🧮 algebra

1. **Problem statement:** We want to find if a mixture of components A, B, and C can produce a food with given percentages of protein (Eiweiß), carbohydrates (Kohlenhydrate), and f

1. **Stating the problem:** We are given that 1 kilometer equals approximately 0.621 mile.

1. **Problem statement:** A tablet screen measures 8 inches by 5 inches, and it has a border of uniform thickness $x$ around it. We need to find expressions and solve for $x$ based

1. The problem is to evaluate fractional exponents and match them with their numerical values. 2. Recall the rule for fractional exponents: $$a^{m/n} = \sqrt[n]{a^m} = (\sqrt[n]{a}

1. **State the problem:** Solve the quadratic equation $$3x^2 - 5x + 2 = 0$$. 2. **Formula used:** The quadratic formula to solve $$ax^2 + bx + c = 0$$ is

1. **State the problem:** Solve the quadratic equation $$x^2 + 2x - 3 = 0$$. 2. **Recall the quadratic formula:** For any quadratic equation $$ax^2 + bx + c = 0$$, the solutions ar

1. **State the problem:** We need to find the sum of the infinite series $$\sum_{n=1}^\infty \frac{e^n}{\pi^n}$$ or determine if it diverges. 2. **Identify the type of series:** Th

1. **State the problem:** We need to find the value of the constant $k$ such that the equation $$\frac{kx^2 + 14x - 20}{3x - 2} = 5x + 8 - \frac{4}{3x - 2}$$ holds true for all $x

1. **State the problem:** Solve the rational equation $$\frac{9}{2} = \frac{7x - 8}{x + 1}$$ and check for extraneous solutions. 2. **Formula and rules:** To solve rational equatio

1. **State the problem:** Solve the rational equation $$\frac{3}{x - 7} = \frac{x + 1}{3}$$ and check for extraneous solutions. 2. **Identify the domain restrictions:** The denomin

1. **Problemstellung:** Auf einem Schachbrett mit 64 Feldern verdoppelt sich die Anzahl der Reiskörner von Feld zu Feld, beginnend mit 1 Reiskorn auf dem 1. Feld.

1. Problemstellung: Sie besitzen 5 Franken, davon 3 Franken werden zuerst 46-mal verdreifacht und dann 20-mal vervierfacht. Die restlichen 2 Franken werden 30-mal verfünffacht. Ges

1. The problem is to find how to get the numbers 9, 17, 36, 47, and 64 from 87 million or understand their relation. 2. Since the question is unclear, let's consider if these numbe

1. We start with the first equation: $x - \sqrt{x^2 - 5} = 1$. 2. Isolate the square root term: $\sqrt{x^2 - 5} = x - 1$.

1. **State the problem:** Given the function $$f(x) = \frac{17 - 10x}{2x - 1}$$ for $$x \in \mathbb{R}$$ and $$x \neq \frac{1}{2}$$, we need to:

1. **State the problem:** Simplify the expression $$\frac{(3^4\cdot 5^2-7^3)+(12^2-8^2)}{2^3}+\sqrt{144}-\frac{6!}{5!}$$. 2. **Recall formulas and rules:**

1. The problem is to understand if you can pick any number to replace $x$ in an expression or equation. 2. In algebra, $x$ is a variable that can represent any number within the do

1. The problem is to analyze and graph the given linear equations: - $y = 3x - 4$

1. The problem asks to create tables of values for each equation in question 6 part a. 2. To create a table of values, choose several values for the independent variable (usually $

1. **State the problem:** Solve the system of linear equations: $$y = 4x + 3$$

1. **State the problem:** Perform the operation and combine into one fraction: $$\frac{2}{x-8} - \frac{7}{x}$$ 2. **Formula and rules:** To subtract fractions, find a common denomi