🧮 algebra

1. The problem involves completing a multiplication table with missing values A, B, C, D, E given some known values and variables a, b, c, d, e. 2. The multiplication table is stru

1. Stwierdźmy problem: Rozwiąż nierówność $$\left| \frac{x^{2} - 5x + 4}{x^{2} - 4} \right| \geq 1$$. 2. Przypomnijmy, że dla dowolnej liczby rzeczywistej $a$ zachodzi $|a| \geq 1$

1. **Simplify \(\sqrt{125}\):** \(\sqrt{125} = \sqrt{25 \times 5} = \sqrt{25} \times \sqrt{5} = 5\sqrt{5}\).

1. **Problem:** Simplify the expression $5^{1/3} \times 5^{2/3}$. 2. **Formula:** When multiplying powers with the same base, add the exponents:

1. The problem is to simplify the expression $$(A + \beta + C) i \overline{\beta}$$ where $A$, $\beta$, and $C$ are variables, $i$ is the imaginary unit, and $\overline{\beta}$ is

1. Énonçons le problème : on doit développer et simplifier la fonction $f(x) = (-1 + 2x)^2 - (3 - 6x)(1 - x)$.\n\n2. Rappel des formules importantes :\n- Le carré d'une somme ou di

1. **State the problem:** Simplify the expression $$\frac{7^8 \times 7^3 \times 7^4}{7^9 \times 7^5}$$. 2. **Recall the exponent rules:** When multiplying powers with the same base

1. **بيان المسألة:** معطى نقطتان على خط مستقيم هما $(1-4,1-3)$ والمعادلة $ص - 3 س = 1 - س = 4$، والمطلوب إيجاد مجموعة قيم $ص$ الممكنة.

1. Simplify the expression $a^2 (2a^{-1})^2$. Step 1: Write the expression clearly:

1. The problem asks to find the equation of the axis of symmetry of the parabola given by the equation $$y = x^2 - 6$$. 2. Recall that for a parabola in the form $$y = ax^2 + bx +

1. The problem is to find the coordinates of the vertex of the parabola given by the equation $$y = x^2 + 14x + 50$$. 2. The vertex of a parabola in the form $$y = ax^2 + bx + c$$

1. The problem is to find the value, but the exact expression or equation is not provided. 2. To solve for a value, we need a specific equation or expression.

1. The problem is to solve the equation $2x + 3 = 7$ for $x$. 2. We use the basic algebraic principle of isolating the variable $x$ by performing inverse operations.

1. **State the problem:** Find the y-intercept of the equation $4y=12x$. 2. **Rewrite the equation in slope-intercept form:** The slope-intercept form is $y=mx+b$, where $b$ is the

1. **State the problem:** Solve the equation $4y = 12x$ for $y$. 2. **Formula and rules:** To isolate $y$, divide both sides of the equation by 4.

1. The problem is to understand the Singapore MOE method for solving linear systems (LS) clearly. 2. The Singapore MOE method often uses a step-by-step approach to solve linear equ

1. **State the problem:** We need to find how many ice cream sticks Peter, Paul, and Gernard each have given these conditions: - Peter and Paul together have 115 sticks.

1. Énonçons le problème : Trouver la valeur de $f(0,14)$ où $f(x) = \arctan\left(\frac{\sqrt{3} x^3 + \sqrt{3}}{x^3 - 1}\right)$.\n\n2. La fonction $\arctan$ est la fonction arc ta

1. **Problem Statement:** We need to sketch the graphs of the inequalities:

1. **Problem a:** Solve $3(y + 1)^2 - 5 = 43$. 2. **Rewrite the equation:** Add 5 to both sides:

1. **State the problem:** Solve the inequalities: