🧮 algebra

1. The problem is to understand the relationship between cups of lemonade mix and cups of water. 2. Given the table:

1. **State the problem:** Factor completely the expression $$-3x^6yz^2 + 2x^2y$$. 2. **Identify common factors:** Look for the greatest common factor (GCF) in each term.

1. The problem is to find a Pythagorean triple, which is a set of three positive integers $a$, $b$, and $c$ such that they satisfy the Pythagorean theorem: $$a^2 + b^2 = c^2$$ 2. T

1. **State the problem:** We are given a point $(1,4)$ on the graph of $y=f(x)$ and need to find the coordinates of its image on the graph of $y=3f[-4(x+1)]-2$. 2. **Understand the

1. **Problema:** Calcula la suma o resta de fracciones y simplifica el resultado. 2. **Ejercicio 10 a):** $\frac{3}{5} + \frac{6}{5} = \frac{3+6}{5} = \frac{9}{5}$ (ya simplificado

1. The problem is to simplify the expression $14a$. 2. Since $14a$ is already in its simplest form, it represents the product of the number 14 and the variable $a$.

1. Let's clarify the origin of the expression $2x - 1$ in the final answer. 2. Typically, $2x - 1$ arises from simplifying or factoring an algebraic expression or solving an equati

1. **Planteamiento del problema:** Simplificar la expresión $$(x+2)^2 - 3(x^2 - 2x + 4)$$ 2. **Expansión de los términos:**

1. **State the problem:** Solve the linear equation $12x + 72 = 10x + 78$ for $x$. 2. **Write down the equation:**

1. **State the problem:** Solve the quadratic equation $9n^2 + 79 = -18n$ by completing the square. 2. **Rewrite the equation:** Move all terms to one side to set the equation to z

1. **State the problem:** We need to divide the polynomial $2x^{3}+3x^{2}+5x-8$ by $x^{2}+2x+3$. 2. **Recall the formula:** Polynomial division is similar to long division with num

1. **State the problem:** We are asked to find how many solutions the system of linear equations has: $$y = -\frac{3}{4}x - 6$$

1. The problem asks for the number of solutions to the system of linear equations: $$y = -5x + 3$$

1. **State the problem:** Solve the quadratic equation $4n^2 + 4n + 36 = 0$ by completing the square. 2. **Write the equation:**

1. **State the problem:** We want to factor the expression $$(x-7)^7 + 7x(x-7)^6$$ into the form $$(x-7)^6((x-7) + 7)$$. 2. **Identify common factors:** Notice that both terms cont

1. **Problem statement:** Schreibe den Term ohne Klammern und fasse so weit wie möglich zusammen. 2. **Formel und Regeln:** Verwende das Distributivgesetz: $a(b+c) = ab + ac$.

1. Problem: Schreibe den Term ohne Klammern und fasse nach Möglichkeit zusammen. 2. Wir betrachten den ersten Term:

1. The problem is to express the repeating decimal $0.5\dot{8}\dot{8}$ as a fraction in simplest form. 2. Let $x = 0.5\dot{8}\dot{8}$, which means $x = 0.588888\ldots$ where the di

1. **State the problem:** Find the greatest common factor (GCF) of the terms $-18x^3$ and $-6x^2$. 2. **List the terms:** The terms are $-18x^3$ and $-6x^2$.

1. **State the problem:** Find the greatest common factor (GCF) of the terms $$8a^4 + 24a^3 - 40a^2$$. 2. **Identify each term's factors:**

1. The problem asks us to find the first three terms of the sequence defined by the formula $T(n) = 5n - 7$. 2. The formula for the $n^{th}$ term of the sequence is given as: