🧮 algebra

1. **State the problem:** We need to find the equation of the line passing through the points $(-3, 2)$ and $(1, -6)$ in slope-intercept form, which is $y = mx + b$. 2. **Find the

1. **Problem:** Simplify the expression $$\frac{x^2 - 4x}{x - 2} \cdot \frac{2 - x}{x}$$ and describe any restrictions on the variables. 2. **Step 1: Factor expressions where possi

1. **State the problem:** We need to graph the line given by the equation $$y=\frac{2}{5}x+1$$ and list two points on the line, then describe the rise/run between those points. 2.

1. **State the problem:** Solve the inequality $$\left|\frac{1 - 3X}{5X - 2}\right| \geq 10$$. 2. **Recall the rule for absolute value inequalities:** For any expression $A$, $$|A|

1. **State the problem:** We need to find the point-slope form of a line with slope $m = -\frac{3}{4}$ passing through the point $(2, -5)$. 2. **Recall the point-slope form formula

1. The problem is to simplify the fraction $\frac{2}{2}$. 2. The formula for simplifying a fraction is to divide both numerator and denominator by their greatest common divisor (GC

1. The problem is to simplify the expression $^{\frac{2}{2}}$. 2. This expression appears to be a superscript notation without a base, which is incomplete or ambiguous in standard

1. **Stating the problem:** We are given the equation $$\frac{2x+3}{x-1} = 4$$ and need to solve for $x$. 2. **Formula and rules:** To solve rational equations, multiply both sides

1. The problem is to understand the letter "P" as it stands alone without additional context or mathematical expression. 2. Since "P" is a single letter, it could represent a varia

1. Vamos analisar a Questão 02, que pede para construir o gráfico de funções do segundo grau, determinando as raízes, o vértice, o ponto de interseção com o eixo y e a imagem da fu

1. We are asked to solve the inequality $$|x^2 - 2x - 3| < 3$$. 2. Recall that for any expression $A$, the inequality $|A| < b$ (where $b > 0$) means $$-b < A < b$$.

1. The problem is to find the value of $\sqrt{8704}$. 2. The square root of a number $x$ is a value $y$ such that $y^2 = x$.

1. **State the problem:** Simplify the expression $15x^2y - 10xy^3$. 2. **Identify common factors:** Both terms have common factors of $5xy$.

1. **State the problem:** Find the x- and y-intercepts of the equation $$y = 15x - 3$$. 2. **Recall the definitions:**

1. **State the problem:** Find the greatest common factor (GCF) of the polynomial expression $15x^2y - 10xy^3$. 2. **Recall the formula and rules:** The GCF of terms is the product

1. The problem involves understanding set notation for domain and range of functions or relations. 2. The domain is the set of all possible input values (x-values), and the range i

1. **State the problem:** We need to graph the function $$y = 5|x - 2| - 7$$ and identify its vertex. 2. **Recall the formula and rules:** The function is an absolute value functio

1. **State the problem:** Solve for $y$ in the equation $$\frac{y + 4}{6y} - \frac{4}{9} = \frac{1}{y}.$$\n\n2. **Identify the common denominator:** The denominators are $6y$, $9$,

1. **State the problem:** Solve the equation $$\frac{2}{u} + \frac{1}{6} = \frac{7}{6u}$$ for $u$. 2. **Identify the common denominator:** The denominators are $u$, $6$, and $6u$.

1. **State the problem:** Solve the equation $$\frac{5}{2w - 3} - \frac{7}{7w} = 1$$ for $w$. 2. **Identify the common denominator:** The denominators are $2w - 3$ and $7w$. The co

1. **State the problem:** We are given a rectangle where the length is three times the width, and the area is 147 cm². We need to find the perimeter. 2. **Define variables:** Let t