🧮 algebra

1. **State the problem:** We want to find how many times more bacteria are in a liter of water compared to what a person can see with a microscope. 2. **Given values:**

1. The problem asks for the sum of the debts $8,000,000$, $46,000,000$, and $2,000,000$ expressed in scientific notation. 2. First, write each number in standard form:

1. We are asked to add the fractions $\frac{16}{7}$ and $\frac{27}{15}$.\n\n2. To add fractions, we need a common denominator. The denominators are 7 and 15. The least common denom

1. **Problemstellung:** Gegeben sind die Kosten eines Betriebs für eine Produktserie mit folgenden Informationen: - Kosten bei Ausbringungsmenge 4 ME: 60 GE

1. **State the problem:** We need to find the total surface area of Earth's water, which includes both saltwater and freshwater, and express the answer in scientific notation. 2. *

1. The problem asks which of the points A-F lies on the curve defined by the equation $$y=\frac{1}{x-3}$$. 2. To check if a point $(x,y)$ lies on the curve, substitute the $x$-coor

1. **Problem Statement:** Simplify the following expressions involving multiplication of surds: - (\sqrt{3} - 1)(\sqrt{3} + 1)

1. Het probleem is om de lineaire functie in de vorm $ax + b$ te begrijpen. 2. De algemene formule voor een lineaire functie is:

1. We beginnen met het probleem: Hoe los je lineaire formules op en hoe interpreteer je hun grafieken? 2. Een lineaire formule heeft de vorm $y = mx + b$, waarbij $m$ de helling is

1. **State the problem:** Solve the equation $X - y = -2$ for $X$ or $y$. 2. **Rewrite the equation:** The equation is already given as $X - y = -2$.

1. **Problem:** Find two numbers whose sum is 54 and whose product is a maximum. 2. **Formula and rules:** Let the two numbers be $x$ and $y$. We know:

1. Planteamos el problema: calcular el rango de la matriz $$\begin{pmatrix} 1 & 2 & 3 & 1 \\ 1 & k & 3 & 2 \\ 1 & 8 - 3k & 3 & -2 \end{pmatrix}$$ según el parámetro $k$ usando el m

1. **Probleem:** Controleer of de uitdrukking $\sqrt{25^{4a}}$ correct is vereenvoudigd. Formule: $\sqrt{x} = x^{1/2}$.

1. **State the problem:** Solve the inequality $$-3 < 2(x + 1) < 7$$. 2. **Understand the inequality:** This is a compound inequality meaning both inequalities must be true simulta

1. **State the problem:** Solve the inequality $5d - 3 > d + 17$ for $d$. 2. **Write down the inequality:**

1. The problem asks to identify which of the given items are expressions. 2. An expression is a mathematical phrase that can contain numbers, variables, and operation symbols but d

1. **State the problem:** Calculate the value of $27 \frac{2}{3} - \left( \frac{1}{8} \right)^{\frac{1}{3}}$. 2. **Convert mixed number to improper fraction:**

1. Stating the problem: Solve the equation $x - 5 = 0$. 2. Formula and rules: To solve for $x$, isolate $x$ by adding or subtracting terms on both sides.

1. We are given the equation: $$2 \log(x - 5) = -1 + 2 \log(x + 3)$$ 2. The goal is to solve for $x$ exactly.

1. **State the problem:** Calculate $\left(1 \frac{3}{4} + 2 \frac{1}{3}\right) \div \frac{5}{6}$.\n\n2. **Convert mixed numbers to improper fractions:**\n$1 \frac{3}{4} = \frac{7}

1. **State the problem:** Simplify the polynomial expression $$(-3x^2 + x) - (x^3 - 7x + 8)$$ by subtracting the second polynomial from the first. 2. **Write the expression clearly