🧮 algebra

1. **State the problem:** Simplify the expression $$\frac{48a^3 b^2}{18a b^5}$$. 2. **Write the formula and rules:** When simplifying fractions with variables, divide coefficients

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

1. **State the problem:** We need to find the value of $f(-2 - g(3))$ given the functions $f(x) = \frac{3}{4}x + 10$ and $g(x) = x^2 - 3$. 2. **Calculate $g(3)$:** Substitute $x=3$

1. **State the problem:** Simplify the expression $\frac{18x}{6x}$. 2. **Recall the rule:** When dividing fractions or terms, divide the numerators and denominators separately. Als

1. The question asks if the problem involves cancellation. 2. Cancellation in math typically occurs when simplifying fractions by removing common factors from numerator and denomin

1. **Stating the problem:** Find the conjugate of the polynomial expression $3 + 4i$. 2. **Formula and explanation:** The conjugate of a complex number $a + bi$ is $a - bi$. This m

1. **Problem Statement:** Find the conjugate of the complex number $z = a + bi$, where $a$ and $b$ are real numbers and $i$ is the imaginary unit. 2. **Formula:** The conjugate of

1. **State the problem:** Simplify the expression $\frac{18x}{6x}$. 2. **Recall the rule:** When simplifying fractions, divide numerator and denominator by their greatest common fa

1. **State the problem:** Simplify the expression $$\frac{18x}{6x}$$. 2. **Recall the rule:** When simplifying fractions, divide the numerator and denominator by their greatest com

1. The problem is to simplify the expression \(\sqrt{x}16\). 2. First, clarify the expression: it likely means \(16\sqrt{x}\) or \(\sqrt{16x}\). We will consider both cases.

1. The problem is to calculate the factorial of 6, denoted as $6!$. 2. The factorial of a positive integer $n$ is the product of all positive integers from 1 to $n$. The formula is

1. **State the problem:** Factor the polynomial $$14x^{2n + 1} + 7x^{n + 3} - 21x^{n + 2}$$ completely. 2. **Identify common factors:** Look for the greatest common factor (GCF) in

1. **State the problem:** Find the inverse of the function $f(x) = 2x - 3$. 2. **Formula and rule:** To find the inverse function $f^{-1}(x)$, swap $x$ and $y$ in the equation and

1. The problem asks to find the solutions of the quadratic function, which are the x-values where the graph intersects the x-axis. 2. The solutions of a quadratic function correspo

1. The problem asks us to find the solutions of a quadratic function using its graph. 2. The solutions of a quadratic function are the x-values where the graph intersects the x-axi

1. **State the problem:** We are given a profit function $p(x) = 2x - 500$, where $x$ is the number of units sold. We need to find the profit when 300 units are sold. 2. **Formula

1. **State the problem:** Find the inverse of the function $f(x) = 2x - 3$. 2. **Recall the formula and rules:** To find the inverse function $f^{-1}(x)$, we swap $x$ and $y$ in th

1. **Stating the problem:** We want to find the domain and range of a relation. A relation is a set of ordered pairs, and the domain is the set of all possible input values (x-valu

1. The problem is to solve the equation $\sin x = x$. 2. We want to find values of $x$ where the sine of $x$ equals $x$ itself.

1. The problem asks us to find three ratios equivalent to $8 : 20$. 2. Two ratios are equivalent if their fractions are equal. The ratio $8 : 20$ can be written as the fraction $\f

1. The problem asks us to find three ratios equivalent to $5 : 2$. 2. Two ratios are equivalent if their fractions are equal. The ratio $5 : 2$ can be written as the fraction $\fra