🧮 algebra

1. **Problem Statement:** Solve the first equation from SET 1: $5(x - 1) = 35$. 2. **Formula and Rules:** To solve linear equations, distribute multiplication over addition/subtrac

1. Problem: Solve for $x$ in the equation $x + 3y = 11$. 2. Formula: To solve for $x$, isolate $x$ on one side of the equation.

1. The problem asks for the slope and length of a line segment, but no specific points or line equation are given. 2. To find the slope between two points $(x_1, y_1)$ and $(x_2, y

1. **Problem Statement:** Sketch the graph of the quadratic function $f(x) = -2x^2 + 5x + 2$ and find its vertex, axis of symmetry, and intercepts.

1. **State the problem:** We are given several linear expressions and asked to analyze or simplify the first expression: $$\frac{2x - 12}{8}$$. 2. **Formula and rules:** To simplif

1. **Problem statement:** Find the intersection points of the parabolas in part (a): $$y = x^2 + 4x - 1$$

1. **State the problem:** Solve the equation $$\frac{2x + 1}{3} = -3$$ for $x$. 2. **Formula and rules:** To solve for $x$, we need to isolate $x$ on one side. Since $2x + 1$ is di

1. **State the problem:** Solve the equation $$\frac{x+4}{3} = -6$$ for $x$. 2. **Formula and rules:** To solve for $x$, multiply both sides of the equation by 3 to cancel the deno

1. Énoncé du problème : Calculer le déterminant de la matrice $$F=\begin{pmatrix}3m+1 & m-1 & m^2+1 \\ -5-m & 2m-2 & 2m \\ 2+2m & -m^2+2m & m+1\end{pmatrix}$$ en le factorisant le

1. **State the problem:** Simplify the expression $$\frac{x^2 - 9}{x^2 - 7x + 12} \div \frac{x}{5x - 20}$$ as a single fraction in fully factorised form. 2. **Rewrite division as m

1. **Énoncé du problème** : Calculer le déterminant de la matrice $F$ donnée par $$F = \begin{pmatrix} 3m + 1 & m - 1 & m^2 + 1 \\ -5 - m & 2m - 2 & 2m \\ 2 + 2m & -m^2 + 1 & m + 1

1. Il problema chiede di determinare per quali valori di $k$ l'equazione $x^2 - 3x + k = 1$ soddisfa alcune condizioni. 2. Riscriviamo l'equazione in forma standard:

1. **State the problem:** Solve for $x$ in the equation $$\sqrt{\frac{(x+2)!}{x!}} = \sqrt{3!} \times 7.$$\n\n2. **Recall factorial properties:** The factorial function $n!$ is the

1. **State the problem:** Evaluate the expression $5(-3)+(6-1)^2$. 2. **Apply order of operations:** First, calculate inside the parentheses and exponents.

1. **State the problem:** Evaluate the expression $5^2 - 4 \cdot 3 + \frac{28}{4}$. 2. **Recall order of operations:** Use PEMDAS (Parentheses, Exponents, Multiplication and Divisi

1. **State the problem:** Solve the system of linear equations: $$\begin{cases} x + y - 9z + w = -8 \\ 3y - 5z - w = 2 \\ 6z - 7w = 7 \\ 3w = 6 \end{cases}$$

1. We are asked to calculate the function $x^3$ using summations. 2. The function $x^3$ can be expressed as the sum of the first $x$ squares using the formula:

1. **State the problem:** Solve for $z$ in the equation $$\frac{5}{5x+7} + \frac{z}{2x+7} = \frac{1}{7-2x}.$$

1. Let's state the problem: Evaluate the expression $3(-2) + 3$ and understand why it equals $-3$ and not $4$. 2. The expression is $3(-2) + 3$.

1. The problem is to identify the variables in a given mathematical expression or equation. 2. Variables are symbols that represent unknown or changeable values in mathematics, oft

1. **Problem statement:** We are given the equation $$y = 3x + 3$$ and asked to: (a) Create a table of y-values for $$x = -2, -1, 0, 1, 2$$.