🧮 algebra

1. **State the problem:** Solve the system of equations and understand their graph shapes: $$x - y + 2 = 0$$

1. **State the problem:** A photograph measures 11 inches wide and 14 inches long. It is enlarged so that the new width is 231 inches. We need to find the new length. 2. **Formula

1. Le problème semble concerner la définition de l'expression $0^0$ et la comparaison avec d'autres expressions comme $0^{1-1}$ ou $\frac{0^1}{0^1}$. 2. En mathématiques, $0^0$ est

1. Énonçons le problème : Pourquoi $0^0 = 1$ alors que $\frac{0}{0}$ n'a pas de valeur définie ? 2. Rappelons que $0^0$ est une forme indéterminée en analyse, mais en algèbre et co

1. **State the problem:** Simplify the expression $$\frac{\frac{(x - 2)^2}{2(x^2 - 5x + 4)}}{\frac{x^2 - 4}{4x - 10}}$$. 2. **Rewrite the complex fraction:** Dividing by a fraction

1. Planteamos el problema: Dado que $\log_{\sqrt[4]{3}} \sqrt[3]{2} = x$, hallar el valor de $$\frac{\log 32}{\log 9}$$. 2. Recordemos que el cambio de base para logaritmos es $$\l

1. **State the problem:** Solve the linear equation $8x + 6 = 22$ for $x$. 2. **Formula and rules:** To solve for $x$, isolate $x$ on one side by performing inverse operations. Rem

1. **State the problem:** We need to find the gradient (slope) of the linear equation $8x + 6 = 22$ and represent it in slope-intercept form. 2. **Rewrite the equation:** Start by

1. The problem is to find the gradient of a function or a line. 2. The gradient (or slope) of a line is given by the formula:

1. **State the problem:** Solve the linear equation $8x + 6 = 22$ for $x$. 2. **Formula and rules:** To solve a linear equation, isolate the variable $x$ by performing inverse oper

1. **Problem Statement:** We are given two relations:

1. **State the problem:** Calculate the value of the expression $$\frac{328-(120+98)}{22}$$. 2. **Apply the order of operations:** First, solve the expression inside the parenthese

1. **Problem:** Find the domain and range of the function $y = x + 4$. 2. **Formula and rules:** For linear functions $y = mx + b$, the domain is all real numbers because $x$ can b

1. The problem is to analyze and understand the given functions: 2. The functions are:

1. The problem asks to find the domain and range of the numbers. 2. The domain of a function or set of numbers is the set of all possible input values (x-values) for which the func

1. The problem is to evaluate the expression $\sqrt[]{}$, which is an incomplete square root notation. 2. The square root symbol $\sqrt{}$ requires a number or expression inside th

1. The problem states that the relationship between $y$ and $x$ is given by the formula $$y = \frac{k}{x^2}$$ where $k$ is a constant. 2. We are given that when $y = 8$, the equati

1. The problem is to find the minimum value of the parabola shown in the graph. 2. The parabola is U-shaped and opens upward, which means it has a minimum point at its vertex.

1. **State the problem:** We are given a parabola opening upward with vertex at about $(0, -2)$ and x-intercepts at about $(-2, 0)$ and $(2, 0)$. We need to find the minimum value

1. El problema nos pide encontrar cuántas sillas debe vender la empresa para maximizar sus ingresos dados por la función $$R(x) = 50x - 0.5x^2$$ donde $x$ es el número de sillas ve

1. The problem is to analyze the function $y=|x|$. 2. The absolute value function $|x|$ is defined as: