🧮 algebra

1. The problem is to analyze the inequality $6 < 2x - 3y$. 2. This inequality involves two variables, $x$ and $y$, and represents a region in the coordinate plane.

1. **State the problem:** Find 12.5% of 480. 2. **Formula:** To find a percentage of a number, use the formula:

1. **State the problem:** Simplify the expression $ (x+y)(x-y) $. 2. **Formula used:** This is a product of conjugates, which follows the identity:

1. **State the problem:** Find 25% of 240. 2. **Formula used:** To find a percentage of a number, use the formula:

1. **State the problem:** Solve the quadratic equation $2x^2 - 12x - 16 = 0$. 2. **Formula and rules:** The quadratic formula to solve $ax^2 + bx + c = 0$ is:

1. **Problem statement:** Find the values of $x$ and $y$ given:

1. **Problem Statement:** We have petrochemical export data for years 2010 to 2014 with values 17, 18, 20, 22, and 23.5 billion respectively. We use two models:

1. Nyatakan masalah: Cari nilai $x$ yang memenuhi persamaan kuadratik $2x^2 - 4x - 6 = 0$. 2. Gunakan formula kuadratik: $$x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}$$ di mana $a=2$, $

1. The problem states a sequence defined by the recurrence relation $$a_n = 2a_{n-1} + 1$$ with the initial term $$a_1 = 1$$. We need to find the 5th term, $$a_5$$. 2. The recurren

1. **State the problem:** We have two matrices $$P=\begin{pmatrix} x^{2} & 3 \\ 1 & 3x \end{pmatrix}$$

1. **State the problem:** Solve the quadratic equation $x^2 + 6x + 4 = 0$. 2. **Formula used:** The quadratic formula is given by $$x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}$$ where $

1. **State the problem:** Solve for $x$ in the equation $3x^2 = 75$. 2. **Formula and rules:** To solve quadratic equations of the form $ax^2 = b$, isolate $x^2$ by dividing both s

1. Masalah: Diketahui perbandingan umur Ayah dan Paman adalah 9:7 dan selisih umur mereka adalah 8 tahun. Kita diminta mencari jumlah umur mereka berdua saat ini. 2. Gunakan variab

1. **State the problem:** We need to simplify and understand the function $y = (x + 1)(7\sqrt{x} + 2)$.\n\n2. **Recall the formula and rules:** The function is a product of two exp

1. Masalah yang ingin kita selesaikan adalah bagaimana membuat sesuatu menjadi lebih mudah dipahami atau diselesaikan. 2. Cara paling mudah adalah dengan memecah masalah besar menj

1. Masalah: Cara cepat menyelesaikan Sistem Persamaan Linear Dua Variabel (SPLDV). 2. Rumus dasar SPLDV adalah dua persamaan linear yang memiliki dua variabel, misalnya:

1. The problem is to find the product of the two expressions: $74x^4 y^5 z^2$ and $120x^3 y^6 z^8$. 2. The formula for multiplying terms with the same base is to add their exponent

1. The problem is to solve the equation $$1499.744 = \frac{1}{3} \times 2 \times \left[a^2 + 16a + 64 + a^2 + \sqrt{a^2 \times (a + 8)^2}\right]$$ for $a$. 2. Simplify the constant

1. Given the volume formula and the equation starting from 1499.744: $$1499.744 = \frac{1}{3} \times 2 \times \left[a^2 + 16a + 64 + a^2 + \sqrt{a^2 \times (a+8)^2}\right]$$

1. The problem is to find a 3x3 determinant that results in a cubic polynomial in the variable $x$. 2. Recall the formula for the determinant of a 3x3 matrix:

1. مسئله را بیان می‌کنیم: باید مجموع ریشه‌های معادله $$2 \left(\frac{x}{4} + 3\right)^2 - \left(\frac{x}{4} + 3\right) - 36 = 0$$ را پیدا کنیم. 2. برای ساده‌تر کردن، متغیر جدیدی تع