🧮 algebra

1️⃣ Factoring helps us find where a graph crosses the $x$-axis. 🌈 2️⃣ Imagine the equation $y = x^2 - 5x + 6$. We want to find where $y=0$.

1. **بیان مسئله:** عبارت درجه دوم $x^2 + 5x + 9$ را تجزیه کنید. 2. **فرمول تجزیه:** برای یک چندجمله‌ای درجه دوم به شکل $ax^2 + bx + c$، به دنبال دو عدد هستیم که حاصل‌ضربشان $ac$ و

1. **State the problem:** Factor the quadratic expression $x^2 + 5x + 9$. 2. **Recall the factoring formula:** For a quadratic $ax^2 + bx + c$, we look for two numbers that multipl

1. **State the problem:** Simplify the expression $$-5^2 + (-5)^2$$. 2. **Recall the order of operations and exponent rules:**

1. **Stating the problem:** Fathi has 1.10 in his printing account. Each sheet of paper costs 0.25. He wants to print a 47-page PDF. He prints on both sides and 2 pages per side.

1. 問題陳述： 假設一個長方形的兩邊分別落在 x 軸和 y 軸上，另一頂點落在直線 $$2x + y = 12$$ 上，求此長方形的最大面積。

1. **Stating the problem:** We are given the system of linear equations:

1. **Problem:** Given that $$\sum_{r=1}^k r^3 = \frac{k^2 (k+1)^2}{4}$$ and $$k$$ is a positive integer, find $$\sum_{r=3}^k (r-1)(r^2 + r + 1)$$ in terms of $$k$$. 2. **Step 1: Si

1. **Problem statement:** Solve the equation $$(x - 2)(x - 3) = 20$$ for $x$. 2. **Formula and rules:** To solve this, first expand the left side using the distributive property (F

1. **State the problem:** Solve the equation $-7(8b-2)=32+3b$ for $b$. 2. **Apply the distributive property:** Multiply $-7$ by each term inside the parentheses:

1. **State the problem:** We are given the system of equations: $$ (x-1)^2 + y^2 = 2 $$

1. The problem is to understand the concepts of GCD (Greatest Common Divisor) and LCM (Least Common Multiple) of two numbers. 2. The GCD of two integers is the largest positive int

1. The problem is to find the value of an expression or function when $X=200$ and $Y=10$. 2. Since the original expression or function is not provided, let's assume a general form

1. **Problem Statement:** We want to determine which XP formula is more effective for reaching level 40. The formulas calculate total XP needed based on base XP per level $X$ and a

1. The problem asks to find the time it will take Sara to drive the remaining distance, given two fractions: $\frac{4}{5}$ and $\frac{4}{3}$. 2. We interpret these fractions as par

1. **Stating the problem:** We need to find the total hours $h$ required to fill a swimming pool. 2. **Understanding the rates:** The problem gives two rates: one filling rate is $

1. المشكلة: فهم كيفية تبسيط التعبيرات الجبرية. 2. القاعدة الأساسية: لتبسيط تعبير جبري، نبحث عن عوامل مشتركة بين الحدود ونستخدم قوانين الجمع والطرح والضرب والقسمة.

1. **Problem statement:** Calculate the value of $\left(\frac{1}{\sqrt{2}} - 1\right)^{-1}$. 2. **Formula and rules:** The expression is a reciprocal (inverse) of $\frac{1}{\sqrt{2

1. **State the problem:** Graph the function $$f(x) = \frac{2x^4 - x^2 + 1}{x^2 - 4}$$ and analyze its key features.

1. **Stating the problem:** Given that $y \propto x$ and $Y \propto \frac{1}{z}$, find the proportionality relation for $y$ in terms of $x$ and $z$. 2. **Recall the meaning of prop

1. **State the problem:** Solve the system of simultaneous equations: $$x^2 = 4 - y$$