🧮 algebra

1. **Stating the problem:** We need to solve quadratic expressions or equations by completing the square. 2. **Formula and rules:** The general form of a quadratic is $$ax^2 + bx +

1. **State the problem:** Solve the quadratic equation $$4x^2 + 5x - 7 = 0$$. 2. **Formula used:** The quadratic formula is $$x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}$$ where the equ

1. **State the problem:** Simplify the expression $$ (f^3 - 5f + 25) - (4f^2 - 12f + 9) $$. 2. **Apply the distributive property:** Remove the parentheses by distributing the minus

1. **State the problem:** Simplify the expression $$(-w^3+8w^2-3w) -(4w^2+5w-7)$$. 2. **Write the expression clearly:**

1. **State the problem:** Solve the quadratic inequality $$x^2 + 3x + 2 < 0$$. 2. **Factor the quadratic expression:**

1. **State the problem:** Graph the inequality $y \leq - \frac{1}{3} x + 2$. 2. **Formula and rules:** The boundary line is $y = - \frac{1}{3} x + 2$.

1. **State the problem:** We are given the function $$y = Ae^{4x} - 2Be^{2x}$$ and we want to understand or analyze it.

1. **State the problem:** We need to find the value of $d$ such that the point $(d, 4)$ lies on the line passing through $(0,7)$ and $(8,0)$. 2. **Find the equation of the line:**

1. **Problem 1: Area of each section of the garden** The farmer has a rectangular garden with length $(x + 6)$ meters and width $3x$ meters. The garden is divided into 3 equal sect

1. **State the problem:** We need to write and simplify the algebraic expression representing the total amount spent by the class buying notebooks, marker bundles, and a decorative

1. **State the problem:** We need to find two numbers where one number is 3 less than the other, and their sum is 177. 2. **Define variables:** Let $x$ be the second number.

1. **State the problem:** We need to find the slope of a line passing through the points approximately $(-4, 5)$ and $(0, 3)$. 2. **Formula for slope:** The slope $m$ of a line pas

1. **State the problem:** We need to find the slope of the line passing through the points $(-2, 3)$, $(-1, 0)$, and $(0, -3)$. 2. **Recall the slope formula:** The slope $m$ betwe

1. **State the problem:** Solve the equation $$\frac{X}{4} = 2x$$ for $X$. 2. **Understand the equation:** The equation states that $X$ divided by 4 equals $2x$. Here, $X$ and $x$

1. **State the problem:** We have two car wash pricing plans:

1. **State the problem:** We want to find the number of shirts where the total cost from Company A equals the total cost from Company B.

1. **State the problem:** We want to find the number of hours $h$ where the total cost for Mia and Emma is the same.

1. **State the problem:** We want to find the number of miles where the cost of Taxi Company A equals the cost of Taxi Company B.

1. **State the problem:** We want to find the number of games where the total cost at Bowling Alley A equals the total cost at Bowling Alley B.

1. **State the problem:** We want to find the number of games where the total cost at Bowling Alley A equals the total cost at Bowling Alley B.

1. **State the problem:** We want to find the number of movies rented where the total cost from Movie Store A equals the total cost from Movie Store B.