🧮 algebra

1. **State the problem:** We need to find the slope of the line passing through the points $(-3, 0)$ and $(1, -3)$ and represent the "rise" and "run" visually. 2. **Formula for slo

1. **State the problem:** We are given two points on a line: $(-3, 0)$ and $(0, -2)$. We need to find the slope of the line by representing the rise and run.

1. **State the problem:** Find the domain and range of the ellipse given by the equation $$\frac{(x-1)^2}{4} + \frac{(y-2)^2}{9} = 1$$ and then graph it.

1. **Problem Statement:** We have a solid cuboid with a square base of side length $x$ units and height $h$ units. The volume is given as 125 units$^3$.

1. **State the problem:** We need to evaluate the expression $$2x + 6y$$ given $$x = -\frac{4}{5}$$ and $$y = \frac{1}{3}$$. 2. **Write the expression with substituted values:**

1. **State the problem:** We need to find how many gallons of gasoline an engine will use in 10 hours if it uses 6 gallons in 7 1\/2 hours and runs at the same speed.

1. **State the problem:** We need to find the value of the expression $x + y$ given $x = -\frac{4}{5}$ and $y = \frac{1}{3}$. 2. **Write the expression:**

1. **Problem 6:** Two sump pumps working at the same rate drain a flooded basement in $69$ hours. Find how long $3$ pumps take. 2. **Formula:** Work rate is additive. If $2$ pumps

1. Potenciación 1. Planteamos el problema: calcular

1. **State the problem:** Two sump pumps working together drain a basement in $69$ hours. We want to find how long $3$ pumps working at the same rate take to drain it. 2. **Formula

1. **State the problem:** Find the equation of the line passing through points $(3, 18)$ and $(8, 33)$. 2. **Formula for slope:** The slope $m$ of a line through points $(x_1, y_1)

1. **State the problem:** Simplify the expression $-20-(-2)$. 2. **Recall the rule:** Subtracting a negative number is the same as adding its positive counterpart. So, $a - (-b) =

1. **Problem 1:** A machine produces 280 pieces in 3.5 hours. Find the time to produce 720 pieces. 2. **Formula:** Use the rate formula $$\text{Rate} = \frac{\text{Quantity}}{\text

1. **Understanding the problem:** We are learning what a quadratic equation is and how to solve it by factorisation. 2. **What is a quadratic equation?**

1. **Problem Statement:** A quadratic equation is a polynomial equation of degree 2, generally written as $$ax^2 + bx + c = 0$$ where $a$, $b$, and $c$ are constants and $a \neq 0$

1. **State the problem:** We are given the line equation $$3x + 4y = 3$$ and asked if the slope of a line perpendicular to this is $$y = \frac{4}{3}x + 3$$. 2. **Find the slope of

1. **State the problem:** We need to identify the property of each equation and each step in the simplification. 2. **Properties for equations 1 to 6:**

1. **State the problem:** We need to solve the equation $$(x - 10)(x + 20) = 0$$.

1. **State the problem:** Solve the equation $$(x - 10)(x + 20) = 0$$ for $x$.

1. **State the problem:** We are given the equations $A \times B = C$, $C + C + C + C + C = 60$, and $B + B + B = 18$. We need to find the value of $A$. 2. **Rewrite the sums as mu

1. **State the problem:** We need to find the values of $A$ and $B$ given the equations: $$ 84 = A \times 12 $$