🧮 algebra

1. **State the problem:** Solve for the unknown in the equation $$2 \frac{2}{5} \times [\ ] = \frac{2}{5}$$. 2. **Convert the mixed number to an improper fraction:**

1. **State the problem:** Simplify the expression $3x^2 + x^2$. 2. **Formula and rules:** When adding like terms, add their coefficients and keep the variable part unchanged.

1. Muammo: Soddalashtiring: $$\sqrt{5} - 2\sqrt{6} - \sqrt{5} + 2\sqrt{6}$$ 2. Formulalar va qoidalar: Radikallarni qo'shish va ayirishda faqat ildiz ostidagi sonlar teng bo'lsa, u

1. **Problem:** Simplify the expression $$\sqrt{5} - 2\sqrt{6} - \sqrt{5} + 2\sqrt{6}$$. 2. **Formula and rules:** When simplifying expressions with square roots, combine like term

1. **Stating the problem:** We are given a geometric sequence starting with terms 5, 5/2, 10, 20, ... and asked to find the next term. 2. **Understanding geometric sequences:** A g

1. **State the problem:** Solve the equation $3x + x + x + x - 3 - 3 = 7 + x + x$ for $x$. 2. **Combine like terms:** On the left side, combine the $x$ terms: $3x + x + x + x = 6x$

1. نبدأ بكتابة المسألة: ضع إشارة < أو > أو = في ● لتكون كل جملة صحيحة. 2. نحلل كل جملة على حدة:

1. **Énoncé du problème :** Factoriser les expressions suivantes : $$A = n^{12} - 2n^6 + 1$$

1. Soal: Tentukan himpunan penyelesaian dari persamaan $2x + 3y = 6$. 2. Gunakan rumus persamaan garis lurus $Ax + By = C$.

1. Masalah: Morgan ingin membuat topi (A) dan terompet (B) dengan anggaran 1000. Biaya topi Rp 25 per unit dan terompet Rp 50 per unit.

1. The problem is to perform math operations as if writing on homework paper. 2. Since no specific math problem is given, I will demonstrate a simple algebraic example: Solve for $

1. نبدأ بكتابة التعبير المطلوب تبسيطه: $$\frac{3}{\sqrt{3}-2}$$

1. **Problem:** Find the slope of the function $P = 12 - Q$ at all values of $Q$. 2. **Formula:** The slope of a function is given by its derivative with respect to the independent

1. مسئله: تعداد ارقام عدد حاصل از ضرب $$40^{18} \times 250^{10}$$ را بیابید. 2. برای یافتن تعداد ارقام یک عدد مثبت $N$، از رابطه استفاده می‌کنیم:

1. **Problem statement:** (a) Chamod's annual income from properties is 200000 rupees. He earns 60000 rupees per month from his job.

1. **Problem statement:** We have the sequence defined by $$u_n = \frac{1}{n+1} + \frac{1}{n+2} + \cdots + \frac{1}{2n}$$ for all $n \geq 1$. We want to show that $$\frac{1}{2} \le

1. **State the problem:** Find the vertex of the quadratic function $g(x) = x^2 - 4x + 7$ and determine its properties. 2. **Formula and rules:** For a quadratic function $ax^2 + b

1. **State the problem:** We are given the function $g(x) = x^2 - 4x + 7$ and want to analyze its properties, including finding the vertex and understanding the shape of its graph.

1. The problem involves understanding the equations $x = y + z$ and $f(x) = a^2 + b^2 = c^2$. 2. The first equation $x = y + z$ is a simple linear relation where $x$ is the sum of

1. **State the problem:** We need to find the cost of one iPhone given the total costs of purchases made by James and Peter. 2. **Define variables:** Let $x$ be the cost of one iPh

1. **State the problem:** Solve the equation $9j + 3 = 3(3j + 1)$. 2. **Write the formula and rules:** Use the distributive property to expand the right side: $a(b + c) = ab + ac$.