🧮 algebra

1. **Problem Statement:** We are given two functions, a rational function $f(x)$ and an absolute value function $g(x)$, graphed on the coordinate plane. We need to find the interva

1. **State the problem:** Find the domain of the function $$f(x,y) = \frac{xy}{y - 2x}$$. 2. **Recall the domain rule:** The domain of a function includes all input values for whic

1. **State the problem:** Solve for $x$ in the equation $x + 2 = 4$. 2. **Formula and rules:** To isolate $x$, subtract 2 from both sides of the equation.

1. **State the problem:** Solve for $x$ in the equation $x + 2 = 4$. 2. **Formula and rules:** To isolate $x$, subtract 2 from both sides of the equation.

1. **Stating the problem:** We have two shopping bags with prices and quantities of two types of compotes: A (abóbora) and M (morango).

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

1. **State the problem:** Solve the equation $$a^3 + a^2 = 36$$ for the variable $a$. 2. **Rewrite the equation:** We want to find $a$ such that $$a^3 + a^2 - 36 = 0$$.

1. Problem: find $\sqrt[3]{64}$. 2. Formula used: if $a^3=b$, then $\sqrt[3]{b}=a$.

1. **State the problem:** If $x+2=4$, find the value of $x$. 2. **Use the subtraction property of equality:** Subtract $2$ from both sides to isolate $x$.

1. **State the problem:** Solve the system of equations: $$\frac{y}{2} - \frac{y+1}{3} = 0$$

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

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

1. **State the problem:** Solve the equation $6x = 18 + 4x$ for $x$. 2. **Write down the formula and rules:** To solve linear equations, we isolate the variable on one side by perf

1. **State the problem:** Maria has only nickels and dimes, totaling 20 coins, worth 165 cents. Find the number of dimes. 2. **Define variables:** Let $n$ = number of nickels, $d$

1. **State the problem:** We need to find the average rate of change of the function $f(x)$ on the interval $[-6, -3]$. 2. **Formula:** The average rate of change of a function $f(

1. The problem is to solve the equation $2x + 3 = 11$ for $x$. 2. The formula used here is to isolate $x$ by performing inverse operations. We subtract 3 from both sides and then d

1. **Problem:** Sarah earned 3 more than double Eric's earnings. The difference is 15. Find their earnings. 2. **Formula:** Let Eric's earnings be $x$. Then Sarah's earnings are $2

1. **State the problem:** Simplify the expression $$7x^3 + \frac{4}{x^5} - \frac{3}{\sqrt[3]{5x}} + \frac{7x^2}{3} - \sqrt[3]{5}.$$ 2. **Recall important rules:**

1. **State the problem:** A grocery store had 2,418 boxes of cereal on Monday. By Friday, customers had bought 1,146 boxes. The remaining boxes were organized on 24 shelves evenly.

1. **State the problem:** We are given a line with equation $y = ax + b$. We need to find the values of $a$ (slope) and $b$ (y-intercept).

1. **Problem:** Factor the polynomial $x^2 + 11x + 28$. 2. **Formula:** To factor a quadratic $x^2 + bx + c$, find two numbers that multiply to $c$ and add to $b$.