🧮 algebra

1. The problem states that a gold necklace chain has 37.5 grams of gold and pure gold is 24 carats. 2. We need to find the carat value of this necklace chain given the amount of go

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