🧮 algebra

1. The problem asks us to simplify the expression \(4 \sqrt{2}\). 2. Here, \(\sqrt{2}\) is the square root of 2, and the number 4 is multiplied by this square root.

1. The problem: Understand what a polynomial means in mathematics. 2. A polynomial is an expression consisting of variables (also called indeterminates) and coefficients, combined

1. **Stating the problem:** The question asks, "What is a constant term?" 2. **Explanation:** In algebra, a constant term is a term in an expression or equation that does not conta

1. a) Solve the equation: $$\frac{m}{2} + \frac{m}{3} + 3 = 2 + \frac{m}{6}$$ Step 1: Find a common denominator for the terms involving $m$, which is 6.

1. The selling price is the amount for which an item is sold to a buyer. 2. Generally, the selling price is calculated based on the cost price and the desired profit or markup.

1. **State the problem:** Solve the quadratic equation $$x^2 - 5x + 6 = 0$$ for $x$. 2. **Factor the quadratic:** We look for two numbers that multiply to $6$ and add to $-5$. Thos

1. **State the problem:** We need to find how many litres of paint are required to paint a wall that is 3 meters wide and 10 meters long if 4 litres cover 20 square meters. 2. **Ca

1. **State the problem:** We need to find how many litres of paint are required to cover a wall that is 3 meters wide and 10 meters long, given that 4 litres of paint can cover 20

1. **Problem statement:** IGI Fashion company buys pants at P120.00 each. The overhead cost is 75% of the product cost, and the owner wants a 40% profit on the selling price. 2. **

1. Le problème demande de déterminer le domaine de définition des fonctions $f(x) = \frac{2x + 3}{x - 5}$ et $g(x) = \frac{x^2 - 4}{x^2 - 9}$. 2. Pour trouver le domaine d'une fonc

1. Solve the equation: $$\frac{m}{2} + \frac{m}{3} + 3 = 2 + \frac{m}{6}$$ Step 1: Find a common denominator for the fractions on the left side. The denominators are 2, 3, and 6. T

1. We are given two vectors \( \mathbf{a} = 2\mathbf{i} - 3\mathbf{j} + 4\mathbf{k} \) and \( \mathbf{b} = \mathbf{i} + 2\mathbf{j} + 2\mathbf{k} \), and we need to find \( \cos\th

1. The expression you provided is $5N^2 + 3N + 2$. This is a quadratic expression where $N$ is a variable, and $5$, $3$, and $2$ are constants called coefficients. 2. The term $5N^

1. Stated problem: Find the value of the expression $31 - 28 \div 7 \times 4$. 2. According to the order of operations (PEMDAS), we first perform division and multiplication from l

1. **State the problem:** Solve the system of equations for $x$ and $y$: $$\begin{cases} x^2 + xy - y^2 + 3x = -4 \\ 2x^2 + 2xy - 2y^2 + 5x - y = -6 \end{cases}$$

1. The problem is to solve the simultaneous equations: $$3x + 2y = 7$$

1. Given the system: $$x \cos A + y \sin A = m$$

1. **State the problem:** We want to evaluate the expression $$31 - 28 \div 7 \times 4\n\n2. **Apply the order of operations (PEMDAS/BODMAS):** First, perform the division and mult

1. **Understanding the problem:** We need to find missing numerators or denominators in equivalent fractions. 2. **Recall the rule:** Two fractions are equivalent if their cross pr

1. The problem provided is unclear as it contains ambiguous notation: F(2;5) and yV(2;3). 2. Typically, notation like F(2;5) or V(2;3) might represent points or function values but

1. Let's understand the problem: We have a Plan A which has a fixed monthly fee of 50 plus a cost of 0.70 per minute used, where $m$ is the number of minutes. 2. The total cost $C$