🧮 algebra

1. **Problem:** A forester wants to plant 68 apple trees and 110 mango trees in equal rows (same number of trees per row). Each row contains only one type of tree. Find the minimum

1. **Problem:** Find the factor of $(a + 5)(a - 9) - 15$ from the given options. 2. **Formula and rules:** Use distributive property to expand and simplify expressions.

1. **Problem:** Find the factor of $(a + 5)(a - 9) - 15$ from the given options. 2. **Formula and rules:** Expand the product and simplify the expression.

1. **State the problem:** Convert a quadratic function from general form $y = ax^2 + bx + c$ to standard (vertex) form $y = a(x-h)^2 + k$. 2. **Formula and rules:** The vertex form

1. The problem is to solve the equation: $0 = 0$. 2. This equation states that zero equals zero, which is always true.

1. **Menyatakan masalah:** Kita diberikan persamaan Diophantine $x + y + z = n$ dengan $n \in \mathbb{N}$ dan diminta menentukan solusi untuk $n=10$ dalam tiga kasus: (a) solusi bi

1. **Menyatakan masalah:** Kita diberikan persamaan Diophantine $x + y + z = n$ dengan $n \in \mathbb{N}$ dan diminta mencari solusi untuk $n=10$. 2. **Aturan dasar:**

1. **State the problem:** Simplify the expression $\sqrt{3} + \sqrt{5}$. 2. **Understand the terms:** $\sqrt{3}$ and $\sqrt{5}$ are square roots of 3 and 5 respectively. They are i

1. The problem is to simplify the fraction $\frac{600}{800}$. 2. The formula to simplify a fraction is to divide the numerator and denominator by their greatest common divisor (GCD

1. समस्या: हमें एक समीकरण हल करना है। 2. सबसे पहले, समीकरण को ध्यान से पढ़ें और समझें कि क्या पूछा गया है।

1. The problem is to simplify the fraction $\frac{200}{800}$. 2. The formula to simplify a fraction is to divide the numerator and denominator by their greatest common divisor (GCD

1. **State the problem:** We have two functions defined as $f(x) = 1 - 2x$ and $g(x) = x^2 - 3$.

1. **State the problem:** Simplify or analyze the expression $\left(\sqrt{x-2}\right) x^2$. 2. **Recall the formula and rules:** The square root function is defined as $\sqrt{a} =

1. **State the problem:** We need to find the value of $V$ given that $V^4 = 16$. 2. **Recall the formula and rules:** To solve for $V$ when raised to a power, we take the root cor

1. The problem is to find the degree of the polynomial $x^3 + 2x^2 + 3x + 4$. 2. The degree of a polynomial is the highest power of the variable $x$ with a non-zero coefficient.

1. **State the problem:** Find the roots or analyze the cubic polynomial $$x^3 + 2x^2 + 3x + 4$$. 2. **Formula and rules:** For a cubic polynomial $$ax^3 + bx^2 + cx + d = 0$$, roo

1. সমস্যাটি হলো: 10 জন ব্যক্তি একটি কাজের অর্ধেক 7 দিনে করতে পারে। তাহলে 5 জন ব্যক্তির ওই কাজটি সম্পূর্ণ করতে কত দিন লাগবে তা নির্ণয় করতে হবে। 2. প্রথমে কাজের হার নির্ণয় করি। 10

1. Problem: Given the equation $$2x + \frac{2}{x} = 3$$, find the value of $$x^2 + \text{?}$$ where the options are \(\frac{1}{6}, \frac{1}{4}, \frac{1}{3}, \frac{1}{5}\). 2. Formu

1. We are given the function $K(n) = 2n^2 - 100n + 1375000$ and asked to analyze it. 2. This is a quadratic function of the form $K(n) = an^2 + bn + c$ where $a=2$, $b=-100$, and $

1. **State the problem:** Solve the quadratic equation $$x^2 - 7x + 10 = 0$$. 2. **Recall the quadratic formula:** For an equation $$ax^2 + bx + c = 0$$, the solutions are given by

1. **State the problem:** Simplify the algebraic expression $3a + 7b + 2a - 4b$. 2. **Identify like terms:** Like terms are terms that have the same variable raised to the same pow