🧮 algebra

1. **Planteamiento del problema:** Dadas las matrices

1. **State the problem:** Solve the complex equation $$z^3 + 2z^2 + (8 + 6i)z + 16 + 12i = 0$$ given that $$z = -2$$ is a root. 2. **Use the factor theorem:** Since $$-2$$ is a roo

1. O problema pede para encontrar os valores de $a$ e $b$ tais que o número complexo $$z = (a - b^2 i)i - 8 - 5i$$ seja um imaginário puro. 2. Primeiro, vamos expandir a expressão

1. Planteamos el problema: Resolver la ecuación $$\frac{5}{4} \cdot \left(1 + \frac{x}{5}\right) = x - 1$$. 2. Usamos la propiedad distributiva para eliminar el paréntesis:

1. Planteamos el problema: Resolver la ecuación $$\frac{4 - (4 - x)}{3} = \frac{4 + (3 - x)}{4} - 1$$ para encontrar el valor de $x$. 2. Simplificamos las expresiones dentro de los

1. The problem asks us to describe Polly's movement based on her distance from the store over time as shown by the graph. 2. The graph starts at zero distance, then increases linea

1. **State the problem:** Solve the equation $ (x + 1)(x - 1) = 0 $ for $ x $. 2. **Formula and rule:** The zero product property states that if a product of two factors is zero, t

1. The problem is incomplete as no equation or expression is provided to solve or simplify. 2. Please provide a complete mathematical expression or question to proceed with the sol

1. **State the problem:** Divide the polynomial $9x^3 - 2x^2 + 3x - 2$ by $x - 1$. 2. **Formula and rule:** Polynomial division can be done using long division or synthetic divisio

1. **State the problem:** We want to find which expression is equivalent to $16 + 2 \cdot 36$. 2. **Calculate the original expression:**

1. **State the problem:** We need to find which expression among F, G, H, and J is equivalent to $1000 + 196$. 2. **Calculate the sum:**

1. Let's evaluate each expression step-by-step. 2. Evaluate $25 - 3^4$:

1. **Stating the problems:** - Problem 1: Find the value equivalent to the expression shown (options: 19, -11, 7, -14).

1. **State the problem:** We need to find which expressions are equivalent to the given sums.

1. **State the problem:** Evaluate the numeric expression $$5^2 - 6(4^2 - 10) - 3$$ and find which value among (A) 19, (B) -11, (C) 7, (D) -14 is equivalent. 2. **Recall the order

1. **State the problem:** Evaluate the expression $5 - 2(3)^2 + 4$. 2. **Recall the order of operations:** Use PEMDAS (Parentheses, Exponents, Multiplication and Division, Addition

1. **State the problem:** We want to find the amount Rosa saves out of 100 dollars, given a ratio table of dollars saved to dollars earned. 2. **Given data:**

1. **State the problem:** Vista pickleball team needs to win 3 out of 15 games. We want to find what percent this represents, which means finding an equivalent ratio with a denomin

1. **State the problem:** Factor the expression $$p^{12}q^{2} - p^{3}q^{6}$$. 2. **Identify the greatest common factor (GCF):**

1. **State the problem:** We need to write a linear function that represents the total cost $y$ of a charity gala based on the number of attendees $x$. 2. **Identify the components

1. **State the problem:** A florist needs 12 roses for each round table and 36 roses for a centerpiece. We want to write an equation for the total number of roses $y$ depending on