🧮 algebra

1. **State the problem:** We need to show that the coordinates of the point common to the curve $$y^2=4ax$$ and the line $$ty - x = at^2$$ are $$(at^2, 2at)$$. 2. **Write down the

1. نبدأ بتحديد المشكلة: لدينا متتالية $u_{m+1}$ ونريد حساب الحد العام للمتتالية $u_m$. 2. لفهم المتتالية، نحتاج إلى معرفة قاعدة التكرار أو العلاقة التي تربط بين الحدود المتتالية. ع

1. The problem states that the y value is 4. 2. Since no specific function or equation is given, we understand that y = 4 is a constant function.

1. **State the problem:** Simplify the expression $$\frac{y^{10}}{y^3} \times \frac{y^4}{y^2}$$. 2. **Recall the exponent rules:** When dividing powers with the same base, subtract

1. **State the problem:** We are given the function $y=2^{x^2-4}$ and want to understand its behavior. 2. **Formula and rules:** The function is an exponential function with base 2

1. The problem is to factor the quadratic expression $6x^2 + x + 12$. 2. The general form of a quadratic is $ax^2 + bx + c$. Here, $a=6$, $b=1$, and $c=12$.

1. The first problem is about the "Teskari funksiya" which means "Inverse function". 2. Problem: Find the inverse of a given function $f(x)$.

1. **State the problem:** We need to find the value of $a$ such that the line $3y = ax + 9$ is tangent to the curve $y^2 = 4x$. 2. **Rewrite the line equation:** Express $y$ in ter

1. **State the problem:** Find how many zeros are at the end of the number $5^4 \times 3^5 \times 4^5$. 2. **Recall the rule for trailing zeros:** The number of trailing zeros in a

1. **State the problem:** We need to find the value of $a$ such that the line $3y = ax + 9$ is tangent to the curve $y^2 = 49$. 2. **Rewrite the line equation:** Divide both sides

1. **Énoncé du problème :** Comparer $3\sqrt{5}$ et $4\sqrt{3}$. 2. **Formule et règles importantes :** Pour comparer deux nombres positifs sous forme $a\sqrt{b}$, on peut comparer

1. **State the problem:** Solve the quadratic equation $x^2 + 20x + 82 = 7$ by completing the square. 2. **Rewrite the equation:** Move the constant term on the left side to the ri

1. Diketahui vektor \(\vec{a} = \begin{pmatrix}2 \\ 1 \\ -1 \end{pmatrix}\), \(\vec{b} = \begin{pmatrix}3 \\ 3 \\ m \end{pmatrix}\), dan \(\vec{c} = \begin{pmatrix}1 \\ -2 \\ 4 \en

1. نبدأ ببيان المشكلة: لدينا كثيرة حدود $f(x)$ وباقي قسمة $f(x)$ على $(x-3)$ هو 4، وباقي قسمة $f(x)$ على $(x+2)$ هو 9. 2. نعلم من نظرية الباقي أن باقي قسمة كثيرة الحدود على قاسم من

1. Risolviamo la prima espressione: $ (x + x^2 - 1)(x - 1) - (x + 1)(1 + x^2 - x) + 4 - 2x^2 $. 2. Applichiamo la proprietà distributiva per espandere i prodotti:

1. **Problem Statement:** Find the equation of the straight line joining the points $(-5, 2)$ and $(3, -4)$. 2. **Formula Used:** The slope $m$ of a line passing through points $(x

1. **State the problem:** 5 men can dig 2 holes in 21 days. We want to find how many more men are needed to dig 6 holes in the same 21 days. 2. **Understand the relationship:** The

1. Bài toán yêu cầu phân tích các đa thức thành nhân tử. 2. Công thức sử dụng: \n\n- Hiệu hai bình phương: $$a^2 - b^2 = (a - b)(a + b)$$\n- Bình phương của một biểu thức: $$(a \pm

1. **State the problem:** A river cruise ship sails 80 miles downstream in 4 hours and returns upstream in 5 hours. We need to find the rate of the ship in still water ($s$) and th

1. **State the problem:** Antony spends parts of his net salary on various expenses and ends up with 15800. We need to find his original salary. 2. **Define variables:** Let Antony

1. نبدأ بكتابة المسألة: حل المعادلة أو التعبير المطلوب. 2. نحدد نوع المسألة: هل هي معادلة جبرية، معادلة خطية، أو غيرها.