🧮 algebra

1. Giải phương trình $x(x + 2) - 2x(x - 3) = 5 - x^2$. Bước 1: Mở rộng và rút gọn các biểu thức.

1. **Problem:** Solve the equation $x(x + 2) - 2x(x - 3) = 5 - x^2$. 2. **Formula and rules:** Use distributive property and combine like terms.

1. **Problem statement:** We have a roller-coaster track modeled by a cubic function $$y = ax^3 + bx^2 + cx + d$$ for $$0 \leq x < 90$$ meters. The track passes through points:

1. **State the problem:** We are given the expression $$n=\frac{(N-1)E^2+Z^2s^2}{N\cdot Z^2\cdot s^2}$$ with values $$N=4999, E=1, Z=1.7507, s=8.9346$$ and need to evaluate $n$.

1. **Stating the problem:** We are given the mass $y$ (in grams) of an ice cube with side length $x$ (in cm) as follows:

1. The user asked to simplify and show a clear answer, but no specific expression or problem was provided. 2. To help, please provide the exact expression or problem you want simpl

1. **State the problem:** We are given two statues, each made of three parts with given heights as mixed numbers. We need to find which statue is taller and the difference in their

1. **State the problem:** Simplify the expression $$\frac{2}{\sqrt[3]{3} - \sqrt[4]{5}}$$. 2. **Formula and rules:** To simplify expressions with radicals in the denominator, we ra

1. The problem is to find the value of $x$ in the equation $$\frac{2x+3}{4} = 5.$$ 2. The formula used here is to solve for $x$ by isolating it on one side of the equation. We do t

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