🧮 algebra

1. **State the problem:** Solve the equation $$7x - 4 - 6x - 14 = 30$$. 2. **Combine like terms:** Group the terms with $x$ and the constants.

1. **Statement of the problem:** We have the function $$f(x) = \frac{1}{6}x^3 - x^2$$ defined on $$\mathbb{R}$$.

1. **State the problem:** Solve the equation $$(3x - 1)^2 - (5x - 3)^2 = (4x - 2)^2$$ for $x$. 2. **Recall the formula:** This is a difference of squares on the left side: $$a^2 -

1. **Nyatakan masalah:** Kita diberikan persamaan beda linear homogen orde dua: $$y(k+2) - 8y(k+1) + 16y(k) = 0$$

1. **State the problem:** Solve for $x$ in the equation $$\frac{3x - 3}{5} = \frac{2x - 2}{4}$$ using cross multiplication. 2. **Formula and rule:** Cross multiplication means mult

1. **Énoncé du problème** : On considère la fonction $f$ définie par $f(x) = 0,05(x - 12)(x + 18)$ avec $\mathrm{dom}\,f = \mathbb{R}$. Il faut déterminer quelle affirmation parmi

1. The problem is to simplify the expression $$\frac{2x^2 - 8}{4x}$$. 2. The formula used here is to simplify fractions by factoring and canceling common factors.

1. The problem asks for the two double inequalities that define the shaded rectangular region bounded by vertical lines at $x=-3$ (dashed) and $x=2$ (solid), and horizontal lines a

1. **State the problem:** Simplify the fraction $\frac{25}{64}$. 2. **Formula and rules:** To simplify a fraction, divide the numerator and denominator by their greatest common div

1. **Planteamiento del problema:** Tenemos un terreno rectangular de área total 8712 m² que debe dividirse en 3 parcelas iguales, cada una con área $\frac{8712}{3} = 2904$ m². 2. *

1. **State the problem:** Solve the expression $5 - 2y$ for a given value of $y$ or simplify it as is. 2. **Understand the expression:** The expression $5 - 2y$ is a linear express

1. **Problem:** Understand where the function $f(x) = -x^2 + 6x - 5$ is increasing and decreasing (part c), and where $f(x)$ is positive or negative (part d). 2. **Recall vertex:**

1. **Problem statement:** We are given the quadratic function $$f(x) = -x^2 + 6x - 5$$ and need to analyze its graph and properties. 2. **Concavity:** The coefficient of $$x^2$$ is

1. The problem is to graph the function $g(x) = \frac{1}{4}x$. 2. This is a linear function of the form $y = mx + b$, where $m$ is the slope and $b$ is the y-intercept.

1. Vamos resolver um problema de álgebra envolvendo a simplificação da expressão $$\frac{2x^2 - 8}{4x}$$. 2. A fórmula que usamos para simplificar frações algébricas é dividir o nu

1. **Problem Statement:** Understand the basics of complex numbers, their properties, and simple examples suitable for 11th standard students. 2. **Definition:** A complex number i

1. **Problemstellung:** Gegeben ist ein parabelförmiger Brückenbogen mit der Spannweite 200 m, beschrieben durch die Funktion $$f(x) = ax^2 + c$$ mit $a,c \in \mathbb{R}^*$. Der Ur

1. Soal menanyakan interval nilai $m$ agar garis $y = mx + 2$ memotong grafik fungsi $f(x) = x^2 - 2x + 6$ di dua titik berbeda dengan absis positif. 2. Titik potong diperoleh deng

1. **State the problem:** Solve the system of equations: $$\sqrt{x} + 5z = 18$$

1. The problem is not explicitly stated, so I will assume you want a general example of solving a linear equation with solution steps. 2. Let's solve the equation: $$3x + 5 = 20$$

1. Solve for $x$: $$2x + 3 = 7$$ 2. Factor the quadratic expression: $$x^2 - 5x + 6$$