🧮 algebra

1. **State the problem:** We need to transport 1200 bags using two types of vehicles: Pickup trucks and Isuzu Diana trucks. 2. **Define variables:** Let $x$ be the number of trips

1. **Restate the question:** Why did we simplify the inequality $240000x + 300000y \leq 2400000$ by dividing by 60000 in step 7? 2. **Original inequality:**

1. **State the problem:** We need to find (a) the total cost to pay for 1200 bags of produce based on past transport costs, and (b) the number of trips each vehicle (Pickup and Isu

1. **State the problem:** Given the system of equations $$x^3 = 3 - y^3$$ and $$x^6 = 27 - y^6,$$ find the value of $x$. 2. **Recall the formulas and rules:** We know that $$x^6 =

1. **Stating the problem:** Factorise the given expression (though the expression is not provided, we will explain the general method). 2. **Formula and rules:** To factorise an al

1. **State the problem:** Simplify the rational expressions: 5°) \(\frac{a^2 + 4a + 4}{a^2 - 4}\)

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