🧮 algebra

1. **State the problem:** Simplify the expression $$\left(81 \frac{1}{4} - \frac{1}{2} \log_9 4 + 25 \log_{125} 8\right) \cdot 49 \log_7 2$$. 2. **Rewrite mixed number:** Convert $

1. **Planteamiento del problema:** Queremos analizar y graficar la función cuadrática $$y = -2x^2 - x + 6$$.

1. **State the problem:** We need to find the ordered pair $(x,y)$ that satisfies both equations represented by the two lines on the coordinate grid. 2. **Identify the lines:** Fro

1. **Planteamiento del problema:** Queremos analizar la función cuadrática $$y = -2x^2 - x + 6$$.

1. The problem asks to find the ordered pair that is a solution to both equations represented by the two lines on the graph. 2. The first line passes through points (-6, -6) and (6

1. **State the problem:** Simplify the expression $$\frac{4x}{2x^2 + x - 3} \cdot \frac{4x^2 + 2x - 6}{12x^3}$$. 2. **Factor all polynomials where possible:**

1. **State the problem:** Simplify the expression \( \frac{4x^3}{2x^3 + x - 3} \cdot \frac{4x^2 + 2x - 6}{12x^3} \). 2. **Write the expression:**

1. **Problem 7: Solve $x + 7 > 18$** We want to find all $x$ such that $x + 7 > 18$.

1. **Problema:** Dado que $\log_a\left(\frac{a^2}{b}\right) = 3$, determine o valor de $\log_a\left(\sqrt{a^5 b^4}\right)$. 2. **Fórmulas e regras importantes:**

1. **State the problem:** We are given the quadratic expression $$4x^2 + 28x + 49$$ and need to factor it or recognize its form. 2. **Recall the formula for factoring perfect squar

1. **State the problem:** We are given a table of visitors to a website over days and asked:

1. **Problem 14: Find the length and width of the Parthenon's base.** The length $L$ is 8 meters more than twice the width $W$, so:

1. Problema: Reducir el polinomio $$x^2y - xy + xy - 8x^2y - x^2y + 10 + x^2y - 7x^2y - 9 + 21x + y - y + 50$$. 2. Fórmula y reglas: Para reducir polinomios, sumamos o restamos tér

1. The problem asks which expression is equivalent to 100,000. 2. Recall that powers of 10 represent 10 multiplied by itself a certain number of times: $$10^n = \underbrace{10 \tim

1. The problem states that the number of miles is always 10 times the number of hours. 2. This relationship can be expressed as a linear function: $$\text{miles} = 10 \times \text{

1. The problem is to solve an algebraic expression or equation step-by-step without providing the final answer. 2. Start by identifying the expression or equation to be solved.

1. **Problem statement:** For the matchstick patterns, find:

1. **State the problem:** Solve the quadratic equation $$9x^2 - 7x - 23 = 0$$ using the quadratic formula. 2. **Quadratic formula:** For any quadratic equation $$ax^2 + bx + c = 0$

1. **State the problem:** Multiply the numbers in scientific notation: $$(8.36 \times 10^3)(7.5 \times 10^{-1})$$ 2. **Recall the multiplication rule for scientific notation:** Whe

1. El problema es evaluar la expresión: $10 - [ ( ) + [5 - (3) ] ]$. 2. Primero, observamos que hay paréntesis vacíos $( )$ dentro de la expresión, que equivalen a 0.

1. **Постановка задачи:** Найти количество решений системы уравнений $$\begin{cases} xy + 3 = 0, \\ 2 - y + x^2 = 0. \end{cases}$$