🧮 algebra

1. **State the problem:** Simplify the expression $$2x \cdot \frac{(x+y)(x-y)+2y^2}{2y(x-y)} \div \frac{x^2+y^2}{xy-y^2}$$. 2. **Rewrite the division as multiplication by the recip

1. Het probleem: Los de vergelijking $3x + 5 = 20$ op. 2. Formule en regels: Om een lineaire vergelijking op te lossen, isoleren we de variabele $x$ door beide zijden van de vergel

1. **Stating the problem:** Risolvi l'equazione $$5x + 2(x+1) - 3x = 4x - 3 + x$$. 2. **Formula and rules:** Per risolvere equazioni lineari, si applica la proprietà distributiva,

1. Il problema chiede di risolvere un'equazione, ma non è stata fornita un'equazione specifica. 2. Per risolvere un'equazione, si applicano regole di algebra come isolare la variab

1. **State the problem:** Solve the equation $$\frac{52}{x+30} - \frac{52}{x} = \frac{27}{10}$$ for $x$. 2. **Formula and rules:** To solve equations involving fractions, find a co

1. **State the problem:** We want to find the number of TV sets $x$ to produce and sell per week to maximize the weekly profit, given the cost function and selling price.

1. **State the problem:** Find two positive numbers whose sum is 300 and whose product is maximum. 2. **Set variables:** Let the two numbers be $x$ and $y$.

1. **Problem statement:** Simplify the algebraic expressions for waagerecht (horizontal) A and B. 2. **Formula and rules:** Combine like terms by adding or subtracting coefficients

1. **State the problem:** We need to find a two-digit number whose digits sum to 12 and when reversed, the new number is \(\frac{4}{7}\) of the original number. 2. **Define variabl

1. The problem asks to identify which of the given systems is a 2x2 system of equations. 2. A 2x2 system means there are 2 equations with 2 variables each.

1. Das Problem ist: "Und die Vereinfachung". 2. Es wurde keine konkrete mathematische Aufgabe angegeben, daher kann ich nichts sinnvoll vereinfachen.

1. **Planteamiento del problema:** Se tiene una empresa que cobra un cargo fijo y un valor por cada kwh consumido. Se conocen tres facturas con consumo y monto pagado:

1. The problem is to solve the system of equations: $$2x + y = 3x - 5y = 13$$

1. **Problem:** Calculate $7 - 9$. 2. **Formula:** Subtraction of integers.

1. **State the problem:** Solve the system of equations: $$4x + 3y = -1$$

1. **State the problem:** We need to find the average rate of change of the distance function from $x = -1$ to $x = 1$. 2. **Recall the formula for average rate of change:**

1. **问题陈述**：根据给出的数字规律，找出横线上的数字，即求表达式 $$10 \;\diamond\; 7 \;\diamond\; 13 = ?$$ 的结果。 2. **观察规律**：给出的等式为：

1. **State the problem:** Find the y-intercept and slope of the line given by the equation $$-3x + y = -5$$. 2. **Rewrite the equation in slope-intercept form:** The slope-intercep

1. Bài toán yêu cầu tìm số nghiệm của phương trình $$\sqrt{3x - 14} = x - 4$$. 2. Điều kiện xác định: biểu thức dưới căn phải lớn hơn hoặc bằng 0 và vế phải cũng phải không âm vì c

1. Bài toán yêu cầu tìm số nghiệm của phương trình $$\sqrt{-40x - 31} = 4x + 1$$. 2. Điều kiện xác định: biểu thức dưới căn phải lớn hơn hoặc bằng 0, tức là $$-40x - 31 \geq 0$$.

1. **State the problem:** Simplify the expression $$ (6x^4y^3)^2 $$ and compare it with $$ 9x^5y $$. 2. **Formula used:** When raising a power to another power, use the rule $$ (a^