🧮 algebra

1. **State the problem:** We want to solve simultaneous inequalities using MATLAB. 2. **Understanding simultaneous inequalities:** These are multiple inequalities that must be true

1. **State the problem:** We have a piecewise function $$k(x) = \begin{cases} \sqrt[3]{x+1} & \text{if } x < 8 \\ -8x + 1 & \text{if } 8 \leq x \leq 16 \\ x + 3 & \text{if } x > 16

1. **State the problem:** We are given a piecewise function: $$m(x) = \begin{cases} 20x + 25 & \text{if } x < 0 \\ 11 - 7x & \text{if } x \geq 0 \end{cases}$$

1. The problem asks to find the exact value of $k(9)$ given the piecewise function: $$k(x) = \begin{cases} x^2 & \text{if } x < 5 \\ x + 2 & \text{if } x = 5 \\ 2 - x & \text{if }

1. The problem is to find the correct graph for the linear equation $3x + 2y = 4$. 2. To graph a linear equation, we find the intercepts where the line crosses the axes.

1. The problem asks to solve a system, but no explicit system of equations is provided in the message. 2. Since no equations or expressions are given, we cannot perform algebraic m

1. Énoncé du problème : Montrer que la fonction $f$ définie par $$f(x) = \frac{1}{x^2 + 2x + 2}$$ est bijective de l'intervalle $[-1, +\infty[$ vers son image, puis déterminer sa f

1. Gegeben ist die Funktion $f(x) = \sqrt{x}$ und ihr Graph $K_f$. 2. Der Graph $K_h$ entsteht durch eine Spiegelung von $K_f$ an der $x$-Achse. Das bedeutet, dass alle $y$-Werte v

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.