🧮 algebra

1. **State the problem:** Find the solutions of the quadratic equation $$2x^2 + 3x = -8$$. 2. **Rewrite the equation in standard form:** Move all terms to one side:

1. **State the problem:** Factor completely the quadratic expression $5x^2 - 50x + 120$. 2. **Identify the greatest common factor (GCF):** The coefficients 5, -50, and 120 all shar

1. **State the problem:** A teacher buys 24 notebooks and 24 packs of pencils for 24 students. Each notebook costs 4 and the total spent on notebooks and pencils is 220. 2. **Defin

1. **State the problem:** Solve the inequality $$(3x - 1)(2x - 3) \geq -2$$ and express the solution in interval notation. 2. **Rewrite the inequality:** Add 2 to both sides to get

1. The problem is to find the value of $T$. 2. Since no additional information or context is provided, we cannot determine $T$ without more details.

1. Masalah ini meminta kita untuk menjadikan beberapa bagian menjadi satu agar lebih mudah dipahami. 2. Dalam matematika, menggabungkan beberapa ekspresi atau langkah menjadi satu

1. Stwierdźmy problem: Obliczyć wartość wyrażenia $\left(2 - 3\sqrt{2}\right)^2$. 2. Użyjemy wzoru na kwadrat różnicy: $$ (a - b)^2 = a^2 - 2ab + b^2 $$

1. **Problem:** Jelaskan pemahaman terkait bentuk dan konsep matriks minor dan kofaktor serta berikan contoh perhitungannya. 2. **Penjelasan:**

1. Stwierdźmy problem: Obliczyć wartość wyrażenia $$(3 - \sqrt{2})^2 + 4(2 - \sqrt{2})$$. 2. Użyjemy wzoru na kwadrat sumy: $$(a - b)^2 = a^2 - 2ab + b^2$$.

1. **State the problem:** We are given the quadratic equation $$kx^2 - 4x + 36k = 0$$ and told it has two equal roots with $$k > 0$$. We need to find the value of $$k$$. 2. **Recal

1. **State the problem:** We have the quadratic equation $$x^2 - (m + 2)x + 3 = 0$$ and one root is the additive inverse of the other. We need to find the value of $$m$$. 2. **Reca

1. The problem asks to find the perimeter of a triangle with sides $2x + 4$, $3x - 2$, and $4x - 1$. 2. The perimeter of a triangle is the sum of the lengths of all its sides.

1. **State the problem:** Simplify and analyze the expression $abc + 2fgh - af2 - bg2 - cf2 = 0$. 2. **Identify terms and variables:** The expression contains variables $a,b,c,f,g,

1. **State the problem:** Find the value of $k$ such that the equation $$x^2 + kxy + 2y^2 + 3x + 5y + 2 = 0$$ represents a pair of straight lines. 2. **Formula and rule:** A second

1. The problem asks if the function $g(x) = \sqrt{e^x}$ is a composite function and to identify the "inner" and "outer" functions if it is. 2. A composite function is written as $w

1. **State the problem:** Solve the equation $$\frac{x^{\frac{3}{2}}}{x-6} = x - 8$$ for $x$. 2. **Rewrite the equation:** Multiply both sides by $x-6$ (assuming $x \neq 6$) to eli

1. مسئله: در یک کلاس با ۴۶ دانش‌آموز، تعداد دانش‌آموزانی که فقط به ریاضی علاقه دارند نصف تعداد دانش‌آموزانی است که نه به ریاضی علاقه‌مند هستند و نه به زیست. اگر تعداد دانش‌آموزانی

1. **Problem statement:** Solve the system of linear equations: $$\begin{cases} x + 2y = 4 \\ -x + 4y = 2 \end{cases}$$

1. The problem is to find the prices after applying a 4% discount to each original price. 2. The formula to calculate the discounted price is:

1. The problem asks to determine the interval(s) where the function $f(x) = -3$ is negative. 2. The function $f(x) = -3$ is a constant function, meaning it has the same value $-3$

1. Mari kita gambarkan grafik fungsi pertama: $$f(x) = \frac{2x}{1 + x^2}$$ 2. Fungsi ini adalah fungsi rasional, dimana pembilang dan penyebut adalah polinomial.