🧮 algebra

1. **State the problem:** We need to determine which polynomial function passes through the points (2,5), (3,2), and (4,5). 2. **Given functions:**

1. **State the problem:** We need to find the equations of lines parallel to given lines (Line 1, Line 2, Line 3) passing through specific points (4,7), (9,6), and (-3,12). 2. **Re

1. State the problem: Solve the equation $2x + 3 = 7$ for $x$. 2. Use the formula for solving linear equations: isolate $x$ by performing inverse operations.

1. The problem is to find the value of $x$ in the equation $$\frac{2x+3}{4} = 5.$$ 2. The formula used here is to solve linear equations by isolating the variable $x$.

1. The problem is to find the value of $x$ in the equation $$\frac{3x+2}{5} = 4.$$\n\n2. The formula used here is to solve linear equations by isolating the variable $x$. The key r

1. **Problem statement:** Find the coefficient of $x^4$ in the expansion of $$\left(\frac{x}{2} - \frac{3}{x^2}\right)^{10}.$$\n\n2. **Formula used:** We use the Binomial Theorem f

1. **State the problem:** We are given the first two terms of a geometric progression (GP): $a_1 = \frac{1}{4}$ and $a_2 = \frac{15}{2}$. We need to find the common ratio $r$ of th

1. **State the problem:** We have a square piece of paper with side length $x$ and area $x^2$. It is divided into smaller squares, each with side length $\frac{x}{4}$. We want to f

1. **Stating the problem:** We have two taps flowing simultaneously. One tap flows at 10 ml/s, the other at 20 ml/s.

1. **State the problem:** Add the expressions $$- \frac{7}{x^2 + 3x - 10} + \frac{12}{x^2 - 2x - 35}$$. 2. **Factor the denominators:**

1. **Stating the problem:** We have two taps flowing simultaneously. One tap flows at 10 milliliters per second, the other at 5 milliliters per second.

1. **State the problem:** Several friends want to buy basketball shoes costing $59.17. They earn $9 per hour doing yard work. We need to find who earned enough money to buy the sho

1. **State the problem:** We want to find which tennis players earned enough money to attend a tennis day camp costing 74.50 each by washing cars at 8.25 per hour. 2. **Write the i

1. Planteamos el problema: El precio inicial de la laptop es 4255 soles y después de 3 años su precio es 3645 soles. 2. La depreciación es lineal, por lo que el precio $P(t)$ en fu

1. **Problem Statement:** We need to find the invariant points of the reciprocal of a linear function. An invariant point is where the function and its reciprocal intersect, meanin

1. **State the problem:** Solve the system of linear equations: $$x + y = -10$$

1. **State the problem:** Find the equation of a circle with center at $(-3,-5)$ and radius $8$ in the form $x^2 + Ax + y^2 + By = C$. 2. **Recall the standard form of a circle's e

1. **Planteamiento del problema:** Calcular los valores de $B$ y $C$ dados por las expresiones:

## Problem Solve the system:

1. **Stating the problem:** We are given two expressions: $$a = 10^2 + 10^{-2} + 10 + 10^{-1}$$

1. Vamos simplificar a expressão dada: $$0,25 - 1 : 12 - 2$$. 2. Primeiro, lembramos que a divisão deve ser feita antes da subtração, então calculamos $$1 : 12 = \frac{1}{12}$$.