🧮 algebra

1. **بيان المسألة:** لدينا العددين 4 و 3\sqrt{2} ونريد مقارنة هذين العددين ثم استنتاج إشارة العدد $$x = 7 / \sqrt{2 + 1}$$.

1. **Problem:** Find the equation of the line passing through points (-1,7) and (2,-6). 2. **Formula:** The slope $m$ of a line through points $(x_1,y_1)$ and $(x_2,y_2)$ is given

1. نبدأ بحصر الأعداد المعطاة حيث $7 \leq x \leq 5$ و $8 \leq y \leq -4$. لاحظ أن هذا غير ممكن لأن $7 \leq x \leq 5$ تعني أن $x$ يجب أن يكون أكبر أو يساوي 7 وأصغر أو يساوي 5 في نفس

1. The user requests solutions for matched problems 1, 2, 3, 6, 7, 8, 9, 10 and interval notations from page 26 table #1. 2. According to the GUEST RULE, only the first distinct pr

1. **State the problem:** Mr. Adu takes 10 days less than Mr. Kubi to build an article. Together, they take 12 days to build it. We need to find how long each takes alone.

1. Պատմենք խնդիրը. Տրված են 4 տարբերական պրոգրեսիայի բանաձևեր $a_n$-ի համար, և անհրաժեշտ է գտնել երկրորդ անդամի երկրորդ համարը, այսինքն՝ $a_2$-ի արժեքը, երբ $n=2$։ 2. Հաշվենք յուրա

1. **State the problem:** Find the truth set of the equation $m(m+2)=3$. 2. **Write the equation:**

1. The problem is to incorporate the given expression or concept into a math problem. Since the user did not specify the exact expression, let's assume we are asked to incorporate

1. نبدأ ببيان المسألة: حل المعادلة $2n^2 + 5n + 3 \geq 0$ في مجموعة الأعداد الحقيقية $\mathbb{R}$. 2. المعادلة هي متباينة من الدرجة الثانية على المتغير $n$.

1. نبدأ بحل السؤال الأول من المسيري الأول: \n\nالمطلوب: \n\n\textbf{عين العدد} $\lambda$ \textbf{حتى يكون} $n - 2$ \textbf{جذر لكثير الحدود} $P(nx)$ حيث \n$$P(nx) = 2 n_x^3 + 5 n_x

1. **State the problem:** We are given the function $f(x) = 2x - 6$ and asked to find the slope (rate of change) of this function. 2. **Recall the formula:** For a linear function

1. **Problem statement:** Find the equation of a parabola with roots at $-2$ and $4$, and determine its domain and range. 2. **Formula and explanation:** The general form of a para

1. **Problem:** Rationalize the denominator and simplify $$\frac{2\sqrt{3}}{\sqrt{2}-2\sqrt{5}}$$. 2. **Formula and rule:** To rationalize a denominator with a binomial containing

1. **Problem statement:** A building measures 80 m by 50 m, and a paved road of uniform width surrounds it. The area of the paved road alone is 7850 m². We need to find the width o

1. **State the problem:** Simplify the expression $$\left(\frac{v}{9}\right)^2$$. 2. **Formula used:** When squaring a fraction, use the rule $$\left(\frac{a}{b}\right)^2 = \frac{a

1. The user asked for "some formula," which is a broad request. 2. A common and fundamental formula in algebra is the quadratic formula, used to solve quadratic equations of the fo

1. The problem is to solve the equation $$\frac{7-1}{5} = ?$$ 2. First, simplify the numerator: $$7 - 1 = 6$$

1. **Problem:** Find the constant of variation if $y$ varies directly as $x$ and $y=35$ when $x=5$. Write the direct variation equation. 2. **Formula:** For direct variation, $y=kx

1. The problem is to understand the meaning or use of the variable $T=30$. 2. Typically, $T$ can represent time, temperature, period, or other quantities depending on context.

1. **Problem Statement:** Calculate the hours of time taken by the workman to complete the work order given the Rowan Plan bonus system.

1. **State the problem:** Find the slope of the line given by the equation $3y - 2x = 4$. 2. **Rewrite the equation in slope-intercept form:** The slope-intercept form is $y = mx +