🧮 algebra

1. **State the problem:** We need to find the slope $m$ of the line passing through the points $(0, -2)$ and $(2, 1)$. 2. **Formula for slope:** The slope $m$ of a line passing thr

1. **State the problem:** Find the slope $m$ of the line passing through the points $(-3, 0)$ and $(0, -5)$. 2. **Formula for slope:** The slope $m$ between two points $(x_1, y_1)$

1. **State the problem:** Solve the equation $$11x + 4 = 10(x - 6) - 5$$ for $$x$$. 2. **Apply the distributive property:** Expand the right side:

1. **State the problem:** We need to solve the equation $$\frac{1}{3} y - 3 = \frac{1}{9} y$$ for $y$. 2. **Write down the equation:** $$\frac{1}{3} y - 3 = \frac{1}{9} y$$

1. **State the problem:** Solve the equation $$9 (x + 1) + 2 = -4 (x - 9) - 4$$ for $$x$$. 2. **Apply the distributive property:**

1. **State the problem:** Solve the equation $$5(2x - 1) = -3x + 4$$ for $$x$$. 2. **Apply the distributive property:** Multiply $$5$$ by each term inside the parentheses.

1. **State the problem:** We need to solve the equation $$6x + 7 = 4x + 6$$ for the variable $$x$$. 2. **Write down the equation:** $$6x + 7 = 4x + 6$$

1. **State the problem:** We need to find which equations have $x=-2$. 2. **Check each equation by substituting $x=-2$: **

1. **State the problem:** Solve the equation $$11 = x^2 + 7$$ for $$x$$. 2. **Isolate the variable term:** Subtract $$7$$ from both sides to isolate $$x^2$$:

1. **State the problem:** We have 6 tasks with times $t_1, t_2, t_3, t_4, t_5, t_6$. The conditions are: - The total time for any 3 adjacent tasks is half the total time for the ne

1. **State the problem:** Jazmin walks a 25.5 km charity walk at 4.25 km/h. We want to find the equation for the remaining distance $y$ after $x$ hours, interpret intercepts, domai

1. **State the problem:** Jazmin is walking a total distance of 25.5 km at a rate of 4.25 km/h. We want to write an equation for the remaining distance $y$ after $x$ hours, analyze

1. **State the problem:** Find the equation of the line passing through points $(0, -1)$ and $(2, -3)$ in slope-intercept form $y = mx + b$. 2. **Calculate the slope $m$:**

1. **Énoncé du problème** : Montrer par récurrence que pour tout $n \in \mathbb{N}$, la somme $S_n = \sum_{k=0}^n \left(-\frac{1}{3}\right)^k$ vérifie la formule $$S_n = \frac{3}{4

1. The problem is to solve the equation $$-t=5$$ for the variable $$t$$. 2. The equation states that the negative of $$t$$ equals $$5$$.

1. **State the problem:** We need to find the difference between the quotient of $2$ and $5$, and the number $4$. 2. **Write the quotient:** The quotient of $2$ and $5$ is $$\frac{

1. **State the problem:** We need to find the square root of the quotient of $11$ and $6$. 2. **Write the expression:** The quotient of $11$ and $6$ is written as $$\frac{11}{6}$$.

1. **State the problem:** Simplify the expression $$2 (3x^2 + 7x + 3) - 3 (2x^2 + 6x + 4)$$ and write it in the form $$ax^2 + bx + c$$. 2. **Use the distributive property:** Multip

1. **State the problem:** Simplify the expression $4 (7x^2 + 6x + 6) - 6 (7x^2 + 2x + 6)$ and write it in the form $ax^2 + bx + c$. 2. **Apply the distributive property:** Multiply

1. **State the problem:** Simplify the expression $$4 (7x^2 + 6x + 6) - 6 (7x^2 + 2x + 6)$$ and write it in the form $$ax^2 + bx + c$$. 2. **Apply the distributive property:** Mult

1. **State the problem:** We are given the side lengths of an original figure and its scaled copy. We need to find the constant of proportionality (scale factor) from the original