🧮 algebra

1. Problem: Find the slope of the line passing through points $K(-2,-6)$ and $L(4,-3)$. 2. Formula: The slope $m$ of a line through points $(x_1,y_1)$ and $(x_2,y_2)$ is given by

1. Problem: Given a linear function $f(x)$ with $f(1) = -3$ and $f(-2) = 4$, find $f(10)$. 2. Since $f(x)$ is linear, it can be written as $f(x) = mx + b$, where $m$ is the slope a

1. Problem: Verilen fonksiyon $f(x) = |2x - 4| + 1$ gerçek sayılar kümesinde tanımlıdır. Bu fonksiyonun parçalı fonksiyon olarak gösterimini bulmamız isteniyor. 2. Mutlak değer fon

1. **Problem statement:** We want to find the optimal ticket price to maximize total revenue and total profit based on attendance changes. 2. **Given data:**

1. Problem: Find the functions given. 2. For each function, we simply write them as given:

1. The problem asks to identify which relation is a function. 2. Recall that a function assigns exactly one output $y$ for each input $x$.

1. نبدأ بكتابة المعطيات: المعادلة القطع الناقص هي $$9x^2 + ky^2 = 9k^2$$. 2. نعلم أن إحدى بؤرتي القطع الناقص هي بؤرة القطع المكافئ المعطى بمعادلته $$\frac{1}{4}y^2 - 4x = 0$$.

1. نبدأ ببيان المشكلة: لدينا طائرة بها 72 راكبًا، ونسبة الذكور إلى الإناث هي 5:3. 2. نستخدم قاعدة النسبة: إذا كانت نسبة الذكور إلى الإناث هي 5:3، فهذا يعني أن لكل 5 ذكور هناك 3 إنا

1. نبدأ بقراءة السؤال: عمر محمد هو 3 أضعاف عمر سعيد. المطلوب هو إيجاد عمر محمد. 2. نفرض أن عمر سعيد هو $x$ سنة.

1. **Problem statement:** Given two functions $f(x) = x^2$ and $g(x) = 2x + 1$, find the following combined functions: $(f+g)(x)$, $(f-g)(x)$, $(fg)(x)$, and $\frac{f}{g}(x)$. 2. *

1. **Problem Statement:** Given two functions $f(x) = x^2$ and $g(x) = 2x + 1$, find the combined functions $(f+g)(x)$, $(f-g)(x)$, $(fg)(x)$, and $\frac{f}{g}(x)$. 2. **Formulas a

1. The problem asks to find the patterns for each item, but no specific items or sequences are provided. 2. To find a pattern, we typically look for a rule or formula that describe

1. **State the problem:** We need to find the sum of the fractions $\frac{1}{628} + \frac{1}{763} + \frac{1}{1469}$.\n\n2. **Formula and approach:** To add fractions, we find a com

1. **Énoncé du problème :** On considère le polynôme $R(x) = x^3 - 5x^2 + 8x - 4$.

1. **State the problem:** Solve the quadratic equation $4x^2 - 5x - 12 = 0$. 2. **Formula used:** The quadratic formula is given by

1. **Problem Statement:** Find the multiplicative inverse $z^{-1}$ of the complex number $z = \sqrt{3} + i \sqrt{7}$ and prove that $zz^{-1} = 1$. 2. **Formula and Rules:** The mul

1. **State the problem:** Solve the equation $$|3x + 2| + |3x - 2| = 5$$ for $x$. 2. **Understand the absolute value:** The absolute value function $|a|$ equals $a$ if $a \geq 0$ a

1. **State the problem:** Find the coefficient of $x^{12}y^{13}$ in the expansion of $(x+y)^{25}$. 2. **Formula used:** The binomial theorem states that

1. **State the problem:** A student has marks in five subjects: English 73, Urdu 82, Maths 80, History 67, and Science 62. The weights for these subjects are 4, 3, 3, 2, and 2 resp

1. **State the problem:** We are given a principal amount $P = 25000$, interest earned $I = 5000$, and time $T = 4$ years. We need to find the rate of interest $R$. 2. **Formula us

1. مسئله: بررسی و مقایسه نامساوی‌ها و تساوی‌های داده شده شامل لگاریتم‌ها و توانی‌ها است. 2. ابتدا تعاریف و قواعد مهم را مرور می‌کنیم: