🧮 algebra

1. 問題陳述：已知 $a,b$ 皆為正實數，函數 $f(x) = x^3 - 3ax^2 + b$ 的圖形中恰有兩處的一次近似為水平線，且其中一條水平線為 $x$ 軸。請問此函數的對稱中心會在下列哪一個函數圖形上？ 2. 重要公式與規則：

1. The problem is to evaluate the expression $8 \div 2 \times 2 \times 2$. 2. According to the order of operations (PEMDAS/BODMAS), division and multiplication are performed from l

1. The problem is to simplify and solve the equation: $$16x^2 - (4x - 1)(4x + 1) + 2x = 7$$

1. **State the problem:** Solve the system of equations by graphing: $$y = 3x - 2$$

1. **State the problem:** Solve the system of equations by graphing: $$y = (x - 1)^2 + 1$$

1. **State the problem:** Solve the equation $$\frac{g+3}{g-2} = \frac{56}{21}$$ for $g$. 2. **Use the cross-multiplication rule:** For two fractions equal to each other, $$\frac{a

1. **State the problem:** Solve the equation $(x-18)-8=-28$ for $x$. 2. **Write down the equation:**

1. **State the problem:** Simplify the expression $$(-5)^2 - 2 \times (-9) + 6$$ using the correct order of operations. 2. **Recall the order of operations:** Parentheses, Exponent

1. The problem asks: If $f$ is a decreasing function, what can we say about the function $g = f \circ f$ (the composition of $f$ with itself)? 2. Recall that a function $f$ is decr

1. Énonçons le problème : vous souhaitez un calcul mathématique méthodique, par exemple une factorisation. 2. Rappelons la méthode de factorisation : pour factoriser une expression

1. **Problem Statement:** Calculate the sum of each pair of integers given. 2. **Formula and Rules:** Adding integers involves combining positive and negative numbers. Key rules:

1. **State the problem:** We are given the expression $a = 5 + x$ and need to understand or work with it. 2. **Explanation:** This is a simple algebraic expression where $a$ depend

1. **State the problem:** Solve the equation $2(m + 3) - 6 = 18$ for $m$. 2. **Use the distributive property:** Multiply 2 by each term inside the parentheses:

1. **Problem statement:** Given real numbers $x$ and $y$ such that $2 \leq x \leq 5$ and $-3 \leq y \leq 4$, find the bounds (range) for the expressions $x+y$, $x-y$, $xy$, and $y^

1. The problem asks: If $f$ is a decreasing function, what is the direction (increasing or decreasing) of the function $g = f \circ f$, which means $g(x) = f(f(x))$. 2. Recall that

1. **State the problem:** Factor the quadratic expression $$x^2 + 3\sqrt{3}x - 30$$. 2. **Recall the factoring formula:** For a quadratic $$ax^2 + bx + c$$, we look for two numbers

1. The problem asks to solve the equation $$2x^3 - 5x = 0$$ by drawing a suitable straight line. 2. First, rewrite the equation as:

1. **State the problem:** Solve for $x$ in the proportion $\frac{7x+1}{2x+3} = \frac{10}{3}$. 2. **Formula and rule:** When two ratios are equal, their cross products are equal. So

1. The problem states: If $23p = 390$, find $p$. 2. The formula to solve for $p$ is to isolate $p$ by dividing both sides of the equation by 23.

1. **Stating the problem:** Calculate the average score for each student based on their Test and Exam scores. 2. **Formula used:** The total score is the sum of Test and Exam score

1. Probleem: Lahendada avaldis $$\frac{x^2(x+3)-2(x+3)}{6xy^2-3xy^2} \div \frac{x^2-9}{3x^2y - x^2y}$$. 2. Kasutame jagamise asemel korrutamist pöördväärtusega: $$\frac{A}{B} \div