🧮 algebra

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

1. **Stating the problem:** We want to find the unit rate, which is the amount of one quantity per one unit of another quantity. 2. **Formula:** The unit rate is found by dividing

1. **Problem Statement:** We are given a piecewise function $c(m)$ that represents cost based on miles driven $m$: $$

1. **State the problem:** We are given a table showing the number of vegetable plants ($x$) and flowers ($y$) planted in a garden. We need to determine if the table shows a proport

1. **Problem (2a):** Find the ratio of First Class seats to Premium seats to Economy seats given 14, 70, and 168 seats respectively. 2. **Formula and rule:** To find the simplest r

1. Тодорхойлж байна: Өгөгдсөн муруй нь $y = 4x + 1$. 2. Өгөгдсөн шулуун нь $32x - y = 15$.

1. **Problem (a):** Luc uses $\frac{3}{4}$ of a tin per door and needs to paint 7 doors. Find the least number of tins needed. 2. **Formula:** Total paint needed $= 7 \times \frac{

1. The problem is to understand where the condition $x=0$ comes from when solving for zeros of a function. 2. When solving for zeros of a function, we are finding the values of $x$

1. The problem is to simplify the expression $$\frac{n+x}{x} - \frac{x}{x}$$. 2. Recall the rule that $$\frac{a}{b} - \frac{c}{b} = \frac{a-c}{b}$$ when the denominators are the sa

1. The problem is to understand the expression $x^x$ and rewrite it using exponential and logarithmic functions for $x > 0$. 2. We start with the expression:

1. Let's start by stating the problem: "Solve for zeros" means finding the values of the variable (usually $x$) that make the function equal to zero. 2. The general formula or rule

1. Let's clarify step 7 in detail. 2. Step 7 involves applying the formula or rule that was introduced earlier in the problem.