🧮 algebra

1. State the problem: Simplify and expand the expression $$(5m - 1)(x^{2}) - (5m + 2)x + 3m$$. 2. Expand the first term: $$(5m - 1)(x^{2}) = 5m x^{2} - x^{2} = (5m - 1)x^{2}$$.

1. Problem statement: Given the sequence $-8, x, y, 19$ in an arithmetic progression, find $x$ and $y$. 2. In an arithmetic progression, consecutive terms differ by a common differ

1. Stating the problem: We need to plot the graph of the simultaneous linear equations: $$y - 2x = 5$$

1. ننص على المشكلة: مقارنة وتعريف التعبيرات الجبرية المختلفة المُعطاة مثل A، B، C، D لحل المعادلات أو تبسيطها وتحليل العلاقة بينها. 2. تحليل تعبيرات A و B و C و D:

1. **Problem:** Given \(f(x) = x^3 - px^2 + qx + 1\), with \(f(3) = -5\) and \(f(-2) = 5\), find \(p\) and \(q\). 2. Substitute \(x=3\):

1. Stating the problem: We have an arithmetic progression sequence $8, x, y, 19$ and need to find $x$ and $y$. 2. Recall that in an arithmetic progression, the difference between c

1. المشكلة: لدينا جملة معادلتين ونريد إيجاد الحلول التي تحقق كلا المعادلتين معًا. 2. الطريقة المستعملة هي طريقة التعويض أو الجمع أو الحذف لحل نظام المعادلات.

1. The problem is to plot a graph for a system of simultaneous equations with specified axis ranges. 2. However, no explicit equations were given in the prompt to plot.

1. Stating the problem: Plot the graph of the system of linear simultaneous equations: $$y-2x=5$$

1. نعتبر الدالة $$f(x) = \frac{2x+5}{x+2}$$ المعرفة على $$\mathbb{R} \setminus \{-2\}$$. 2. نريد إيجاد العددين $$a$$ و$$s$$ بحيث تحقق المعادلة:

1. The problem is to simplify the expression $2\frac{1}{2} + \frac{1}{2} - 3\frac{1}{5} \times \frac{2}{4} \div 2\frac{4}{5}$.\n\n2. First, convert mixed numbers to improper fracti

1. The problem states that the numbers 11, p, q, and 21/1/2 (which is 21.5) form an arithmetic progression (AP). 2. In an arithmetic progression, the difference between consecutive

1. **State the problem:** We need to plot the graph of the system of linear equations: $$y - 2x = 5$$

1. Problem 17: Find $k$ if $k+7$, $2k-2$, and $2k+6$ are three consecutive terms of an AP. Step 1: In an arithmetic progression (AP), the difference between consecutive terms is co

1. **Problem:** If the zeroes of the quadratic polynomial $ax^2 + bx + \frac{2a}{b}$ are reciprocal of each other, find the value of $b$. Step 1: Let the roots be $\alpha$ and $\be

1. Problem: Two cars A and B take 30 minutes and $p$ minutes respectively to complete 1 round. They meet first time after 90 minutes at the starting point.

1. **State the problem:** Solve the system of linear equations: $$x+y+z=5$$

1. We are given the system of equations representing two circles: $$ (x-10)^2 + (y-5)^2 = 25 $$

1. **نص المشكلة:** لدينا عددان \( a = \frac{\sqrt{5} + \sqrt{3}}{\sqrt{5}} \) و \( b = \frac{\sqrt{5} - \sqrt{3}}{\sqrt{5}} \). المطلوب هو كتابة كل منهما على شكل نسبة مقاماها عدد ن

1. نبدأ بتوضيح قيم $a$ و $b$: $$a = \frac{\sqrt{5} - 1}{\sqrt{5}}, \quad b = \frac{\sqrt{5} - 1}{\sqrt{5}}$$

1. **State the problem:** We are given the system of equations: $$2x + y + z = 6$$