🧮 algebra

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

1. **State the problem:** Simplify the expression $6 - 6 \times 6 + 6 \div 6$. 2. **Recall the order of operations (PEMDAS/BODMAS):**

1. **State the problem:** Given the equation $(2x - 1) - p(x^2 + 2) = 0$, where $p$ is a constant, we need to show that $2p^2 + p - 1 \leq 0$ for the equation to have real roots, a

1. The problem is to subtract the mixed number $-3 \frac{1}{6}$ from $-4 \frac{3}{4}$ and express the answer in fraction form. 2. First, convert the mixed numbers to improper fract

1. **Problem Statement:** Given the function $f(x) = 3x + 3$, find: (a) the $x$-intercept and $y$-intercept,

1. The problem is to subtract the mixed number $-2 \frac{1}{4}$ from $3 \frac{2}{5}$.\n\n2. First, convert the mixed numbers to improper fractions.\n\nFor $3 \frac{2}{5}$: $$3 \fra

1. **Problem Statement:** Express the given ratios as percentages. 2. **Formula:** To convert a ratio $a:b$ to a percentage, use the formula:

1. **State the problem:** We are given a point $P = \left(x, \frac{2}{3}\right)$ that lies on the unit circle centered at the origin. We need to find the value of $x$ in simplest f

1. **Problem:** Find the determinant of the matrix \(\begin{bmatrix} l & o \\ v & e \end{bmatrix}\). 2. **Formula:** The determinant of a 2x2 matrix \(\begin{bmatrix} a & b \\ c &

1. Diketahui barisan aritmetika dengan jumlah 8 suku pertama $S_8 = 260$ dan suku pertama $a_1 = 5$. 2. Rumus jumlah $n$ suku pertama barisan aritmetika adalah $$S_n = \frac{n}{2}