🧮 algebra

1. **State the problem:** We have a piecewise function defined as $$f(x) = \begin{cases} -2x & \text{if } x < 0 \\ 2x & \text{if } x \geq 0 \end{cases}$$

1. Das Problem lautet: Bestimme den Scheitelpunkt der quadratischen Funktion $$f(x) = (x - 2)^2 + 8$$. 2. Die allgemeine Form einer Parabel in Scheitelpunktform ist $$f(x) = a(x -

1. The problem involves interpreting the graph of an investment account where the x-axis represents the Account Balance and the y-axis represents Time in years. 2. From the graph d

1. **State the problem:** Mateo and his cousins invest 25,000 in an account earning 8% interest annually. Mateo proposes the equation $$y = 25,000(0.08)^x$$ to find the amount of m

1. **Problemstellung:** Bestimme den Funktionsterm der Parabel mit Scheitelpunkt $S(0|0)$, die durch den Punkt $P(-10|-8)$ verläuft. 2. **Formel:** Für eine Parabel mit Scheitelpun

1. Das Problem lautet: Bestimme den Scheitelpunkt der quadratischen Funktion $$f(x) = (x + 9)^2 - 7$$. 2. Die allgemeine Form einer Parabel mit Scheitelpunkt ist $$f(x) = a(x - h)^

1. **Problem statement:** We are given two functions: a line $f(x)$ (graph shown) and a quadratic function $g(x) = -x^2 - 3x - 5$. We need to find the intersection points of their

1. **Énoncé du problème :** a) Dans un triangle, le petit côté mesure $x$ cm. Le grand côté mesure le double du petit, et le côté moyen mesure 2 cm de plus que le petit. Exprimez l

1. Das Problem ist, den Ausdruck b-f zu berechnen. 2. Um b-f zu berechnen, subtrahieren wir den Wert von f vom Wert von b.

1. **Problemstellung:** Wir wollen die Grundform einer linearen Funktion aufstellen und die Parameter $m$ (Steigung) und $b$ (y-Achsenabschnitt) bestimmen. 2. **Formel:** Die Grund

1. **Find the 15th term of the arithmetic sequence: 3, 7, 11, ...** The formula for the $n$th term of an arithmetic sequence is:

1. **State the problem:** Solve the equation $$\frac{x^2 + 25 + 10x}{x^2 + 2x - 15} \left( \frac{x}{x+5} - \frac{x}{x+2} : \frac{x+1}{x+2} \right) = 0$$

1. The problem asks us to compare the intercepts of two functions: \(a(x) = -x^3 + 8\) and function \(b\) represented by the given graph. 2. First, find the intercepts of function

1. **Stating the problem:** Solve exercice 2, question 3, part a. Since the exact problem statement is not provided, please provide the full problem text for precise assistance. 2.

1. The problem asks to identify the inequality that represents the domain of the exponential piece of the function $f$, which is composed of an exponential piece and a polynomial p

1. **State the problem:** We need to identify which piecewise function matches the given graph. 2. **Analyze each piece of the graph:**

1. The problem is to reduce the given algebraic expression to its simplest form. 2. To reduce an expression, we combine like terms and simplify any fractions or factors.

1. **State the problem:** Simplify the expression given by the top-left, top-right, and bottom-right parts: Top-left: $7 - \frac{24 - 4n}{2}$

1. The problem asks for the range of an exponential function whose graph approaches the horizontal asymptote $y=3$ on the left and passes through points $(-1, 3.25)$, $(0, 3.5)$, a

1. The problem asks to identify which graph corresponds to the function $$y=3\left(\frac{1}{2}\right)^x$$. 2. The function is an exponential decay because the base $$\frac{1}{2}$$

1. The problem asks us to determine which ordered pairs lie on the graph of the exponential function $$f(x) = 3 \left(\frac{1}{4}\right)^x$$. 2. To check if a point $ (a, b) $ lies