🧮 algebra

1. **State the problem:** Given that $a - b = b - c = 2$, find the value of $$\frac{(a - b)^2 + (b - c)^2}{(a - c)^2}$$

1. **Problem statement:** Solve the system of linear equations $2x+y=8$ and $2x-y=12$. 2. **Formula/rule used:** To solve a system, we can add the equations to eliminate one variab

1. **State the problem:** Solve the system of linear equations: $$2x + y = 8$$

1. Planteamos el problema: Queremos encontrar el tiempo mínimo $x$ en horas para que la temperatura $f(x)$ sea menor o igual a 5 grados centígrados. 2. La función dada es $$f(x) =

1. **State the problem:** Solve the system of linear equations for $x$ and $y$: $$2x + y = 8$$

1. **State the problem:** We need to find the value of $x$ such that $f(x) = 4$ given the function $f(x) = 2x + 2$. 2. **Write the equation:** Set the function equal to 4:

1. **State the problem:** Solve $a^3+a^2=36$ for $a$. 2. **Write the equation in standard form:**

1. The problem is to find the common denominator (common denominator) for the fractions $\frac{1}{3}$ and $\frac{3}{5a}$. 2. To add or compare fractions, they must have the same de

1. The problem asks to find the cube root of 64, written as $\sqrt[3]{64}$.\n\n2. The cube root of a number $x$ is a value $y$ such that $y^3 = x$.\n\n3. We need to find $y$ such t

1. **State the problem:** Solve the system of equations for $x$ and $y$: $$2x + y = 8$$

1. **State the problem.** We need to simplify the expression

1. **State the problem:** We have 10 boys and 20 girls in a class. The mean mark for the whole class is 60, and the mean mark for the girls is 54. We need to find the mean mark for

1. **Problem:** Solve the system of equations. $$2x+y=8$$

1. The problem is to solve the equation given by the user, but since no specific equation was provided, let's consider a general example: Solve for $x$ in the equation $2x + 3 = 7$

1. **Problem statement:** Solve the first system of equations and find the value of $x+y$. 2. **Write the equations:**

1. **State the problem:** We have a rectangular frame made from metal pieces with side lengths 12 m and 5 m. We need to find the total weight of the metal in the frame. 2. **Identi

1. **Problem:** You are asking why, in a union graph, we only show $3$ in the middle. 2. **Formula used:** The union is written as $A\cup B$ and means all elements in $A$, in $B$,

1. **Problem:** You are asking whether $3$ is the union, or whether union means both joining. 2. **Formula used:** The union of two sets is written as $A\cup B$.

1. **Problem:** Draw $A$ or $B$ with an example. 2. **Formula used:** In set notation, “or” means the union, written as $A\cup B$.

1. **Problem:** Find the difference between $A$ and $B$, and explain $A$ or $B$. 2. **Formula used:**

1. **Problem statement:** Draw a simple example of sets like $A$ or $B$. 2. A set is just a collection of distinct items. A helpful way to show a set is to use a circle labeled wit