🧮 algebra

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

1. **State the problem:** Solve the equation $4y + 2x = 754$ for $y$. 2. **Formula and rules:** To solve for $y$, isolate $y$ on one side of the equation by moving other terms to t

1. **State the problem:** Simplify the expression $$\frac{2}{x+5} + \frac{2}{x^2-25}$$. 2. **Recognize the formula and rules:** The expression involves adding two rational expressi

1. **State the problem:** We need to find a one-to-one correspondence (bijection) function from set $A=[0,1]$ to set $B=[1,2]$. 2. **Recall the definition:** A function $f:A \to B$

1. The first question asks which options about asymptotes are correct. 2. Recall the rules for asymptotes of rational functions $f(x) = \frac{P(x)}{Q(x)}$ where $P$ and $Q$ are pol

1. **State the problem:** Simplify the expression $$\frac{2}{x+5} + \frac{2}{x^2+25}$$. 2. **Identify the denominators:** The denominators are $x+5$ and $x^2+25$.

1. **State the problem:** Greg fills his mug and pours it into jug A three times, and Martin fills his mug and pours it into jug B six times. We need to find how many more millilit

1. **State the problem:** Calculate the value of $$5^{-4} \div \left(3^{3} \div 5^{7}\right)$$. 2. **Recall the rules:**

1. **State the problem:** Calculate the value of the expression $$5^{-4} \div \left(3^{3} \div 5^{7}\right)$$. 2. **Recall the rules:**