🧮 algebra

1. **State the problem:** Find the reciprocal of $$\frac{1}{\frac{a}{b}} + \frac{1}{\frac{c}{ab}}$$. 2. **Rewrite the expression:** The expression inside the reciprocal is $$\frac{

1. **State the problem:** Solve the equation $$3x = 21$$. 2. **Formula and rules:** To solve for $x$, divide both sides of the equation by the coefficient of $x$, which is 3.

1. **Problem:** Given matrix $$M = \begin{pmatrix} 2 & 5 \\ 7 & 15 \end{pmatrix}$$ i) Show that $$M$$ is non-singular.

1. **State the problem:** Malcolm lost 8 kg and now weighs 64 kg. We need to find what percentage of his original weight he lost. 2. **Identify the known values:**

1. **State the problem:** Find the equation of the straight line $L$ in the form $y = mx + c$ given two points on the line: $(0, 2)$ and $(3, 0)$. 2. **Recall the formula:** The eq

1. **State the problem:** Solve the equation $(x - y) + 3i = 4 + yi$ for real numbers $x$ and $y$. 2. **Recall the rule:** For two complex numbers to be equal, their real parts mus

1. **State the problem:** Determine if the line $y=8-x$ is tangent to the curve defined by $2x^2 + xy = -16$. 2. **Substitute the line equation into the curve:** Replace $y$ in the

1. **State the problem:** Solve for $x$ and $y$ in the equation $(x+yi)(-i)=3$ where $x$ and $y$ are real numbers. 2. **Recall the formula and rules:** Multiplying complex numbers

1. Planteamos el problema: Resolver la ecuación $$\frac{2(x - 1)}{3} + 1 = \frac{1}{5} - x$$. 2. Usamos la fórmula para resolver ecuaciones lineales: despejar $x$ aislando términos

1. **Problem statement:** Divide the polynomial $f(x) = x^3 + 4x^2 + x - 6$ by the linear factor $(x - 1)$. Find the quotient polynomial. 2. **Formula and rules:** Polynomial divis

1. The problem asks to graph the functions $-f(x)$, $f(-x)$, and $-f(-x)$ based on a given function $f(x)$. 2. These transformations relate to reflections of the graph of $f(x)$:

1. Il problema chiede se l'espressione $-2a + a^2$ è un monomio. 2. Un monomio è un'espressione algebrica costituita da un solo termine, cioè un prodotto di numeri e variabili con

1. **State the problem:** Simplify the expression $-2a + a^2$. 2. **Identify terms:** The expression has two terms: $-2a$ (a linear term) and $a^2$ (a quadratic term).

1. Problem: What is the sum of -3 and 5? 2. Formula: To find the sum of two numbers, add them using the rule for addition of integers.

1. The problem asks to make three numbers each having five digits from the number 47102. 2. A five-digit number must have exactly five digits, and the digits can be rearranged to f

1. **Stating the problem:** We want to learn how to add and subtract algebraic fractions, which are fractions that contain variables in the numerator, denominator, or both. 2. **Fo

1. Let's start by stating the problem: How to add and subtract algebraic expressions. 2. Algebraic expressions are combinations of variables, numbers, and operations like addition

1. **State the problem:** Solve the equation $$\frac{\frac{1}{2}X^{-1/2}}{2} = \frac{1}{4}$$ for $X$. 2. **Rewrite the equation:** The numerator is $\frac{1}{2}X^{-1/2}$ and the de

1. **Problem:** Bestimme die Nullstellen der Geraden. 2. **Formel:** Nullstellen erhält man, indem man $f(x) = 0$ setzt und nach $x$ auflöst.

1. The problem asks: What is "y"? 2. To answer this, we need an equation or context that defines "y". Without additional information, "y" is typically a variable representing a val

1. The problem asks for the slope of the line passing through the points $(-8, 3)$ and $(4, 1)$. 2. The formula for the slope $m$ between two points $(x_1, y_1)$ and $(x_2, y_2)$ i