🧮 algebra

1. **State the problem:** Solve the quadratic equation $$x^2 + 7x + 5 = 0$$ for $x$. 2. **Formula used:** The quadratic formula to solve $ax^2 + bx + c = 0$ is

1. **Nyatakan masalah:** Diberi nombor kompleks $z = 4 - \sqrt{3}i$, kita diminta untuk:

1. **Problem statement:** Consider the expansion of $ (2 + x)^n $, where $ n > 3 $ and $ n \in \mathbb{Z} $. The coefficient of $ x^3 $ is four times the coefficient of $ x^5 $. Fi

1. **Problem Statement:** Consider the expansion of $(2 + x)^n$, where $n > 3$ and $n \in \mathbb{Z}$. The coefficient of $x^3$ is four times the coefficient of $x^5$. Find the val

1. **State the problem:** We need to find the values of the function $y = x^2 + 2x + 1$ for $x$ from 1 to 2. 2. **Formula and explanation:** The function is a quadratic polynomial.

1. **State the problem:** We need to find the values of the function $y = x^2 + 2x + 1$ for $x$ from 1 to 2. 2. **Recall the function:** The function is a quadratic polynomial give

1. **Stating the problem:** We want to find the values of $m$ such that the expression $w - 9\tau - x(\tau - m) \geq 0$ is always positive (or zero) for all $x$ and $\tau$. 2. **Re

1. **State the problem:** We are given two vertices of a triangle, $A(2,1)$ and $B(3,-2)$, and the area of the triangle is 5. The third vertex $C$ lies on the line $y = x + 3$. We

1. **State the problem:** Find the equation of the straight line passing through points (0,7) and (1,0) in the form $y = mx + c$. 2. **Formula and rules:** The equation of a line i

1. **State the problem:** We are given a piecewise function defined as: $$f(x) = \begin{cases} -2x - 7 & \text{if } x \leq -5 \\ \frac{2}{5}x + 5 & \text{if } x > -5 \end{cases}$$

1. **State the problem:** We need to graph the system of linear inequalities: $$y < -3x + 3$$

1. **State the problem:** Solve the system of equations using elimination: $$\begin{cases} 3x + 10y = -4 \\ 2x + 2y = 2 \end{cases}$$

1. **State the problem:** Solve the system of equations using substitution: $$y = -8x + 10$$

1. **State the problem:** We need to solve the system of equations by graphing: $$y = \frac{1}{2}x + 1$$

1. **State the problem:** We need to divide $w$ by 3, then multiply $v$ by the result. 2. **Write the expression:** Dividing $w$ by 3 is written as $\frac{w}{3}$.

1. The problem is to subtract the fractions $\frac{9}{10}$ and $\frac{1}{2}$. 2. To subtract fractions, they must have a common denominator. The denominators here are 10 and 2.

1. The user asks if their simplification is correct, but no specific expression or problem is provided. 2. To verify simplification, one must provide the original expression and th

1. **State the problem:** Simplify the expression $\frac{7}{10} - \left(-\frac{1}{2}\right)$. 2. **Recall the rule:** Subtracting a negative number is the same as adding its positi

1. **State the problem:** Find the slope $m$ of the line passing through points $(1,7)$ and $(2,10)$. 2. **Formula:** The slope formula is $$m = \frac{y_2 - y_1}{x_2 - x_1}$$ where

1. **Problema:** Encontrar a função volume $V(x)$ de uma caixa feita a partir de um retângulo de papelão, onde $x$ é o tamanho do recorte quadrado nas extremidades. 2. **Fórmula us

1. **State the problem:** We need to evaluate the function $f(x) = -3x + 3$ at $x = 2$. 2. **Formula used:** The function is given by $f(x) = -3x + 3$. To find $f(2)$, substitute $