5 = w^2$$ using the quadratic formula and express the solutions in simplest form. 2. **Rewrite the equation:**

1. Problem 1a: Solve the inequality $3x^3 - x^2 - 3x + 1 \le 0$. 2. Strategy: Factor the polynomial to find its real roots and then use a sign chart to determine where the product