🧮 algebra

1. **State the problem:** Find the distance between the points $A(15, -10)$ and $B(15, 22)$. 2. **Formula used:** The distance between two points $(x_1, y_1)$ and $(x_2, y_2)$ is g

1. The user asked "nilai n nya berapa" which means "what is the value of n?" but no specific problem or equation involving n was provided. 2. To find the value of n, we need an equ

Lo siento, no tengo los números que mencionas. Envíame los valores (por ejemplo: 2, 5, 9) y dime qué ejercicio o qué operación hay que hacer con ellos.

1. Planteamiento del problema: Una bacteria se duplica cada hora, y empiezas con $1$ bacteria. ¿Cuántas habrá en $5$ horas? 2. Modelo (fórmula): si se duplica cada hora, entonces

1. **State the problem:** Solve the equation $$\frac{3}{2}x - \frac{7}{2} = \frac{19}{10} + \frac{9}{4}x$$ for $x$. 2. **Write down the equation:**

1. **State the problem:** We are asked to find how many solutions exist for the system of linear equations: $$y = 3x + 8$$

1. **State the problem:** We need to find how many solutions exist for the system of linear equations: $$y = 2x + 5$$

1. The problem involves computing and simplifying fractions given in a grid format. 2. We use the central grid cell at position_hint=center to compute the fraction values: 4, \frac

1. **State the problem:** Solve the system of linear equations: $$2x + y = 8$$

1. **State the problem:** Solve the system of linear equations for $x$ and $y$: $$2x + y = 8$$

1. **State the problem:** We need to find the equations that model the locus of the line graphed on the coordinate plane, given $d=3.5$ and a horizontal line segment at $y=2$. 2. *

1. **State the problem:** We have two inequalities and sets of possible solutions. We need to determine which numbers satisfy each inequality.

1. The problem appears to involve the expression $x i 2 2 \Sigma - b2$, which seems unclear but likely involves summation and algebraic terms. 2. Let's clarify the expression: if i

1. State the problem. We have the system of equations:

1. State the problem: Compute the determinant of the coefficient matrix for the system $x+y+z=6$, $2x+y+z=9$, $x+2y+z=7$. 2. Identify the coefficient matrix $A$:

1. The problem is to simplify the expression: $$24uv^2 - 2g - 70$$. 2. We look for common factors in each term to factor the expression.

1. **State the problem:** Simplify the expression $$3y(5 - 8y^2)(4x + 8y) - (3 - 5y)(20 - 7) + 5y^2$$. 2. **Apply the distributive property and simplify constants:**

1. **Simplify the expression (6k − 4) + (2k + 4):** Combine like terms: $6k + 2k = 8k$ and $-4 + 4 = 0$

1. **State the problem:** Find the inverse of the function $g(x) = \frac{3x+1}{5x+3}$. 2. **Formula and rules:** To find the inverse function $g^{-1}(x)$, we swap $x$ and $y$ and s

1. The problem asks to find the value of $h^{-1}(3)$ given that $h(5) = 3$. 2. Recall that $h^{-1}$ is the inverse function of $h$, which means that if $h(a) = b$, then $h^{-1}(b)

1. **Stating the problem:** Simplify and solve the equation given: $$8x = 28 \times 2 + 6x$$ 2. **Write down the equation:** $$8x = 56 + 6x$$ because $28 \times 2 = 56$