🧮 algebra

1. **State the problem:** Solve the inequality $x^2 - 5x + 6 < 0$. 2. **Recall the formula:** This is a quadratic inequality. We first find the roots of the quadratic equation $x^2

1. **State the problem:** Simplify the expression $10 - (4 + 2) \times 2$. 2. **Recall the order of operations:** Parentheses first, then multiplication, and finally subtraction.

1. **State the problem:** Solve the equation $2-\frac{1}{2}n=3n+16$ for $n$. 2. **Write down the equation:**

1. **State the problem:** Solve the equation $9e+4 = -5e+14 + 13e$ for $e$. 2. **Rewrite the equation:** The equation is $9e + 4 = -5e + 14 + 13e$.

1. **بيان المسألة:** لدينا الدالة $$f(x) = x \sqrt{x^2 - 1}$$ ونريد دراسة سلوكها على المجال $$I = [1, +\infty[\,$$ ومقارنتها مع الخط المستقيم $$y = x$$. 2. **فهم الدالة:** الدالة ت

1. **بيان المسألة:** حل المعادلة في مجموعة الأعداد الحقيقية IR:

1. **بيان المسألة:** لدينا الدالة $$f(x) = x \sqrt{x^2 - 1}$$ ونريد دراسة خصائصها ضمن المجال $$I = ]-\infty, +1]$$. 2. **تحديد المجال:** الجذر التربيعي يتطلب أن يكون التعبير داخل ا

1. Let's start by stating the problem: We want to understand why a given equation represents a hyperbola. 2. The general form of a hyperbola centered at the origin is given by the

1. **Problem Statement:** Given the conic section equation $$9x^2 - 4y^2 + 18x - 8y + 6 = 0,$$ we need to:

1. Das Problem lautet: Finde die kubische Funktion $f(x) = ax^3 + bx^2 + cx + d$, die durch den Ursprung geht, bei $x=4$ ein Minimum hat mit Funktionswert $-80/3$ und bei $x=-2$ ei

1. **State the problem:** Solve the quadratic equation $x^2 + 6x - 5 = 0$ for $x$. 2. **Formula used:** The quadratic formula is used to solve equations of the form $ax^2 + bx + c

1. The problem states that $x$, 17, $3x - y^2 - 2$, and $3x + y^2 - 30$ are four consecutive terms of an increasing arithmetic sequence. 2. In an arithmetic sequence, the differenc

1. **State the problem:** We need to find the value of $h$ such that $$4^8 \times 8^{12} = 2^h.$$\n\n2. **Rewrite the bases as powers of 2:**\n- $4 = 2^2$\n- $8 = 2^3$\n\n3. **Subs

1. **بيان المسألة:** لدينا متتالية حسابية $(U_n)$ حيث الحد الأول $U_0$ والأساس $r$. المعطيات: $$U_2 - U_0 = 4$$

1. **Problem Statement:** Determine the slope and intercepts of the linear equation $3x + 2y = 12$ using substitution. 2. **Formula and Rules:**

1. The problem is to graph the function $f(x) = \sqrt{x + 4}$ and plot four points on it, including the leftmost point. 2. The function $f(x) = \sqrt{x + 4}$ is defined for $x + 4

1. مسئله: محاسبه مقدار عبارت $(-1)^3 \times 1^6$ است. 2. قانون توان: هر عددی به توان 1 برابر خود عدد است و توان‌های دیگر با ضرب‌های متوالی تعریف می‌شوند.

1. مسئله: مقدار عبارت $$\sqrt[7]{\sqrt{13} + \sqrt{5}} \times \sqrt[7]{18 - 7 \sqrt{5}}$$ را بیابید. 2. قانون استفاده شده: ضرب دو رادیکال با ریشه هفتم برابر است با رادیکال هفتم حاص

1. **Problem Statement:** We are given the quadratic function $$y = -2x^2 + 2x + 24$$ defined for $$-4 \leq x \leq 4$$.

1. **Problem:** Calculate $5 \times 7 \times 2$ using the Commutative or Associative Property. 2. **Formula and Properties:**

1. **State the problem:** We need to find the value of $t$ given the formula $t = k(4k + n)$ with $k = -2$ and $n = 13$. 2. **Write the formula:**