🧮 algebra

1. The problem asks to write the given numbers in standard form (scientific notation). 2. Standard form expresses numbers as $a \times 10^n$ where $1 \leq |a| < 10$ and $n$ is an i

1. Given the problem to solve, we start by writing the equation or expression. 2. Apply the relevant formula or algebraic manipulation.

1. **State the problem:** We have 47 employees in total, with 29 part-time employees. We need to find the percentage of full-time employees. 2. **Identify the number of full-time e

1. The problem is to simplify the expression $$\frac{6}{c+5} + \frac{7}{c+2}$$. 2. To add these fractions, we need a common denominator. The common denominator is $$(c+5)(c+2)$$.

1. **State the problem:** We want to write the expression $$\frac{7}{4} + \frac{5f}{3f+2}$$ as a single fraction in simplest form. 2. **Find a common denominator:** The denominator

1. **State the problem:** Solve the equation $$\frac{2x+4}{x-3} = 3$$ for $x$. 2. **Formula and rules:** To solve a rational equation, multiply both sides by the denominator to eli

1. **State the problem:** We are given two equations:

1. The problem states that $A = \frac{\sqrt{3}}{2} \cdot N$. We want to understand or simplify this expression. 2. This expression means that $A$ is equal to $N$ multiplied by $\fr

1. Planteamos el problema: dividir el polinomio $x^3 - 1$ entre el binomio $x - 5$. 2. Usamos la división sintética o división larga para polinomios. La fórmula general para dividi

1. The problem is to simplify the expression $\frac{h^{14}}{h^{8}}$. 2. Use the rule of exponents for division: $\frac{a^m}{a^n} = a^{m-n}$.

1. The problem is to express a given value or expression in fractions. 2. To convert decimals or other forms into fractions, we use the fact that any decimal can be written as a fr

1. **State the problem:** We need to write a compound inequality that describes the graph. 2. **Analyze the graph:** There are two filled circles at $-7$ and $-2$.

1. The problem asks to write a compound inequality that describes the graph shown. 2. The graph shows a number line with a highlighted segment between 0 and 3.

1. The problem is to find the value of $-7 + 11$. 2. We use the rule of addition for integers: adding a positive number to a negative number involves subtracting the smaller absolu

1. **Problemstellung:** Gegeben ist die Funktion $f(x) = \frac{a}{x+b} + c$ mit $a,b,c \in \mathbb{Q}$ und $a \neq 0$. Gesucht sind zu den geschätzten Werten der Parameter $b$ und

1. The problem is to simplify the expression $(3)5$. 2. This expression means multiplying 3 by 5.

1. We are asked to find the maximum and minimum values of the functions $\max(-m, 2m^3)$ and $\min(m, -2m^3)$.\n\n2. The problem involves comparing two expressions for each functio

1. **State the problem:** Given the points $(-4,-4), (-2,-1), (0,2), (2,5), (4,8), (6,11)$, find the equation of the line passing through these points. 2. **Formula used:** The equ

1. (a) Evaluate each expression exactly. (i) Evaluate $$\left(\frac{3}{2}\right)^2 - 1 + 6$$.

1. **State the problem:** Given the table of points, find the equation of the line that passes through these points and describe its graph. 2. **Identify the points:** The points g

1. **Stwierdzenie problemu:** Znajdź równanie stycznej do wykresu funkcji $$f(x) = \frac{4x + 2}{x + 1}$$ w punkcie $$x_0 = 1$$. 2. **Wzór na równanie stycznej:** Równanie stycznej