🧮 algebra

1. Problema: Calcula simplificando durante el cálculo siempre que sea posible la expresión a) $\frac{3}{5} + \frac{2}{3} \cdot \frac{1}{5} + \frac{1}{3}$. 2. Fórmulas y reglas impo

1. **State the problem:** Given $|a|=5$, $|b|=20$, and $|a-b|=15.5$, find $|a+b|$. 2. **Recall the formula:** For any vectors or numbers $a$ and $b$, the identity

1. The problem is to verify if the given evaluated expressions are correct for the specified variable values. 2. We will check each expression step-by-step by substituting the give

1. **Problem statement:** Find an explicit formula for the sequence defined by $a_1 = -4$ and the recursive relation $a_n = a_{n-1} + 9$ for $n \geq 2$. 2. **Understanding the prob

1. **State the problem:** Evaluate the expression $$2 + 3t$$ for $$t = 10$$. 2. **Write the formula:** The expression is $$2 + 3t$$.

1. **State the problem:** We need to find the equation of a circle given its center and radius from the graph. 2. **Recall the formula for a circle's equation:** The standard form

1. **Stating the problem:** We need to verify if the answers given for the algebra questions are correct. 2. **Definition of a variable:** A variable is an unknown number or symbol

1. **State the problem:** We need to find the equation of a circle centered at the point $(5, 1)$ with a radius of $2$ units. 2. **Recall the formula for a circle's equation:** The

1. **State the problem:** We need to find the equation of a circle given its center and radius. 2. **Recall the formula:** The standard form of a circle's equation with center $(h,

1. The problem is to solve the equation $2x + 3 = 11$ for $x$. 2. We use the basic algebraic principle of isolating the variable $x$ by performing inverse operations.

1. The problem asks to write an equation representing the distance $d$ in kilometers of each bird after $t$ hours. 2. To write such an equation, we need to understand the relations

1. **State the problem:** Find the product of the polynomials $$(x^3 + 2x^2 - x - 2)(x^2 + x - 1).$$ 2. **Recall the distributive property:** To multiply two polynomials, multiply

1. **Problem:** Find the zeroes of the polynomial equation $$x^8 - 26x^4 + 25 = 0$$ and factor it. 2. **Step 1: Recognize the substitution.** Let $$y = x^4$$. Then the equation bec

1. **State the problem:** We need to determine which system of inequalities matches the graph described. 2. **Analyze the graph:**

1. **State the problem:** Find the product of the polynomials $$(x^2 - x^3 + 1)(x^2 - 1).$$ 2. **Recall the distributive property:** To multiply two polynomials, multiply each term

1. **State the problem:** We need to determine which system of inequalities matches the described graph. 2. **Analyze the given lines:**

1. **Problem 25:** Determine which of the options is NOT a factor of the trinomial $24x^3 - 6x^2 - 9x$. 2. **Step 1:** Factor out the greatest common factor (GCF) from the trinomia

1. **State the problem:** Eric and Lucia play a game where points are earned by traveling to asteroids and planets. Eric travels to 1 asteroid and 8 planets, earning 132 points. Lu

1. **State the problem:** We need to divide the polynomial $9x^3 + 18x^2 - 4x + 8$ by the binomial $3x + 2$ and express the result in the form of a quotient plus a remainder over t

1. **State the problem:** You and your friend each have a meal with given costs, sales tax, and tips. We need to calculate the total amount each person spends and determine who spe

1. **State the problem:** We are given the polynomial $$f(x) = 4x^3 + 15x^2 - 63x - 54$$ and told that one zero is $$x = -6$$. We need to find another zero of $$f(x)$$. 2. **Use th