🧮 algebra

1. **Planteamiento del problema:** Queremos encontrar la ecuación vectorial de la recta $M$ que pasa por el punto $P=(7,2)$ y tiene como vector dirección $\vec{v} = (5, -6)$.

1. **Problem statement:** Solve the system of equations using the addition (elimination) method. 2. **Method:** The addition method involves adding or subtracting the equations to

1. **State the problem:** We need to fill in digits 1 to 9 in three logarithmic expressions to produce specified types of numbers: an integer, an irrational number, and a rational

1. **State the problem:** Find the equation of the line joining the points (4,1) and (7,3). 2. **Formula used:** The slope $m$ of a line through points $(x_1,y_1)$ and $(x_2,y_2)$

1. **State the problem:** Find the equation of the line passing through the points (4,1) and (7,3), and also the line passing through (-5,1) and (-3,-2). 2. **Formula used:** The s

1. **State the problem:** Simplify the expression $-(-526+-350)-150+74$. 2. **Rewrite the expression:** Note that $-(-a) = a$, so

1. **Problem:** Find the equation of the line joining the points (4,1) and (7,3). 2. **Formula:** The slope $m$ of the line through points $(x_1,y_1)$ and $(x_2,y_2)$ is given by:

1. **State the problem:** We need to find the range of values of $a$ (where $a \neq 0$) such that the cubic equation $$2x^3 - 3ax^2 + a^3 - 2a = 0$$ has exactly one real root. 2. *

1. **Problem 2:** Find the gradient for each line and express the equation in the form $ax+by+c=0$. 2. **Problem 3:** Find the equation of the line through point $(2,5)$ with gradi

1. The problem is to find the gradients (slopes) of the lines given by the equations j: 4x - y = 8, k: x + 2y - 2 = 0, and l: 4x = 2 + 3y by rearranging them into the form $y = mx

1. **Problem:** Find the equation of the line that passes through the point (6, -7) and is parallel to the line $$2x - 3y + 4 = 0$$. 2. **Formula and rules:**

1. Planteamos el problema: Simplificar las siguientes operaciones con raíces de distintos índices. 2. Recordemos que para multiplicar o dividir raíces del mismo índice, podemos ope

1. **Find the equation of the line that passes through (4,3) with gradient $g=2$.** The formula for the equation of a line with gradient $m$ passing through point $(x_1,y_1)$ is:

1. **State the problem:** We are given a function $f(x)$ and asked to find the values of $x$ for which $f(x) = 0$. 2. **Understand the problem:** The values of $x$ where $f(x) = 0$

1. **Find the equation of the line that passes through (4,3) with gradient 2.** The formula for the equation of a line with gradient $m$ passing through point $(x_1,y_1)$ is:

1. The problem is to find the gradient of a line given by the equation $ax + by + c = 0$. 2. The formula to find the gradient $m$ of a line in the form $ax + by + c = 0$ is:

1. **State the problem:** Solve the equation $5^n = n + 2^n$ for $n$. 2. **Understand the equation:** We want to find the value(s) of $n$ such that the exponential expression $5^n$

1. **State the problem:** Solve the equation $25^{x-1} = 125^{2-x}$ for $x$. 2. **Recall the formula and rules:** We can express both sides with the same base to simplify the equat

1. **State the problem:** Solve the equation $$7^{x+2} - 7^{x+1} + 7^x = 86$$ for $x$. 2. **Rewrite the equation using properties of exponents:** Recall that $$7^{x+2} = 7^x \cdot

1. **State the problem:** We need to find the coordinates where the graph of the function $g(x) = 7x - 7$ intersects the X-axis. 2. **Recall the rule:** The graph intersects the X-

1. **State the problem:** We are given a system of equations: $$x - xy + y = -7$$