🧮 algebra

1. **Problem statement:** Given total monthly profit Rs. 250000, monthly revenue is twice the monthly cost minus Rs. 60000. We need to find monthly revenue and monthly cost. 2. Let

1. **State the problem:** We are given the price per product unit as Rs. 1200, delivery fee per product as Rs. 200, and a discount of 4% applied if the total amount exceeds Rs. 500

1. **প্রশ্ন:** (a) যোগফল নির্ণয় কর

បញ្ហា: ដោះស្រាយសមីការ $x^2 - 5x + 6 = 0$. 1. យើងចាប់ផ្តើមដោយពិនិត្យថាតើអាច factor សមីការនេះបាន ឬទេ។

1. **State the problem:** We need to express the variable $p$ in terms of the variable $q$ given an equation or relationship involving $p$ and $q$. 2. **Identify the relationship:*

1. We start with the given expression: $$(1+q)^2 - 4(1+q)(p+q)$$ 2. Expand each term:

1. The problem states: t is proportional to the square root of d, with t = 12 when d = 4. 2. To express t in terms of d, write $$t = k\sqrt{d}$$ for some constant k.

1. Stating the problem: Given that when $e^y$ is plotted against $x^3$, the graph is a straight line passing through points $(1, 13.5)$ and $(7.5, 0.5)$. 2. Find the equation of th

1. **State the problem:** Find the function $f: \mathbb{R} \to \mathbb{R}$ such that for all real numbers $m, n$, $$f(m + n f(m)) + m = f(m f(n)) + f(n f(m))$$

1. **Stating the problem:** We want to find the term independent of $x$ (the constant term) in the expansion of $$\left(2 + \frac{3}{x^2}\right)^{10} \left(1 - 4x^2\right)^2.$$\n\n

1. The given expression is $2x+3y$. 2. This is a linear algebraic expression involving variables $x$ and $y$ with coefficients 2 and 3 respectively.

1. **State the problem:** We want to find the function $f : \mathbb{R} \to \mathbb{R}$ such that for all real numbers $m, n$, the equation $$ f(m + n f(m)) + m = f(m f(n)) + f(n f(

1. **State the problem:** Find the coordinates of the points A and B where the line $y=4x-3$ meets the curve $y=3+5x-2x^2$. Then find the area of triangle $POQ$ formed by the perpe

1. Problem 1: Solve $5x^2 = 30x$ - Divide both sides by $5$: $x^2 = 6x$

1. The problem states: Solve for $y$ in the function $y = a^x$ where $a > 0$ and $a \neq 1$. 2. This means the function represents an exponential function with base $a$.

1. The problem asks to "Give answers to blanks," but no specific blanks or expressions were provided. 2. Please provide the equations or expressions with blanks for me to solve or

1. Problem 11: Solve for $u-v$ from the system: $$3u-2v=9$$

1. Prove the commutative law of addition for matrices A and B where: $$A=\begin{bmatrix}3 & 4 \\ 2 & 5\end{bmatrix},\quad B=\begin{bmatrix}3 & 2 \\ 1 & 1\end{bmatrix}$$

1. The problem is to find the values of $X$ and $y$ from the equation $$X^2 + y^2 = (1 + xi)(3 + i)$$ where $i$ is the imaginary unit. 2. First, expand the right-hand side by multi

1. Let's first understand the context: you want a more detailed explanation of solving a math problem. 2. When solving algebraic problems, we proceed step-by-step, breaking down ea

1. We are given the first equation to solve: $$(z^2 - 2yz - y^2)p + (xy + zx)q = xy - zx.$$ 2. We are also given the second equation: $$(3x + y - z)p + (x + y - z)q = 2(z - y).$$