🧮 algebra

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 $$x = -2, -1, 0, 1, 2$$.

1. Vamos analisar a função quadrática dada: $$f(x) = 2x^2 - 20x + 5$$. 2. O contradomínio de uma função quadrática é o conjunto de valores que a função pode assumir. Como o coefici

1. **State the problem:** Simplify the expression $ (16 + 39) \times 2 \times 90 - 16 + 293 $. 2. **Apply the order of operations (PEMDAS):**

1. **Problem 11:** Solve the equation $$\frac{x+5}{2} - \frac{4-x}{3} = 1$$. 2. To solve, find a common denominator for the fractions, which is 6.

1. **Problem statement:** Find the equation of the parabola passing through the given points for 2b and 2c, and then solve problem 3 about shifting the coordinate system for the pa

1. **State the problem:** Simplify the expression $2(5x^2 - 10)$. 2. **Recall the distributive property:** $a(b + c) = ab + ac$. This means we multiply each term inside the parenth

1. **State the problem:** Simplify the expression $$(x+1)(x-1)$$. 2. **Formula used:** Use the distributive property (also known as FOIL for binomials):

1. **State the problem:** Simplify the expression $$x^{-2}y^{-2}(x^2 y - 1 - y^2 x^{-1})$$. 2. **Recall the rules:**

1. **State the problem:** Simplify or analyze the expression $4x - 3y$. 2. **Understand the expression:** This is a linear expression with two variables $x$ and $y$. It cannot be s

1. Das Problem: Warum ist die Wurzel in mathematischen Ausdrücken vorhanden? 2. Die Wurzel, insbesondere die Quadratwurzel, ist die Umkehrfunktion der Potenzierung mit 2. Das bedeu

1. Problem 7: Simplify $m + n + \frac{1}{m - n}$. We are given an expression and asked to simplify it or write it as a single fraction.

1. **State the problems:** We have two problems to solve:

1. Stating the problem: Factorise the quadratic expression $$9x^2 + 3xy - 2y^2$$. 2. Formula and rules: To factorise a quadratic in two variables, look for two binomials of the for

1. **State the problem:** Simplify or analyze the expression $4x^2 + x$. 2. **Identify the terms:** The expression consists of two terms: $4x^2$ and $x$.

1. **State the problem:** We need to express the area $A$ of the figure as a function of one variable $x$. The figure consists of a rectangle and two right triangles on top. 2. **I

1. **State the problem:** Expand the expression $ (a - 4)(a^2 + 2a - 3) $. 2. **Recall the distributive property:** To expand, multiply each term in the first parenthesis by each t