🧮 algebra

1. مسئله را بیان می‌کنیم: (ب) مقدار ماکزیمم یا مینیمم تابع $$f(x) = -(x + 1)^2 - 3$$ را پیدا کنید.

1. The problem is to find the value of $a - b + c$ given a parabola with vertex at $(-1, -4)$ and equation $f(x) = ax^2 + bx + c$. 2. The vertex formula for a parabola is $x_0 = -\

1. Muammo: Parabolaning uchi $(-1; -4)$ nuqtada joylashgan va $f(x) = ax^2 + bx + c$ tenglama berilgan. $a - b + c$ ni toping. 2. Parabolaning uchi koordinatalari $x_0 = -\frac{b}{

1. Muammo: Parabolani $y = 3x^2 + 2x - 7$ dan $b(-3;4)$ vektor bo'yicha parallel ko'chirish natijasida hosil bo'lgan parabolaning tenglamasini toping. 2. Parallel ko'chirishda yang

1. **State the problem:** Solve the exponential equation $$2^{2x+1} = 3^{x+1}$$. 2. **Recall the properties of exponents:** For any base $a > 0$, $a^{m+n} = a^m \cdot a^n$ and if $

1. **State the problem:** Solve the equation $$2x + \frac{1 - x}{4} = 3$$ and fully reduce the answer. 2. **Identify the formula and rules:** To solve linear equations with fractio

1. **State the problem:** Solve the equation $$5x - (12 + x) = -13$$ and simplify the answer fully. 2. **Apply the distributive property:** Remove the parentheses by distributing t

1. **Problem Statement:** We have a sequence of shapes with a number of tiles depending on $n$. The given values are $n=4, 8, 7, 5$ with corresponding tile counts $4, 8, 7, 5$. We

1. **State the problem:** We have a pattern of L-shaped figures made of tiles for values $n=1, 2, 3$. We want to find the number of tiles when $n=4$ and express the number of tiles

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.