🧮 algebra

1. **State the problem:** Solve the system of equations: $$x = y + 7$$

1. **State the problem:** Solve for $y$ in the equation $X = y + 7$. 2. **Formula and rules:** To isolate $y$, subtract 7 from both sides of the equation.

1. **State the problem:** Simplify the expression $$\frac{(q r p^{-2})^{-2} p^{-2} q^{5} r^{0}}{q r}$$ and verify if the result is $$\frac{1}{q^{4} r^{3} p^{6}}$$. 2. **Recall the

1. **State the problem:** Simplify the expression $\frac{(q r p^{-2})^{-2} p^{-2} q^{5} r^{0}}{q r}$.\n\n2. **Recall exponent rules:**\n- $(a^m)^n = a^{m \cdot n}$\n- $a^{-m} = \fr

1. The problem is to simplify or understand the expression $\frac{1}{q^4 r^3 p^6}$.\n\n2. This expression is a fraction with variables $q$, $r$, and $p$ raised to powers 4, 3, and

1. **State the problem:** Solve the system of equations by elimination. For example, consider the system: $$\begin{cases} 2x + 3y = 8 \\ 4x - y = 2 \end{cases}$$

1. **State the problem:** Simplify the expression $\frac{(q r p^{-2})^{-2} p^{-2} q^{5} r^{0}}{q r}$. 2. **Recall the rules:**

1. The problem is to find the reciprocal of a given number or expression. 2. The reciprocal of a number $x$ is defined as $\frac{1}{x}$, provided $x \neq 0$.

1. **Problem:** Determine if the graphs of the given equations are parallel, perpendicular, or neither for problems 7-17, then write equations of lines perpendicular to given lines

1. **State the problem:** Simplify the expression $$\left(\frac{x^{-3} y^{3} z^{0}}{x^{4} y^{0} z^{-4} (y^{0})^{3}}\right)^{4}$$. 2. **Recall the rules:**

1. **Problem statement:** Find the perimeter of each figure given the side lengths. 2. **Formula for perimeter:** The perimeter $P$ of a polygon is the sum of the lengths of all it

1. The problem is to determine if a point or value lies to the left or right on a number line or coordinate system. 2. The general rule is: if a value is less than a reference poin

1. **State the problem:** Solve the equation $x(x+6(18-2x))=432$ for positive values of $x$. 2. **Expand and simplify the expression inside the parentheses:**

1. **State the problem:** Find the equation of the line passing through points $(1,2)$ and $(3,-4)$. 2. **Formula used:** The slope $m$ of a line through points $(x_1,y_1)$ and $(x

1. **State the problem:** Solve the equation $x^3 + y^3 = 1$ for $y$ in terms of $x$. 2. **Recall the formula:** The sum of cubes factorization is $a^3 + b^3 = (a + b)(a^2 - ab + b

1. O problema pede para resolver uma expressão ou equação com denominador $x^3 - 1$. 2. Primeiro, vamos fatorar o denominador usando a diferença de cubos: $$x^3 - 1 = (x - 1)(x^2 +

1. Vamos analisar a expressão do denominador que é $x^3 - 1$. 2. Essa expressão é uma diferença de cubos, que pode ser fatorada usando a fórmula:

1. Vamos analisar a expressão dada, que é $4x^3$ seguida de um sinal negativo, ou seja, $4x^3 - \ldots$. 2. O sinal negativo indica que o próximo termo da expressão será subtraído

1. **Problem:** A salesperson sold 6 air-conditioning systems at $2320 each with a 12% commission rate. 2. **Step 1: Calculate total sales.**

1. **State the problem:** We have a total length of steel measuring 54,259.2 cm, and we want to find out how many rods this length can make. 2. **Assumption:** To find the number o

1. The problem asks us to write the slope-intercept form of a line given the slope $m = -1$ and the y-intercept $b = 8$. 2. The slope-intercept form of a line is given by the formu