🧮 algebra

1. The problem is to understand and simplify the expression $\sqrt[n]{x}$, which represents the $n$-th root of $x$. 2. The $n$-th root of $x$ is defined as the number which, when r

1. **State the problem:** Simplify the expression $$\frac{x+5}{9x+27} \cdot \frac{x^2 - 9}{x^2 + 2x - 15}$$. 2. **Factor all polynomials:**

1. **State the problem:** Simplify the expression $$\frac{x-6}{5x} \cdot \frac{x^2-49}{x^2+x-42}$$. 2. **Factor all polynomials:**

1. The problem asks us to determine if the point $(4, 11)$ is a solution to the system of inequalities: $$\begin{cases} y \leq 2x \\ y > x + 3 \end{cases}$$

1. **State the problem:** Simplify the expression $$\frac{12 \sqrt{60}}{3 \sqrt{5}}$$. 2. **Recall the rules:**

1. **State the problem:** Tony has 12 dollars to buy apples and bananas. Apples cost 2 dollars per pound, bananas cost 1 dollar per pound. We want to write an inequality to represe

1. The problem is to write formulas for linear systems, which are sets of linear equations with multiple variables. 2. A linear system can be written as:

1. Let's clarify the factoring process where the $\frac{1}{3}$ was factored out in the second step. 2. Suppose the original expression was something like $\frac{1}{3}x + \frac{2}{3

1. Let's clarify the factoring process where $\frac{1}{3}$ was factored out. 2. Suppose you have an expression like $\frac{1}{3}x + \frac{2}{3}y$.

1. The problem asks us to find the slope of the line passing through the points $(1, -6)$ and $(5, -1)$. 2. The formula for the slope $m$ between two points $(x_1, y_1)$ and $(x_2,

1. Vamos interpretar o problema: você quer resolver uma expressão que envolve $x = \frac{4 \pm 0}{2}$. 2. A fórmula geral para expressões do tipo $\frac{a \pm b}{c}$ é simplesmente

1. **State the problem:** Solve the exponential equation $$2^{2x} - 2^x - 12 = 0$$ for $x$. 2. **Rewrite the equation:** Notice that $2^{2x} = (2^x)^2$. Let $y = 2^x$. Then the equ

1. **State the problem:** Solve for $x$ in the equation $$\sqrt{x + 4!} + \sqrt{x} = 12.$$ 2. **Recall the factorial:** $4! = 4 \times 3 \times 2 \times 1 = 24$. Substitute this in

1. **State the problem:** Simplify the expression $\left(3x^2-\frac{1}{10}\right)\left(3x^2+\frac{1}{10}\right)$. 2. **Formula used:** This is a product of conjugates, which follow

1. **State the problem:** Simplify the expression $$(9abx^4 - cx^7)(9abx^4 + cx^7)$$. 2. **Formula used:** This is a product of conjugates, which follows the difference of squares

1. **State the problem:** Simplify the expression $$-1 \times \ln\left(\frac{s^2 - 2}{\sqrt[3]{s^2 + 2}}\right)$$. 2. **Recall logarithm properties:** For any positive $a,b$ and re

1. The problem asks to compare the two expressions and insert the correct inequality symbol (> , < , or =). 2. The expressions are not visible as text, but based on the user's sele

1. The problem asks us to determine if the pair of ratios forms a proportion. 2. A proportion means two ratios are equal, i.e., \( \frac{a}{b} = \frac{c}{d} \).

1. The problem is to solve for $X$ given the equation $X=???$. 2. Since the equation is incomplete and contains question marks, we cannot determine a specific value or expression f

1. **State the problem:** Simplify or factor the quadratic expression $12x^2 + 16x + 12$. 2. **Recall the factoring formula:** For a quadratic $ax^2 + bx + c$, we look for factors

1. **State the problem:** Find the greatest common factor (GCF) of $44by$ and $38$. 2. **Recall the definition:** The GCF of two numbers is the largest number that divides both wit