🧮 algebra

1. **Determine the roots and x-value of the vertex for each function:** **a.** $f(x) = (x-2)$

1. **State the problem:** Evaluate the expression $$\left(1024^{\frac{1}{4}}\right)^{\frac{4}{5}}$$ and select the correct answer from the choices: -4, 4, 256, -256. 2. **Recall th

1. **State the problem:** Simplify the expression $\left(5x^{4}y^{-3}\right)^{-2}$. 2. **Recall the exponent rules:**

1. The problem is to solve the equation given in "opg 3" (assuming it is a math problem, but no explicit equation was provided by the user. Since no specific equation is given, I c

1. **Stating the problem:** We have two questions:

1. The problem is to solve the equation $2x + 3 = 11$ for $x$. 2. The formula used here is to isolate $x$ by performing inverse operations. We subtract 3 from both sides and then d

1. The problem asks to find the function that completes the function machine. 2. The inputs are variables $n$, $c$, and $a$.

1. **State the problem:** We need to find the numbers $A$ and $B$ such that: - $7 \times A = 21$

1. **State the problem:** We are given four ordered pairs: (16, 18), (12, 12), (9, 10), and (3, 6). We need to find which one does not lie on the same line formed by the other thre

1. **State the problem:** We need to find the value of the function $K(x) = 2x^2 - 5x + 3$ when $x = -3$. 2. **Formula used:** The function is given by

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