🧮 algebra

1. **State the problem:** We need to find which polynomial has a leading coefficient of 4 and a degree of 3. 2. **Recall definitions:**

1. **State the problem:** We are given the system of equations: $$\begin{cases} x + 3y = 10 \\ -2x - 2y = 4 \end{cases}$$

1. **State the problem:** We need to find which expression has a leading coefficient of 3 and a constant term of -4. 2. **Recall definitions:**

1. **State the problem:** We need to find the value of $x$ that satisfies the equation $$\frac{x-3}{4} + \frac{2}{3} = \frac{17}{12}.$$\n\n2. **Write the formula and rules:** To so

1. **State the problem:** Calculate $8$ squared divided by $4$ times $2$ to the third power. 2. **Write the expression:** $$\frac{8^2}{4} \times 2^3$$

1. **State the problem:** You spent 11 on pencils and pens. Pencils cost 0.25 each, pens cost 2 each, and you bought a total of 30 items. 2. **Define variables:** Let $x$ be the nu

1. **State the problem:** Determine the number of solutions for the system of equations: $$\begin{cases} y = -x - 3 \\ -2x - 2y = 6 \end{cases}$$

1. 题目：如何分解因式（因式分解）一个代数表达式。 2. 公式和规则：分解因式的基本方法包括提取公因式、使用平方差公式、完全平方公式和分组分解法。

1. **Stating the problem:** Mary starts saving with 136 coins worth 51 euros. Each week, she receives 8 more coins worth 3 euros (1 coin of 1 euro, 2 coins of 0.5 euro, and 5 coins

1. Das Problem: Wir wollen verstehen, wie man Bruchgleichungen löst. 2. Eine Bruchgleichung ist eine Gleichung, in der Variablen im Nenner von Brüchen vorkommen, z.B. $\frac{1}{x}

1. Il problema chiede di risolvere o semplificare l'espressione $Y - x^{2y} = ?$. 2. La notazione $x^{2y}$ indica che la base $x$ è elevata alla potenza $2y$, cioè $x$ elevato al p

1. **Stating the problem:** Vi har en parabel, der beskriver hvælvingen i vinkælderen med funktionen $$f(x) = -1,6x^2 + 3,4x$$ hvor $f(x)$ er højden over gulvet i meter, og $x$ er

1. The problem is to solve the inequality $$5x^2 + 5x > 10$$. 2. First, rewrite the inequality by moving all terms to one side:

1. **State the problem:** Solve the system of linear equations: $$2x + y = 7$$

1. **State the problem:** Solve the linear equation $2x + y = 7$ for $y$ in terms of $x$. 2. **Formula and rules:** To isolate $y$, subtract $2x$ from both sides of the equation.

1. **State the problem:** Harry converted 560 pounds to euros in February, then converted his remaining euros back to 120 pounds in April. We need to find how many euros he spent o

1. **State the problem:** We need to find the formula for cost based on the mass of coal, given by the linear equation: $$\text{cost} = m \times \text{mass of coal} + c$$

1. **State the problem:** Solve the equation $$\frac{1}{3}(x-3) - x + \frac{1}{3} + 3 + \frac{x}{3} = \frac{1}{3} - z - \frac{x}{3} + \frac{x}{3} + 1$$ for $x$ and $z$. 2. **Simpli

1. **State the problem:** Solve the equation $$\frac{1}{3}(x - 3) - \frac{x+1}{3} + \frac{3+x}{3} = \frac{1}{3} - \frac{2-x}{3} + \frac{y}{3} + 1$$ for $x$ and $y$. 2. **Rewrite th

1. We are asked to find the values of $g(0)$, $g(2)$, and $g(4)$ for the function $g(x) = -5x$. 2. To find $g(0)$, substitute $x=0$ into the function:

1. **State the problem:** Solve the equation $16 - 2t = 5t + 9$ for $t$. 2. **Write down the equation:**