🧮 algebra

1. **State the problem:** Determine if the function $F(x,y) = xy^2 - y^2\sqrt{x}$ is separable. 2. **Recall the definition:** A function $F(x,y)$ is separable if it can be written

1. **State the problem:** We need to find the fixed connection fee and the cost per minute from the given graph of cost versus time. 2. **Identify the fixed connection fee:** The f

1. **Stating the problem:** We are given expressions involving $v$ and areas in $m^2$ related to vegetable patches. We want to understand and possibly relate these expressions. 2.

1. **Stating the problem:** We have two isosceles triangles with sides labeled as expressions involving $x$. In the first triangle, side $BC = 13x - 12$ and sides $AB$ and $AC$ are

1. The problem is to simplify the expression $8\sqrt{x}975$. 2. First, recognize that the expression likely means $8 \times \sqrt{x} \times 975$ since there is no operator between

1. **State the problem:** Simplify the expression $x - 8$. 2. **Understand the expression:** The expression $x - 8$ is already in its simplest form. It represents a linear expressi

1. Let's start by stating the problem: solving simultaneous equations means finding values of variables that satisfy all given equations at the same time. 2. Consider two linear eq

1. The problem involves solving two systems of linear equations. 2. First system:

1. **Problem Statement:** We need to find the graph of the direct variation equation $$y = -x$$. 2. **Understanding Direct Variation:** A direct variation equation has the form $$y

1. **State the problem:** We need to find the graph of the direct variation equation $$y = \frac{2}{3}x$$. 2. **Recall the formula for direct variation:** A direct variation equati

1. **State the problem:** We are given a system of two linear equations: $$2 + 4y = 5$$

1. **State the problem:** We need to find the graph of the direct variation equation $$y = -2x$$. 2. **Recall the formula for direct variation:** A direct variation equation has th

1. **State the problem:** Factor the quadratic expression $x^2 + 6x + 5$. 2. **Recall the factoring formula:** For a quadratic $ax^2 + bx + c$, we look for two numbers that multipl

1. Problema: Apskaičiuokime sumą $$-18 + 24 - 7$$, sudedant skaičius su skirtingais ženklais. 2. Formulė ir taisyklės: Kai sudedame skaičius su skirtingais ženklais, suma turi to s

1. **State the problem:** Simplify the expression $\frac{n \times n + n}{n}$ and find the value of $n$ such that the expression equals 10. 2. **Write the expression:**

1. **State the problem:** Evaluate the following expressions step-by-step:

1. Let's start by understanding the problem: you want a simple explanation suitable for grade 10 level. 2. In math, we often solve problems step-by-step to make them easier to unde

1. **State the problem:** Solve the system of linear equations using the Gauss elimination method: $$\begin{cases} x - y + z + 2w = 6 \\ 2x + y + 2z + w = 6 \\ 2x + 2y - z + w = 10

1. **State the problem:** We are given the quadratic equation $$3x^2 - 6(2a - b)x + ab = 0$$ and told that the sum of its roots is 4 and the product of its roots is 8. We need to f

1. **State the problem:** A person is 5 times as old as his daughter. After 8 years, the sum of their ages will be 70. We need to find their present ages. 2. **Define variables:**

1. **Énoncé du problème 25** : Soient $x$ et $y$ deux réels tels que $2 < x < y$. 2. **Exprimer $|x - y|$ et $|x + y - 4|$ sans valeur absolue** :