🧮 algebra

1. **Problem statement:** We have two snails, Flash and Trovão, racing. Flash moves at a constant speed of 5 cm per minute.

1. **State the problem:** Identify which expressions are equivalent to $6^3 \cdot 3^3$. 2. **Recall the property of exponents:** For any positive numbers $a$ and $b$, and exponent

1. **State the problem:** Identify which expressions are equivalent to $5^5 \cdot 5^{-2}$. 2. **Recall the exponent multiplication rule:** When multiplying powers with the same bas

1. **State the problem:** Solve the inequality $$3x > 9$$ and graph the solution. 2. **Formula and rules:** To solve inequalities, we use the same rules as equations, but when mult

1. **State the problem:** Use the Greatest Common Factor (GCF) to write an equivalent expression for $60 + 72$ using the distributive property. 2. **Find the GCF of 60 and 72:**

1. **State the problem:** We need to find a quartic function $f(x)$ that produces a W-shaped curve opening upward with x-intercepts at approximately $x=-2$ and $x=3$, and a local m

1. **State the problem:** Use the Greatest Common Factor (GCF) to write an equivalent expression for $60 + 72$ using the distributive property. 2. **Find the GCF of 60 and 72:**

1. **State the problem:** Find the equation of the straight line in the form $y = mx + c$ given it crosses the y-axis at 16 and passes through the point $(2, 40)$. 2. **Recall the

1. **Énoncé du problème :** Simplifier l'expression suivante : $$\frac{8 \times (7 \times 5)^5 \times 5^2 \times 7^{-1}}{(7 \times 5^5 \times 7^{-2})^2}$$

1. El problema es entender por qué la expresión $a^2 + 2a + 1$ no se opera como una cuadrática común y si debería dar lo mismo el valor de $a$. 2. La expresión $a^2 + 2a + 1$ es un

1. **State the problem:** Simplify the expression $$\frac{6x - y}{10xy} + \frac{1}{2x} - \frac{2y - 7x}{5xy}$$ and show it equals $$\frac{k}{y}$$ where $$k$$ is an integer. 2. **Id

1. **State the problem:** Solve the simultaneous equations: $$\begin{cases} x + y = 2 \\ y + 2z = 12 \\ 5x + 7y + z = 13 \end{cases}$$

1. **State the problem:** Simplify the expression $$\frac{6x - y}{10xy} + \frac{1}{2x} - \frac{2y - 7x}{5xy}$$ and show it equals $$\frac{k}{y}$$ where $$k$$ is an integer. 2. **Id

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

1. **State the problem:** Graph the inequality $x < 4$ on a number line. 2. **Understand the inequality:** $x < 4$ means all values of $x$ are less than 4 but do not include 4 itse

1. **State the problem:** Solve the system of equations: $$\begin{cases}-6x - y = 23 \\ y = 4x + 7 \end{cases}$$

1. **State the problem:** Solve the simultaneous equations for integers $x, y, z$: $$\begin{cases} x - 2y = -3 \\ 2y + z = 3 \\ z - 2x = -3 \end{cases}$$

1. **State the problem:** Simplify the expression $$\sqrt[3]{\frac{49}{27}} \cdot j^{\frac{1}{3}}$$. 2. **Recall the formula:** The cube root of a fraction is the cube root of the

Let's find out how many values of $p$ make the difference quotient on $[2, p]$ equal to $0.5$! 1. Imagine you have points on the graph at $x=2$ and $x=p$. We want the average rate

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

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