🧮 algebra

1. مسئله: محاسبه محيط شکل داده شده به صورت جبری. 2. فرمول محيط برای شکل چهارضلعی: جمع طول تمام اضلاع.

1. **State the problem:** Solve the equation $$\frac{3^x}{81} = -27$$. 2. **Recall the properties:** The base 3 raised to any real power is always positive, so $$3^x > 0$$ for all

1. **State the problem:** Solve the quadratic equation $$2x^2 + x - 6 = 0$$ using factorisation. 2. **Rewrite the equation:** The equation is already in standard form $$ax^2 + bx +

1. समस्या: अरूणा ने 25 रु. में 8 केले खरीदे और 20 रु. में 6 केले बेचे। हमें प्रतिशत लाभ या हानि ज्ञात करनी है। 2. पहले, हम प्रति केले की क्रय मूल्य (CP) और विक्रय मूल्य (SP) निकाले

1. **Problem statement:** We have a trapezium with top base $x+7$, bottom base $2x+1$, height $x$, and area 42 cm². 2. **Formula for area of trapezium:**

1. نبدأ بقراءة المسألة: لدينا دالة د(س) = (س)س^2 + 12 حيث س \neq 0، ونعلم أن د(2) = 8. 2. نريد إيجاد قيمة د(2) بناءً على الدالة المعطاة.

1. **State the problem:** Solve for all possible values of $x$ in the equation $$\sqrt{48 - 6x} = x - 8.$$\n\n2. **Understand the domain:** The expression under the square root mus

1. نبدأ بذكر المسألة: لدينا الدالة ق(س) = س^2 + 12. 2. هذه دالة تربيعية حيث ق(س) = س^2 + 12.

1. **State the problem:** Solve for all possible values of $x$ in the equation $$\sqrt{6x + 40} = x + 8.$$\n\n2. **Recall the domain and formula:** The square root function $\sqrt{

1. **State the problem:** Solve for $y$ in the equation $$5 \times 10^{-4} \times \frac{\pi}{4} \times \cos\left(\frac{\pi y}{2 \times 4}\right) = \frac{\pi}{8} \times 5 \times 10^

1. **State the problem:** Simplify or analyze the quadratic expression $5t^2 - 7t - 124$. 2. **Formula and rules:** This is a quadratic expression of the form $at^2 + bt + c$ where

1. The problem is to multiply the fractions $\frac{4}{5}$, $\frac{9}{10}$, and $\frac{1}{5}$.\n\n2. The formula for multiplying fractions is to multiply the numerators together and

1. **State the problem:** We are given a $3 \times 3$ matrix:

1. Állítsuk fel a problémát: Meg kell vizsgálnunk, hogy a $k=-1$ érték egy szabály-e egy adott összefüggésben vagy képletben. 2. Fontos megérteni, hogy a $k$ változó értéke attól f

1. **State the problem:** Find the angle between the two lines given by their parametric equations: Line 1: $x = -2t - 9$, $y = 10t - 1$, $z = -2t - 9$

1. समस्या: एक व्यक्ति ने दो किस्म के सेब खरीदे, पहली किस्म 3 सेब 2 रु. में और दूसरी किस्म 1 रु. प्रति सेब की दर से। दोनों किस्म के सेब समान संख्या में खरीदे। सभी सेबों को 1 रु. प्र

1. **State the problem:** Express the given series in summation notation and find the general term. 2. **Identify the sequences:**

1. **State the problem:** Simplify the expression $$\frac{x^2 - xy + y^2}{x - y} - \frac{x^2 + xy + y^2}{x + y}$$. 2. **Recall the formula and rules:** We want to simplify each rat

1. The problem asks to analyze and sketch the graph of the function $$y = 21 (x - 3)^2 + 2$$ by translating, reflecting, compressing, and stretching the graph of the base function

1. **State the problem:** Simplify the expression $$\left(\frac{48}{2}\right) - \frac{17}{1} + 14^{-2} \times \frac{2}{1}$$. 2. **Recall the order of operations:** Perform division

1. **State the problem:** Simplify the expression $$\frac{3}{x^2 - 4} + \frac{1}{(x-2)^2}$$. 2. **Recall the formula and rules:** Recognize that $$x^2 - 4$$ is a difference of squa