🧮 algebra

1. **Problem statement:** Given the function $f(x) = \sqrt{x}$ and its graph $K_f$, we want to find how the graph $K_h$ of $h(x)$ is derived from $f(x)$. 2. **Understanding transfo

1. **Problem statement:** Given the function $f(x) = \sqrt{x}$ and its transformations in Aufgabe (A), describe how multiplication by a factor $a$ affects the graph. 2. **Formula a

1. **Problem Statement:** Given the circle equation $$(x + h)^2 + (y + k)^2 = r^2$$ with radius $r > 0$, determine which of the statements I. $hk < 0$, II. $h > -r$, and III. $k <

1. **State the problem:** We are given the function $$f(x) = \frac{2x^2 - 1}{x^2 - 5x + 6}$$ and we want to analyze it. 2. **Factor the denominator:** The denominator is a quadrati

1. State the problem: Solve the equation or expression given. 2. Write down the formula or expression to be used.

1. **State the problem:** We are given the function $f(x) = 2x^2 - 1$ and want to understand its properties. 2. **Formula and rules:** This is a quadratic function of the form $f(x

1. The problem is to simplify the expression $32b$. 2. Here, $32b$ means $32$ multiplied by the variable $b$.

1. The problem statement is not provided explicitly, but since you asked for steps for question 32, I will demonstrate a general approach to solving algebraic problems. 2. Typicall

1. **Problem statement:** Given the function $f(x) = \frac{2x^2 - 1}{x^2 - 5x + 6}$, we need to analyze its domain, limits, asymptotes, derivatives, and graph. 2. **Condition for $

1. **Statement of the problem:** We are given the function $$g(x) = 2 - x - \ln{(x-1)^2}$$ defined on the domain $$]1, +\infty[$$. We need to calculate the limits $$\lim_{x \to +\i

1. The problem states: Solve the equation when $x+2 = x+1$. 2. To solve this, we use the property of equality: if two expressions are equal, their simplified forms must also be equ

1. The problem is to isolate the variable $y$ in an equation where $y$ is mixed with other terms. 2. To isolate $y$, you need to get $y$ alone on one side of the equation. This usu

1. The problem is to simplify or understand the expression $\frac{7}{2 - y}$. 2. This is a rational expression where 7 is the numerator and $2 - y$ is the denominator.

1. **State the problem:** Solve the equation $X = \frac{7}{2} - y$ for $y$. 2. **Isolate $y$:** To solve for $y$, we want to get $y$ alone on one side of the equation.

1. Persamaan linear dua variabel adalah persamaan yang melibatkan dua variabel, biasanya $x$ dan $y$, dan berbentuk garis lurus ketika digambarkan pada bidang koordinat. 2. Bentuk

1. **State the problem:** Simplify the expression $\frac{2}{3} + \frac{3}{6}$.\n\n2. **Recall the rule for adding fractions:** To add fractions, they must have a common denominator

1. مسئله: بررسی اینکه آیا $x$ به توان $-n$ برابر است با چه مقداری. 2. فرمول اصلی: برای هر عدد حقیقی $x \neq 0$ و عدد صحیح مثبت $n$، تعریف توان منفی به صورت زیر است:

1. **State the problem:** Simplify the expression $\left(4 \frac{1}{15} - 3 \frac{9}{10}\right) \times 6 \frac{6}{7} + 2$. 2. **Convert mixed numbers to improper fractions:**

1. **State the problem:** Solve the system of equations using the elimination method: $$\begin{cases} 2x + 3y = 12 \\ 2x + 3y = 1 \end{cases}$$

1. **Problem:** A trader sold a wrist watch for 3150 after giving a 10% discount. Find the marked price of the watch. 2. **Formula:** The selling price (SP) after discount is given

1. **Énoncé du problème :** Nous avons une suite $(u_n)$ définie par :