🧮 algebra

1. Let's state the problem: We want to differentiate between the expressions "Multiply n by two, then add three" and "Add three to n, then multiply by two". 2. First expression: "M

1. **State the problem:** Solve the equation $\ln(x) - \ln(3) = 2$ for $x$. 2. **Recall the logarithm property:** The difference of logarithms is the logarithm of a quotient:

1. Das Problem lautet: Entferne das Vorzeichen "-0,25" vor der Klammer in einer Gleichung. 2. Die Regel, die wir hier verwenden, ist das Ausmultiplizieren (Distributivgesetz):

1. **State the problem:** Evaluate the expression $$6 \div 2(1+2)$$. 2. **Apply the order of operations (PEMDAS/BODMAS):**

1. **Problem statement:** Gegeben ist die Funktion $f(x) = -0,25(x - 4)^2 + 4$. Wir sollen die Funktion in die allgemeine Form umwandeln. 2. **Formel und Regeln:** Die allgemeine F

1. Il secondo passaggio si riferisce generalmente a un passaggio intermedio in un problema matematico o di algebra. 2. Per spiegare il secondo passaggio, è importante sapere quale

1. **Stating the problem:** Risolvere il sistema di equazioni:

1. **State the problem:** Solve the inequality $$|2x + 3| - |x + 4| < 2$$. 2. **Recall the definition of absolute value:** For any expression $A$, $$|A| = \begin{cases} A & \text{i

1. **Énoncé du problème :** Calculer la longueur totale du tube IRL nécessaire pour réaliser un coude avec un rayon de 90 mm (9 cm) et des longueurs droites Lg1 = Lg2 = 15 cm.

1. The problem is to simplify an expression or solve an equation to get a final answer with no natural logarithm (ln) inside. 2. To remove ln from an expression, we often use the p

1. **State the problem:** We are given the initial value of a house $P=265000$, the final value after 4 years $F=370000$, and the time period $t=4$ years. We need to find the annua

1. **State the problem:** We need to solve for $x$ given an equation where the answer is 114. 2. **Identify the equation:** Since the exact equation is not provided, let's assume a

1. **State the problem:** Simplify the expression $x^2 - \sqrt{x}$. 2. **Recall the definitions:**

1. **Stating the problem:** We need to determine the two correct rules when dividing two integers with different signs (one positive, one negative).

1. **Problem Statement:** Determine if the set of vectors of the form $nx + my$ where $n, m$ are integers and $x, y$ are vectors, forms a subgroup of the group of translations. 2.

1. **Problem Statement:** Identify the graph of an odd function among the given four graphs. 2. **Definition of Odd Function:** A function $f(x)$ is odd if it satisfies the conditi

1. The problem asks to find the graph of an even function. 2. An even function satisfies the property $$f(-x) = f(x)$$ for all $x$ in its domain.

1. **State the problem:** A drink-seller had 520 cups in total: small (S), medium (M), and large (L). She used 34 small cups and 20% of medium cups. Then she increased large cups b

1. The problem is to convert the fraction $\frac{54}{60}$ into a percentage. 2. To convert a fraction to a percentage, use the formula:

1. The problem is to convert the fraction $\frac{53}{60}$ into a percentage. 2. The formula to convert a fraction to a percentage is:

1. **State the problem:** We have a cubic polynomial $$h x^3 + 7 x^2 - 48 x + 49$$ that leaves the same remainder when divided by $$x + k$$ and $$x - k$$. We need to find possible