🧮 algebra

1. Prime Factorization and Number Theory 1.1) Express 660 as a product of its prime factors.

1. The problem is to solve the compound inequality $$14 \leq 6x + 4 \leq 24$$ and express the solution as a fraction in simplest form. 2. We use the property that if $$a \leq b \le

1. **State the problem:** Solve the compound inequality $$-2 < 2x + 11 < 12$$ for $x$. 2. **Understand the inequality:** This is a double inequality, meaning $2x + 11$ is greater t

1. **Stating the problems:** - Find $k$ if $f(3k - 2) = 2k + 3$ given $f(x) = 4x + 1$.

1. The problem asks which equation represents an inverse variation. Inverse variation means $y$ varies inversely as $x$, so $y = \frac{k}{x}$.

1. **Problem Statement:** Convert improper fractions to mixed numbers and mixed numbers to improper fractions. 2. **Formulas and Rules:**

1. **Calculate the area of quadrilateral ABCD** Since the problem does not provide coordinates or side lengths, we cannot calculate the area without additional information.

1. **Evaluate** $\frac{2 + \sqrt{2}}{\sqrt{2}}$. Use the property $\frac{a+b}{c} = \frac{a}{c} + \frac{b}{c}$.

1. Problem: A machine fills 680 bottles in 5 hours. How many bottles will it fill in 3 hours? Formula: Bottles filled are directly proportional to time.

1. **State the problem:** Solve the proportion $4 : x = 9 : 18$ to find the value of $x$. 2. **Recall the rule for proportions:** If $a : b = c : d$, then $\frac{a}{b} = \frac{c}{d

1. **State the problem:** We want to simplify and understand the expression $$63.72 + 1.96 \left( \frac{1.9}{\sqrt{n}} \right)$$ where $n$ is a positive number.

1. **Problem Statement:** Determine the domain and range of the relation defined by the vector \(\vec{AB} = -4\hat{i} + 2\hat{j}\) where point A is at (-1, -1) and point B is at (3

1. **Problem Statement:** Simplify each algebraic expression by factoring and combining like terms. 2. **Expression 1:** $4x^3yz - 8x^2y^2 + 12xy$

1. The problem asks to identify which equation represents an inverse variation. Inverse variation means $y$ varies inversely as $x$, so $y = \frac{k}{x}$ where $k$ is a constant.

1. We gaan de balansmethode gebruiken om een vergelijking op te lossen. 2. De balansmethode houdt in dat je aan beide kanten van de vergelijking dezelfde bewerking uitvoert, zodat

1. Evaluate $\frac{2 + \sqrt{2}}{\sqrt{5}}$. We rationalize the denominator by multiplying numerator and denominator by $\sqrt{5}$:

1. We gaan een vergelijking oplossen met de balansmethode. Dit betekent dat we aan beide kanten van de vergelijking dezelfde bewerking doen om de onbekende te isoleren. 2. Stel de

1. **Stel het probleem vast:** We hebben twee formules voor het gewicht van geitjes Bibi en Boa in kilogram, afhankelijk van de tijd $t$ in maanden: $$\text{Bibi gewicht} = 40 + 25

1. **State the problem:** We are given the function $y = x^3 - 3x^2 + x$ and asked to:

1. **Stating the problem:** We are given three points on a 2D Cartesian coordinate system: (1,1), (2,3), and (3,6). We want to find the equation of the line passing through these p

1. The problem asks for the constant of proportionality (unit rate) between Goblins (x) and power points (y) from the graph. 2. The constant of proportionality in a direct variatio