🧮 algebra

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.

1. Muammo: Ko'phadlar bilan ishlash - ko'paytirish, bo'lish, qo'shish, ayirish va qisqartirishni o'rganamiz. 2. Ko'phadlar (polinomlar) - bu ko'plab o'zgaruvchilar va ularning dara

1. প্রশ্ন ১৮ প্রশ্ন-১: আসল মুনাফা-আশুলের মুনাফার হার $x\%$ এবং $n$ বছরে $x\%$ মুনাফা হয়, ৫$n$ বছরে ২$x\%$ মুনাফা হয়। 2. মুনাফার হার $x\%$ হওয়ার মানে প্রতি বছর মুনাফা $x\%$। অর্থ

1. **State the problem:** We are given a piecewise function: $$f(x) = \begin{cases} x + 1 & \text{if } x < 4 \\ (x - 4)^2 + 3 & \text{if } x \geq 4 \end{cases}$$

1. Diberikan sistem persamaan linear: $$\begin{cases} x + 2y + z = 15 \\ -x - y + 2z = 11 \\ 2x - 2y + z = -7 \end{cases}$$

1. The problem asks to analyze the function $f(x) = 16^{9-x}$. 2. This is an exponential function where the base is 16 and the exponent is $9-x$.

1. **Problem:** Find the length of the transverse axis of the ellipse given by $$\frac{x^2}{25} + \frac{y^2}{9} = 1$$ 2. **Formula and Explanation:**

1. **State the problem:** Solve the equation $45 - p = 32$ for $p$. 2. **Formula and rules:** To isolate $p$, we use the rule of adding or subtracting the same value on both sides

1. 题目描述：小平从家到电影院，先以每分钟50米的速度走了2分钟。如果继续以这个速度走，他将迟到8分钟。后来他改为每分钟60米的速度，结果提前5分钟到达。求家到电影院的距离。 2. 设家到电影院的距离为 $d$ 米，正常到达电影院所需时间为 $t$ 分钟。

1. **State the problem:** Make $A$ the subject of the equation $$B = \frac{k}{A^2} + h$$. 2. **Isolate the term with $A$:** Subtract $h$ from both sides to get $$B - h = \frac{k}{A

1. **State the problem:** We are given the cost of 12 quintals of soyabean as 36000 rupees and need to find the cost of 8 quintals. 2. **Formula used:** Cost is directly proportion

1. **Problem:** Find the positive solution of the quadratic equation $$x^2 - x - 1 = 0$$ to two significant figures. 2. **Formula:** The quadratic formula for roots of $$ax^2 + bx

1. **Problem statement:** Find the slope $m$ of the line $y=mx$ that is tangent to the circle given by $$(x-2)^2 + (y-6)^2 = 4.$$\n\n2. **Formula and concept:** A line is tangent t