🧮 algebra

1. **State the problem:** We have 24 players on a baseball team. Seventh graders are \(\frac{1}{6}\) of the players. These seventh-grade players represent about 3% of all seventh-g

1. Problem 16: Given the function $g(x) = -f(x-3)$, solve the inequality $g(x) < 0$ and find the interval where this holds. 2. Since $g(x) = -f(x-3)$, the inequality $g(x) < 0$ is

1. Planteamos el problema: Resolver la ecuación fraccional $$\frac{3}{1 - x} = \frac{6}{2x + 5}$$. 2. Usamos la regla de igualdad de fracciones: si $$\frac{a}{b} = \frac{c}{d}$$ y

1. **State the problem:** Find the equation of the line passing through the points $(-2,6)$ and $(1,-3)$.\n\n2. **Formula used:** The slope $m$ of a line through points $(x_1,y_1)$

1. **State the problem:** Solve the inequality $$-x + 2 + 3x \geq \frac{1}{2}$$. 2. **Combine like terms:** Combine the terms with $x$ on the left side.

1. The problem is to calculate the simple interest $I$ using the formula: $$I = prt$$

1. **Stating the problem:** Solve the equation $$2x + 4 = 2x + 4$$ for $$x$$. 2. **Formula and rules:** When solving equations, if after simplifying both sides are identical, it me

1. Problema: Duota sekos $a_n = -n^2 + 26n - 91$ formulė. Reikia nustatyti, kiek teigiamų narių turi ši seka. 2. Formulė ir taisyklės: Sekos narys yra teigiamas, jei $a_n > 0$. Tod

1. Planteamos el problema: Factorizar la expresión $$9x^2 - 6xy + y^2$$. 2. Recordemos que para factorizar un trinomio cuadrado perfecto de la forma $$a^2 - 2ab + b^2$$, el resulta

1. **Problem Statement:** Solve the equation $$\frac{2x+3}{4} = 5$$ for $x$. 2. **Formula and Rules:** To solve for $x$, we need to isolate $x$ on one side of the equation. We can

1. **State the problem:** Simplify the expression $$2\sqrt{5} + \sqrt{5} + \sqrt{20}$$. 2. **Recall the rules:**

1. El problema es graficar la función $$f(x) = \log_{\frac{1}{2}}(x)$$. 2. Esta es una función logarítmica con base $$\frac{1}{2}$$, que está entre 0 y 1, por lo que la función es

1. **State the problem:** A company donates 7.20 each time a social media post is shared. The post is shared 2731 times, and the total donation is divided evenly among 4 charities.

1. **Problem:** Determine if the pairs of lines are parallel, perpendicular, or neither. 2. **Recall:**

1. **State the problem:** Solve the system of equations: $$3x - 5x = 11 - 5$$

1. **State the problem:** Solve the equation $3(x - 2) = 12$ for $x$. 2. **Use the distributive property:** Multiply 3 by each term inside the parentheses.

1. **State the problem:** Simplify the expression $$\frac{3x - 2}{x^2 - 2x} - \frac{2}{x - 2}$$. 2. **Factor the denominators:**

1. **Problem:** Simplify the expression $$\frac{a - b}{ab} + \frac{b - c}{bc} + \frac{c - a}{ca}$$ 2. **Formula and rules:** To add fractions, find a common denominator. Here, the

1. **State the problem:** Calculate the value of the complex number expression $ (2 + 3i)^2 $. 2. **Formula and rules:** To square a complex number $ (a + bi) $, use the formula:

1. **State the problem:** We are given two functions $f(x) = -2x^2$ and $g(x) = -4x^2$ and the domain $-4 \leq x \leq -2$. We want to analyze these functions over this interval. 2.

1. The problem involves simplifying and evaluating the expression given in the first question, which is a combination of logarithms, powers, and arithmetic operations. 2. Recall th