🧮 algebra

1. Problem statement: - A parish agricultural officer has 450 kilograms of fertilisers and 120 litres of anti-tick vaccine to distribute equally among farmers. We need to find the

1. Let's define the problem clearly: we need to solve the given math problem step-by-step. 2. Since no specific problem was given, I will provide a generic algebra example: Solve f

1. The problem is to solve for $x$ in the equation $2x + 3 = 11$. 2. Start by isolating the variable term: subtract 3 from both sides to get $2x = 11 - 3$.

1. **State the problem:** We are given an initial road length 13 years ago, $L_0 = 1350$ km.

1. **Evaluate and simplify each expression:** 2. Simplify $\frac{8x^{2}y^{2}}{12x+y}$ as is, since no further factorization is possible without more information.

1. **State the problem:** We need to find consecutive positive integers whose sum is 2024 and determine the largest integer in such a sum. There must be at least 2 terms. 2. Let th

1. Problem a: Find total future profits of a tool with a net return decreasing by 10% annually and a current gain of 400. 2. Since net return decreases by 10% annually, the common

1. The question "when do we half the number" relates to situations where a quantity is reduced to half its original value. 2. This commonly appears in problems involving exponentia

1. The problem: Find the equation of an ellipse given its vertices. 2. Recall the standard form of the ellipse equation centered at the origin with horizontal major axis:

1. **Problem 20:** Given height equation $$h = -16t^2 + 96t$$ , find $$t$$ when $$h = 144$$ feet. 2. Substitute $$h = 144$$:

1. 問題陳述：已知 $x,y,z$ 均為正實數，且滿足條件 $$x^{2}+y^{2}+z^{2}=1$$ 求表達式 $$\sqrt{2}xy + yz$$ 的最大值。

1. Problem statement: Evaluate $y$ for the linear function $y = -\frac{1}{3}x - \frac{2}{5}$ at $x = 0$, and describe the graph. 2. Substitute $x = 0$ into the formula to get $y =

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 $m, n$, $$f(m + n f(m)) + m = f(m f(n)) + f(n f(m))$$