🧮 algebra

1. **State the problem:** Find the average rate of change of the function $f(x)$ from the point $(-1, 2)$ to the point $(3 \frac{1}{2}, 2)$. 2. **Recall the formula:** The average

1. **State the problem:** Solve the system of equations by substitution: $$\begin{cases} x + y = 5 \\ -x + 7y = 19 \end{cases}$$

1. Stating the problem: Simplify the expression $$2a(-3a)^3 + (-4a^2)^2 + 7a^2 - (-3a)(-2a) - a^2$$. 2. Recall the rules:

1. The problem is to solve $4 \times \frac{3}{4}$ using division. 2. Recall that multiplication by a fraction can be interpreted as division: multiplying by $\frac{3}{4}$ is the sa

1. **Stating the problem:** We are given a parabolic graph representing height $y$ (in meters) as a function of time $x$ (in seconds). The parabola opens downwards, starts at $(1,1

1. Problem: Solve the two-step equation $2x + 3 = 15$. 2. Formula and rules: To solve two-step equations, first undo addition or subtraction, then undo multiplication or division.

1. **State the problem:** Solve the equation $$\frac{x}{3} \cdot \frac{x - 2}{2} = \frac{13}{5}$$. 2. **Write the formula and rules:** We need to solve for $x$ by first simplifying

1. **State the problem:** Simplify the expression $$\frac{\sqrt[4]{5}}{3\sqrt[4]{4}}$$. 2. **Recall the properties of roots:** The 4th root of a number $a$ is $a^{\frac{1}{4}}$.

1. **State the problem:** We have the equation describing the total distance traveled by a car:

1. Planteamos el problema: Encontrar los valores de la función $f(x) = 3x^2 - 3$ para diferentes valores de $x$. 2. La fórmula dada es $f(x) = 3x^2 - 3$. Esta es una función cuadrá

1. **State the problem:** We are given the perimeter of a triangle as the polynomial $3x^2 - 5x + 2$ and two sides as $x^2 + 3x + 5$ and $x^2 - x - 8$. We need to find an expressio

1. **Problem statement:** We have a line $l$ passing through the point $(4, 2)$ that intersects the x-axis at $(x_1, 0)$ and the y-axis at $(0, y_1)$. The triangle formed by this l

1. **Problem Statement:** Graph the function $s(d)$ where $s$ is the speed in miles per hour and $d$ is the distance in feet the driver brakes.

1. Planteamos el problema: Resolver la ecuación $$2(3x - 2) - x = 3(2x - 1)$$ para encontrar el valor de $x$. 2. Aplicamos la propiedad distributiva para eliminar los paréntesis:

1. Problemstellung: An einem Arbeitstag bearbeiten 7 Mitarbeiter insgesamt 56 Akten. Heute fallen 2 Mitarbeiter aus. Wie viele Akten können die übrigen Mitarbeiter heute bearbeiten

1. **Stating the problem:** We are given a sequence of figures where the number of squares in each figure follows a pattern. The table shows figure number $x$ and number of squares

1. **Problem Statement:** Graph the polynomial function $f(x) = x^3 + x^2 - 4x - 4$ given that $(x+1)$ is a zero.

1. The problem is to identify the domain and range of the function $$y = \sqrt{x - 4}$$. 2. The domain of a square root function $$y = \sqrt{f(x)}$$ requires the expression inside

1. **State the problem:** Simplify the expression and solve the equation if possible. Given expressions:

1. Das Problem lautet: Soll man die Klammer in einem Ausdruck einfach weglassen oder ausmultiplizieren? 2. Die Regel lautet: Wenn vor der Klammer ein Pluszeichen steht, kann man di

1. Das Problem lautet: Löse die Gleichung $ (3x-4)-(x+1)-13=0 $. 2. Zuerst entfernen wir die Klammern und fassen ähnliche Terme zusammen: