🧮 algebra

1. Énonçons le problème : Résoudre l'équation quadratique $$10x^2 + 3x - 18 = 0$$. 2. La formule générale pour résoudre une équation quadratique $$ax^2 + bx + c = 0$$ est :

1. **Planteamiento del problema:** Resolver la ecuación $$-3x - 4 = 20$$ para encontrar el valor de $$x$$. 2. **Fórmula y reglas:** Para resolver ecuaciones lineales, aislamos la v

1. **State the problem:** Solve the inequality $$4x^2 + 12x + 9 > 0$$. 2. **Identify the type of inequality:** This is a quadratic inequality. We will analyze the quadratic express

1. **State the problem:** Isabelle needs to reduce her remaining practice hours by driving 4 hours a week for 3 weeks. We want to find expressions that represent the change in her

1. The problem asks to identify which inequality corresponds to the shaded region on the graph. 2. The line given is $y = 4x - 2$, and it is dashed, indicating a strict inequality

1. **State the problem:** We need to find the equation that best represents the savings data where the amount saved increases each month. 2. **Identify the variables:** Let $x$ be

1. **Problem statement:** Given functions $f(x) = 8x^3$ and $g(x) = -2x^{3/2}$, find $(fg)(x)$ and $\left(\frac{f}{g}\right)(x)$, state their domains, and evaluate both at $x=4$. 2

1. **State the problem:** Simplify the expression $10 - (1 + 3) + 7$. 2. **Apply the order of operations:** First, simplify inside the parentheses.

1. The problem asks for an expression representing the total number of marbles in 8 bags, each containing $v$ marbles. 2. To find the total number of marbles, we multiply the numbe

1. **State the problem:** A farmer has two adjacent rectangular fields sharing a common lengthwise fence. The total length of the combined fields is $50 \frac{1}{8}$ meters and the

1. Planteamos el problema: Resolver la expresión $$ (x^{-1})^{3^2} - ((x^{-1})^3)^2 \cdot x^{15} = 1 $$ 2. Recordemos las propiedades de potencias importantes:

1. **State the problem:** Factor the expression $$x^3 - 64$$ completely. 2. **Recognize the formula:** This is a difference of cubes since $$64 = 4^3$$.

1. **Problem: Factor completely** the expression $25x^2 - 9$. 2. Recognize this as a difference of squares since $25x^2 = (5x)^2$ and $9 = 3^2$.

1. **Problem 1: Factor completely** the expression $$25x^2 - 9$$. 2. This is a difference of squares since $$25x^2 = (5x)^2$$ and $$9 = 3^2$$.

1. **State the problem:** Divide the polynomial $$x^4 - 3x^3 - 7x - 14$$ by $$x - 4$$. 2. **Formula and rule:** Polynomial division is similar to long division with numbers. We div

1. **State the problem:** We need to analyze the function $$y=4x^2-81$$. 2. **Formula and rules:** This is a quadratic function in the form $$y=ax^2+bx+c$$ where $$a=4$$, $$b=0$$,

1. **State the problem:** Factor and solve for the x-intercepts of the quadratic function $$y=3x^2 - 36x + 60$$. 2. **Formula and rules:** To find x-intercepts, set $$y=0$$ and sol

1. **State the problem:** We want to analyze the sign of the function $$f(x) = x^3 + 2x^2 - 13x + 10$$ by creating a sign chart. 2. **Find the roots of the polynomial:** To create

1. **State the problem:** Simplify the expression $$\frac{\sqrt[5]{\sqrt[10]{.}} \sqrt[10]{a^2 b}}{\sqrt[10]{10}}$$

1. **State the problem:** Simplify the expression $$y = \frac{(-5)^2 - 4^2 + \left( \frac{1}{5} \right)^0}{3^{-2} + 1}$$. 2. **Recall important rules:**

1. **State the problem:** We need to create a sign chart for the function $$g(x) = -x^4 + 2x^3 + 8x^2$$ to determine where the function is positive, negative, or zero. 2. **Find th