🧮 algebra

1. **State the problem:** Solve the inequality $$x\left(\frac{1}{2}-\frac{1}{3}\right)^{-1} + \frac{(x-1)^2}{2} + \frac{1}{2}x^2 \geq 5x\left(\frac{1}{2}+\frac{1}{3}\right)^{-1} +

1. **Problem a:** Berechne $$-2 \frac{1}{4} \cdot \frac{2}{3} - \left[\left(-5 \frac{1}{2}\right) - \left(-1 \frac{1}{2}\right) : \frac{4}{5}\right]$$ 2. **Umwandlung in unechte Br

1. **State the problem:** We are given a piecewise graph and several statements about the function $f$. We need to determine which statements are true. 2. **Analyze the statements:

1. **State the problem:** We need to find the range of a piecewise function described by three horizontal segments: - A segment at $y=3$ extending right from an open circle at $x=1

1. **State the problem:** We need to find the range of a piecewise function whose graph consists of three horizontal pieces with constant y-values -3, 0, and 3. 2. **Recall the def

1. **State the problem:** We are given the formula for cardiac output $D = V \cdot R$, where $D$ is the cardiac output, $V$ is the volume of blood pumped per heartbeat, and $R$ is

1. The problem asks for the domain of a function based on the given graph description. 2. The domain of a function is the set of all possible input values (x-values) for which the

1. The problem states that two divers are underwater, one at a depth of 32 meters, and the other diver's depth $x$ satisfies the equation $$|x - 32| = 11.$$ 2. This is an absolute

1. **State the problem:** Simplify the expression $$\frac{x^6}{x^7}$$ using properties of exponents. 2. **Recall the quotient of powers rule:** When dividing powers with the same b

1. **Problem:** A local print shop charges 0.10 per page to print black and white documents with no flat rate. Find the algebraic model and complete the table. 2. **Formula:** Cost

1. **State the problem:** Callie's company has fixed monthly expenses of $3200 and variable costs of $2.40 per pillow. Each pillow sells for $18. We want to find the number of pill

1. Problemi: Zgjidh ekuacionin linear $2x + 3 = 7$. 2. Formula dhe rregullat: Për të zgjidhur ekuacionet lineare, qëllimi është të izolosh $x$ në njërën anë të ekuacionit duke krye

1. Problem: Berechne günstig den Ausdruck a) $-12,6 - (+250) - (+7,4)$. 2. Wir verwenden das Kommutativgesetz der Addition, das besagt, dass die Reihenfolge der Summanden vertausch

1. **Stating the problem:** We need to describe the slopes of parallel and perpendicular lines and determine the relationship between line segments AB and CD for given points.

1. **State the problem:** Determine if the line segments AB and CD are parallel, perpendicular, or neither for the points given in problem 18: A(-4, 3), B(2, -12), C(10, 5), and D(

1. **Problem statement for 4.60:** Vis at $(x - 1)$ er en faktor i $P(x) = x^3 + 4x^2 + x - 6$.

1. **State the problem:** Simplify the expression $$\sqrt[3]{-64x^6y^9}$$. 2. **Recall the cube root properties:**

1. **State the problem:** Simplify the expression $$\frac{x^3}{x^{1/2}}$$ and find the value of $a$ such that $$\frac{x^3}{x^{1/2}} = x^a$$. 2. **Recall the exponent rule:** When d

1. **Problem statement:** Solve the system of equations $$2x + y = 10$$

1. **Problem statement:** Given the function $g(x) = \frac{1}{9}x^3 - 3x$, analyze its properties as requested in parts a) to g). 2. **Part a) Graph sketch:** The function is cubic

1. **Stating the problem:** Finn stigningstallet til linja som går gjennom punktene (1, 1) og (4, 7). 2. **Formel for stigningstall:** Stigningstallet $m$ mellom to punkter $(x_1,