🧮 algebra

1. **Problem:** Henri purchased a stereo for 400 and sold it for 450. Find the markup as a percentage of the purchase price. 2. **Formula:** Markup percentage = \( \frac{\text{Sell

1. **State the problem:** Solve the system of linear equations for $x$ and $y$: $$2x + y = 8$$

1. **State the problem:** We are given the system of equations: $$2x + 3y = 7$$

1. **State the problem:** Solve the equation $16 - 2t = 5t + 9$ for $t$. 2. **Write down the formula and rules:** To solve for $t$, we want to isolate $t$ on one side of the equati

1. Planteamos el problema: Resolver la ecuación $2x + 3 = 11$. 2. Usamos la fórmula para despejar $x$ en una ecuación lineal: $$ax + b = c \implies x = \frac{c - b}{a}$$ donde $a$,

1. **State the problem:** Solve the system of equations for $x$ and $y$: $$2x + y = 8$$

1. **State the problem:** Solve the equation $$\frac{8}{x + 2} - \frac{5}{3} = \frac{x - 1}{3}$$ for $x$. 2. **Identify the formula and rules:** To solve rational equations, first

1. **State the problem:** Solve the quadratic equation $$f(x) = x^2 - 2x - 3 = 0$$. 2. **Recall the quadratic formula:** For any quadratic equation $$ax^2 + bx + c = 0$$, the solut

1. **State the problem:** Solve the equation $$\frac{8}{x + 2} - \frac{5}{3} = \frac{x - 1}{3}$$ for $x$. 2. **Identify the formula and rules:** To solve rational equations, first

1. **State the problem:** Solve the system of linear equations: $$2x + y = 8$$

1. **State the problem:** We are given the set of ordered pairs \(\{(1, 2), (2, 3), (3, 4), (3, 5), (4, 3)\}\) and asked which coordinate must be removed so that the set represents

1. The problem is to solve for $x$ in the equation $2x + 3 = 7$. 2. We use the basic algebraic principle: to isolate $x$, perform inverse operations on both sides of the equation.

1. **Problemstellung:** Gegeben ist die Funktion $f(x) = -5x^2 + 20$. (a) Berechne $f(1)$.

1. **Stating the problem:** Convert the given fractions and mixed numbers to decimals and percentages. 2. **Formula and rules:**

1. O problema pede para resolver o "2", que interpretamos como o número 2, mas para dar um exemplo matemático, vamos considerar a equação simples $x = 2$. 2. A equação $x = 2$ sign

1. **Problem:** Solve the first-degree equation analytically and graphically: $$3 \cdot \left( \frac{2x - 1}{3} - \frac{1 - 2x}{2} \right) = \frac{2 - x}{3} - 1 + x$$

1. **State the problem:** We need to find the solution point $S$ where the two lines given by the system of equations intersect: $$\begin{cases} y = -4x + 2 \\ y = 3x - 5 \end{case

1. The problem asks to classify each equation as linear or nonlinear. 2. A linear equation in two variables $x$ and $y$ has the form $$Ax + By = C$$ where $A$, $B$, and $C$ are con

1. **State the problem:** We are given the system of equations: $$2x + 3y = 7$$

1. We start by solving the first logarithmic equation: $$^2\log(16) + ^2\log(x) = 6$$ 2. Recall the logarithm property: $$\log_b(a) + \log_b(c) = \log_b(ac)$$. Here, the base is 2,

1. **State the problem:** Solve the system of linear equations for $x$ and $y$: $$2x + y = 8$$