🧮 algebra

1. **State the problem:** We have two quadratic functions: $$f(x) = a(x - 3)^2 + 5$$

1. **Stating the problem:** We have four quadratic functions with parameter $m > 6$, $m \in \mathbb{N}$: $$f(x) = x^2 - 6x + m$$

1. The problem is to simplify the expression $8 \times 9 / 5 + 1 \times x$. 2. According to the order of operations (PEMDAS/BODMAS), multiplication and division are performed from

1. **State the problem:** We are given a polynomial function $f(x)$ such that $$f(x) f(1) = f(x) + f(1)$$ and the value $$f(3) = 28.$$ We need to find $$f(4).$$ 2. **Analyze the gi

1. El problema es graficar la función cuadrática $$y = -x^2 + 6x - 9$$. 2. La fórmula general de una función cuadrática es $$y = ax^2 + bx + c$$, donde $a$, $b$ y $c$ son constante

1. Planteamos el problema: Simplificar y expresar con exponentes positivos la expresión $$\left( \frac{3^3 \cdot \sqrt{9ay^3 \cdot a^3}}{81a^{-1} y^5} \right)^{-2}$$

1. **State the problem:** We are given the sequence $10 \frac{1}{9}$, $11 \frac{1}{2}$, $13 \frac{2}{7}$, $15 \frac{11}{14}$ and asked to find the next number. 2. **Convert mixed n

1. مسئله: دنباله اعداد داده شده را بررسی کنیم و عدد بعدی را پیدا کنیم. 2. دنباله اعداد: $$10 \frac{1}{9}, 11 \frac{1}{2}, 13 \frac{2}{7}, 15 \frac{11}{14}$$

1. **State the problem:** Find the next number in the sequence: $10 \frac{1}{9}$, $11 \frac{1}{2}$, $13 \frac{2}{7}$, $15 \frac{11}{14}$. 2. **Convert mixed numbers to improper fra

1. **State the problem:** We need to analyze and rewrite the conic section given by the equation $$-16x^2 + 25y^2 - 32x - 150y - 191 = 0$$. 2. **Rewrite the equation grouping $x$ a

1. **Problem statement:** Simplify the expression $$A = \frac{1}{\sqrt{x} + 1} + \frac{x}{\sqrt{x} - x}$$. 2. **Recall important rules:**

1. **State the problem:** Simplify the expression $$\left( \frac{1}{x-4} - \frac{1}{x+4\sqrt{x}+4} \right) : \frac{\sqrt{x}}{x+2\sqrt{x}}.$$\n\n2. **Rewrite the division as multipl

1. **Stating the problem:** We need to create an equation that equals 10 using only the digits 6, 6, 7, and 7 exactly once each, and no other numbers.

1. The problem states: Interpret the inequality $N(8) > 2 \cdot N(5)$ where $N(g)$ represents the number of students who scored grade $g$ on the exam. 2. The inequality means the n

1. The problem asks whether the given graph represents a function. 2. A graph represents a function if and only if every vertical line intersects the graph at most once. This is kn

1. 문제를 이해하기: 수현이는 일정한 빠르기로 50분 동안 7km를 달렸습니다. 같은 빠르기로 6km를 달리는 데 걸리는 시간을 구하는 문제입니다. 2. 속력 공식: 속력은 거리 나누기 시간입니다.

1. **State the problem:** Solve the quadratic equation $x^2 - 2x = 8$ for $x$. 2. **Rewrite the equation:** Move all terms to one side to set the equation equal to zero:

1. **State the problem:** We are given the equation $$\frac{4}{9} = \frac{8}{3} m$$ and need to find the value of $m$. 2. **Write the formula and explain:** To solve for $m$, we wa

1. **Stating the problem:** Calcolare il valore dell'espressione:

1. **State the problem:** Simplify the expression $$A = (x+2)(x^2 - x - 1) + (x-1)(x+2)$$. 2. **Recall the distributive property:** To simplify, we will expand each product using t

1. **Stating the problem:** We have three shapes with numbers arranged in a pattern. The first shape (triangle) has numbers 44, 7, and 23. The second shape (rounded rectangle) has