🧮 algebra

1. **Problem statement:** A merchant marks up everything by 40%. Find the retail price of an item costing the merchant 15. 2. **Formula:** Retail price = Cost price + Markup

1. The problem is to factor the quadratic expression $x^2 - 7x - 78$. 2. The general form of a quadratic expression is $ax^2 + bx + c$. Here, $a=1$, $b=-7$, and $c=-78$.

1. **State the problem:** We have a piecewise function defined as: $$

1. **State the problem:** We are given the system of equations: $$9x + y = 28$$

1. **State the problem:** Factor the expression $$5a^2 + 10ab - 3a - 6b$$. 2. **Identify the method:** We will use factoring by grouping, which involves grouping terms to find comm

1. **State the problem:** Factor the quadratic equation $$2x^2 = 3x + 35$$ into its factored form. 2. **Rewrite the equation:** Move all terms to one side to set the equation to ze

1. **State the problem:** We have two playlists: Han's playlist is described by the equation $$y = 4x + 20$$ where $x$ is the number of days and $y$ is the total number of songs.

1. **State the problem:** We need to find the Instantaneous Rate of Change (IROC) of the function $$y = 4\sqrt{100} - 2t$$ at $$t = 15$$ without using derivatives. 2. **Rewrite the

1. **State the problem:** Simplify the expression $$\frac{(2 a^3 b^2 c^{-2})^3}{16} a^{-4} b^5 c^{-6}$$. 2. **Apply the power to each factor inside the parentheses:**

1. The problem asks to express 143 cents in dollars. 2. We know that 100 cents equal 1 dollar.

1. Stating the problem: Solve the equation $$\frac{X}{20} - 5 = -4$$ for $X$. 2. Add 5 to both sides to isolate the fraction term:

1. Stating the problem: Solve for $X$ in the equation $$\frac{X}{8} + 4 = 12$$. 2. Formula and rules: To isolate $X$, we first need to eliminate the constant term on the left side

1. **State the problem:** Solve the equation $$\frac{3}{x-2} - \frac{6}{x^2-4} = \frac{2}{x^2-1}$$. 2. **Identify excluded values:** The denominators cannot be zero, so exclude val

1. **Problem:** Write equations for the lines shown on the graph. 2. **Step 1: Find the equation of the first line passing through points (-6,0) and (0,6).**

1. The problem is to solve a system of linear equations by graphing. 2. To solve by graphing, we first write each equation in slope-intercept form $y=mx+b$ where $m$ is the slope a

1. The problem is to solve the system of equations: $$y = -x - 2$$

1. **State the problem:** Solve the equation $$\frac{5x}{2} = 11 + \frac{2x}{3}$$ for $x$. 2. **Identify the goal:** We want to isolate $x$ on one side of the equation.

1. **State the problem:** Write an equation in slope-intercept and standard form that passes through the point $(5, -5)$ and is parallel to $y = -\frac{7}{5}x - 5$. 2. **Identify t

1. **State the problem:** We have a polygon with edges and angles, and three pairs of congruent edges: - $15x + 17 = 3z - 5$

1. **State the problem:** Simplify the expression involving powers of $g$ given as $$\frac{g(x)}{g^9} = \frac{4}{g^9}$$ and related expressions using exponent rules. 2. **Recall th

1. **State the problem:** Find the equation of a graph that is a horizontal line with a y-intercept of -3. 2. **Recall the formula for a horizontal line:**