🧮 algebra

1. **State the problem:** Solve the equation $25(x + 2)^2 = (x - 7)^2 - 81$ for $x$. 2. **Rewrite the equation:**

1. **State the problem:** Solve the exponential equation $$4^x = 2^6$$ for $$x$$. 2. **Rewrite bases as powers of the same base:** Note that $$4 = 2^2$$, so rewrite the equation as

1. **State the problem:** Solve the equation $$25(x + 2)^2 = (x - 7)^2 - 81$$ for $x$. 2. **Rewrite the equation:** Expand both sides.

1. **State the problem:** Solve the equation $ (x+1)(2x+5) = (2x+3)(x-4) + 5 $. 2. **Use the distributive property (FOIL) to expand both sides:**

1. **State the problem:** We have the homogeneous system of equations: $$x + 3y = 0$$

1. **State the problem:** Simplify the expression $$\left(\frac{-8x^2}{-4x^3}\right)$$ and verify it equals $$2x \boxed{1}$$. 2. **Recall the formula and rules:** When dividing pow

1. El problema es reducir los términos semejantes de la expresión algebraica: $$-a + b + 2b - 2c + 3a + 2c - 3b$$

1. **State the problem:** We need to find the distance the bus travels between Emmanuel Street and Coleridge Road given the average speed is 23 km/h. 2. **Identify the time taken:*

1. **State the problem:** We need to find the average speed of a bus that travels 36 miles in 1 hour and 30 minutes. 2. **Formula used:** Average speed is calculated by dividing th

1. **State the problem:** We need to find the equation of the trend line passing through the two yellow points on the scatter plot, which are approximately at coordinates $(40, 10)

1. **State the problem:** You asked how we got the 4 inside the expansion of $(x - 2)^2$. 2. **Recall the binomial square formula:**

1. **State the problem:** We are given the function $$f(x) = 3(x - 2)^2 - 7$$ and asked to write it in standard form. 2. **Recall the formula:** The standard form of a quadratic fu

1. **Planteamiento del problema:** Se nos pide reducir la expresión $$A = \left(\frac{1}{3}\right)^{-1} + (2012 + \sqrt{2013})^0 + 81^{1/4}$$. 2. **Fórmulas y reglas importantes:**

1. Planteamos el problema: Dada la función afín $f(x) = \frac{1}{2}x - 3$, debemos encontrar las coordenadas donde la recta corta al eje $x$ y al eje $y$. 2. Para encontrar la inte

1. **Planteamiento del problema:** Se nos da un ingreso por plato con un componente fijo y uno variable según ingredientes premium, y un costo por turno con costos fijos y variable

1. **Planteamiento del problema:** Se nos dan fórmulas para ingresos y costos en función de platos producidos $p$ e ingredientes premium usados $x$.

1. Resolver el primer problema: \[

1. **State the problem:** Express the rational function $$\frac{5x^2 + 2}{2x^2 + x}$$ as a sum of partial fractions. 2. **Factor the denominator:**

1. **State the problem:** Express the rational function $$\frac{5x^2 + 2}{2x^2 + x}$$ as a sum of partial fractions. 2. **Factor the denominator:**

1. **Planteamiento del problema:** Se nos da una gráfica con una función lineal $g(x)$ que sube diagonalmente de izquierda a derecha en los cuadrantes I y II. 2. **Fórmula para la

1. El problema nos pide construir las funciones lineales que generan dos gráficas dadas. 2. Para la gráfica izquierda, observamos que la línea pasa por los puntos aproximados $(-2,