🧮 algebra

1. **State the problem:** Expand and simplify the expression $ (6x + 7)^2 $. 2. **Formula used:** The square of a binomial $ (a + b)^2 = a^2 + 2ab + b^2 $.

1. **State the problem:** Solve the equation $$\frac{x^2 + x - 30}{x - 5} = 1$$ for $x$. 2. **Recall the formula and rules:** To solve rational equations, multiply both sides by th

1. **State the problem:** Simplify the expression $32x - 11 \times 3x$. 2. **Recall the order of operations:** Multiplication must be done before subtraction.

1. **State the problem:** Simplify and analyze the expression $3^x \times (3^x - 11)$. 2. **Recall the formula:** When multiplying terms with the same base, use the property $a^m \

1. Das Problem lautet: Löse die Gleichung $$\frac{2x+4}{3} = 6$$. 2. Die Formel, die wir verwenden, ist das Lösen von Gleichungen durch Multiplikation beider Seiten mit dem Nenner,

1. The problem is to solve the equation or expression given previously, but using a different method as requested. 2. Since the original problem is not restated, let's assume it in

1. **State the problem:** Write the quadratic equation $$y = -\frac{7}{4}x^2 - \frac{1}{2}x + 2$$ in vertex form, and identify the vertex, direction of opening, and y-intercept. 2.

1. **State the problem:** Solve the equation $$\frac{2x+4}{3} = 5$$ for $x$. 2. **Formula and rules:** To solve for $x$, we need to isolate $x$ on one side of the equation. We can

1. **State the problem:** Find the number of zeros for the quadratic function given by $$y = -2(x - 3)^2 - 4$$

1. **State the problem:** Solve the equation $$\log x^2 + 15x = 2$$ given that $$x = e^{\frac{t}{3}}$$. 2. **Rewrite the logarithm:** Recall that $$\log x^2 = 2 \log x$$ by the log

1. **State the problem:** We are given the equation of a circle in standard form: $$ (x + \frac{5}{7})^2 + (y + \frac{7}{4})^2 = \frac{64}{81} $$

1. **State the problem:** We have 3 pieces of rope with lengths in the ratio 2:3:5, and their combined length is 80 feet. 2. **Set up variables:** Let the lengths be $2x$, $3x$, an

1. **State the problem:** We want to find the value of $a$ for which the system of equations $$-x + 6y = 7$$

1. **State the problem:** We are given the equation of a circle: $$(x + 1.6)^2 + y^2 = 7.84$$

1. Planteamos el problema: Analizar la función $$f(x) = \sqrt{\frac{x^3+1}{x}}$$ para encontrar dominio, puntos de corte, asíntotas y extremos. 2. Dominio: La expresión dentro de l

1. Planteamos el problema: Encontrar la función dada por $$f(x) = \sqrt{\frac{x^3 + 1}{x}}$$. 2. Recordemos que la raíz cuadrada de una fracción es igual a la raíz cuadrada del num

1. **State the problem:** We are given the system of equations:

1. El problema es encontrar el dominio de la función $f(x) = e^{-|x|}$.\n\n2. El dominio de una función es el conjunto de todos los valores de $x$ para los cuales la función está d

1. **State the problem:** Calculate the value of $$M_{r\max} = 400 \times 530 \times 0.025 \times 0.85 \times 300 \times \left( 530 - \frac{0.85 \times 300 \times 530 \times 0.025}

1. Stating the problem: Calculate the value of $x_b$ given by the formula $$x_b = \frac{700}{700+300} \times (600-70)$$

1. **State the problem:** Solve the inequality $$|x - 1| \geq 13$$ algebraically. 2. **Recall the definition of absolute value inequality:** For $$|A| \geq B$$ where $$B \geq 0$$,