🧮 algebra

1. **State the problem:** Find the equation of the line that bisects the obtuse angle between the lines $x - 2y + 4 = 0$ and $4x - 3y + 2 = 0$. 2. **Formula and rules:** The angle

1. The problem is to find the values of $t$ that satisfy a given equation or condition, which seems to be related to roots or solutions. 2. Typically, when solving quadratic equati

1. **State the problem:** Solve the quadratic equation $$x^2 + 5x - 3 = 0$$ for $x$. 2. **Formula used:** The quadratic formula to solve $ax^2 + bx + c = 0$ is

1. **State the problem:** Simplify the expression $$\frac{x^3 + x - 2}{x^3 + 1}$$ or analyze it. 2. **Recall formulas and rules:**

1. **State the problem:** Solve the quadratic equation $$x^2 + 9x + 2 = 0$$. 2. **Formula used:** The quadratic formula for solving $$ax^2 + bx + c = 0$$ is

1. **State the problem:** We are given a graph with points (0,3), (1,1), and (3,-3). We need to find:

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 $\frac{w}{3}$.