🧮 algebra

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 $$B \geq 0$$,

1. The problem is to solve the compound inequality: $$28 < 4x - 8 \text{ or } 4x - 8 > 36$$ 2. We will solve each inequality separately and then combine the solutions using the "or

1. State the problem. Solve the equation $\sqrt[3]{5x+5}+4=-1$.

1. **State the problem:** Find the value of $f(3)$ given $f(x) = \sqrt{x} + 1 + 5$.

1. **Stating the problem:** We are given a graph with points at (-9,7), (-3,-2), (0,5), (4,9), and (9,0) and asked to analyze the behavior of the function $y=f(x)$ over the interva

1. **State the problem:** Solve the equation $$\frac{x + 9}{7} = \frac{5x - 8}{6}$$ for $x$. 2. **Use the cross-multiplication formula:** When two fractions are equal, their cross

1. **State the problem:** Simplify the expression $6 + 6 \div 3 \times 4$. 2. **Recall the order of operations:** Use PEMDAS/BODMAS rules: Parentheses, Exponents, Multiplication an

1. **State the problem:** Solve for $x$ in the equation $$\frac{6}{x+5} = \frac{7}{x-7}.$$\n\n2. **Use the cross-multiplication rule:** When two fractions are equal, their cross pr

1. **State the problem:** Calculate $25$ to the power of $2$ divided by $22.3452$. 2. **Write the expression:** The problem can be written as $$\frac{25^2}{22.3452}$$.