🧮 algebra

1. **State the problem:** We are given an expression for the perimeter of a rectangle as $8w$, where $w$ is the width in inches. 2. **Recall the formula for the perimeter of a rect

1. El problema es evaluar la expresión $$3\cdot(4-6)^2 + \sqrt{5+\sqrt{36}} - 5$$. 2. Primero, recordemos que la potencia y la raíz cuadrada tienen prioridad sobre la suma y resta.

1. **State the problem:** Simplify the expression $a^2 + a^2 - 36$ when $a = 3$. 2. **Write the formula and rules:** The expression involves squaring a variable and combining like

1. Planteamos el problema: calcular el impuesto predial que consta de un valor fijo más dos componentes variables. 2. Definimos las variables:

1. Let's clarify the factorization of the quadratic expression $x^2 + 7x + 12$. 2. The goal is to find two numbers that multiply to the constant term 12 and add up to the coefficie

1. **State the problem:** Solve the equation $7x + 12 = (x + 3)(x + 4)$ and understand how the factors 3 and 4 appear. 2. **Expand the right side:** Use the distributive property (

1. The problem is to find the x-intercepts of the quadratic function $y = x^2 + 7x + 12$. 2. X-intercepts occur where $y=0$, so we solve the equation $x^2 + 7x + 12 = 0$.

1. **Problem Statement:** Factor the quadratic expressions: a) $y = x^2 + 13x + 12$

1. **State the problem:** We are given the expression for the total number of candies in $b$ bags as $$bg + by$$ where $g$ is the number of green candies per bag and $y$ is the num

1. The problem is to evaluate the function $f(x) = x^2 \sqrt{4x} + 20$ at $x=0$. 2. The formula given is $f(x) = x^2 \sqrt{4x} + 20$.

1. **State the problem:** Solve the system of equations by the addition method: $$\begin{cases} x + y = -3 \\ x - y = 11 \end{cases}$$

1. **State the problem:** Solve the system of linear equations: $$\begin{cases} x + y = -3 \\ x - y = 11 \end{cases}$$

1. The problem is to solve the equation $17 = 0$. 2. This is a simple equation where we check if the number 17 equals zero.

1. **State the problem:** Solve the equation $$0.1p - 0.2p + 2 = -4.6$$ 2. **Combine like terms:**

1. **Problema:** Resolver a equação $x + 2y = 1$ em ordem a $x$. 2. **Fórmula e regra:** Para isolar $x$, subtraia $2y$ dos dois lados da equação.

1. **State the problem:** Solve the inequality $2x^2 + 3x - 5 \leq 0$. 2. **Formula and rules:** To solve a quadratic inequality, first find the roots of the quadratic equation $2x

1. The problem is to express the phrase "MAKE it algabretic" algebraically, which likely means to translate a statement or instruction into an algebraic expression or equation. 2.

1. The problem is to verify the domain of the function $y = \frac{\sqrt{3x-4}}{x}$ given as $\left(\frac{4}{3}, \infty\right)$.\n\n2. The domain of a function is the set of all $x$

1. Let's state the problem: Find the value of $x$ in the equation $$3x + 5 = 20$$. 2. The formula used here is to isolate $x$ by performing inverse operations. Important rules: add

1. The problem asks to evaluate or simplify several mathematical expressions involving roots, powers, and fractions. 2. We will evaluate each expression step-by-step using the orde

1. **State the problem:** We need to find an angle whose complement is 5 times as large as the angle itself. 2. **Recall the definition of complementary angles:** Two angles are co