🧮 algebra

1. Find four consecutive even integers such that 4 times the sum of the first and fourth is 8 greater than 12 times the third. Let the four consecutive even integers be $x$, $x+2$,

1. **Problem:** Find four consecutive even integers such that 4 times the sum of the first and fourth is 8 greater than 12 times the third. 2. **Step 1: Define variables.** Let the

1. **Problem:** Find four consecutive even integers such that 4 times the sum of the first and fourth is 8 greater than 12 times the third. 2. **Step 1: Define variables.** Let the

1. **State the problem:** Simplify or factor the quadratic expression $4y^2 - 3y - 27$. 2. **Formula and rules:** To factor a quadratic expression $ay^2 + by + c$, we look for two

1. **State the problem:** Calculate the value of the expression $$\frac{735 + \sqrt{987,654,321} - 293,847 \times 476}{1,829} + 37^4$$. 2. **Recall formulas and rules:**

1. Planteamos el problema: calcular los valores de $K_1$ y $K_2$ para el tiempo $40$ minutos. 2. Para resolverlo, necesitamos la fórmula o relación que vincule $K_1$, $K_2$ y el ti

1. **State the problem:** Simplify the expression $$1 - \frac{a^2 - 2}{a^2 - 16} + \frac{4 - a}{a^3 - 4a^2 - 16a + 64}$$. 2. **Identify and factor denominators and numerators where

1. **Énoncé du problème :** Simplifier l'expression $$A = \frac{e^{x+5} \times e^{3x-3}}{e^{-2x+4}}$$ en utilisant les propriétés des exponentielles.

1. **State the problem:** Solve the system of equations using substitution: $-x + y = 4$

1. The problem states that the function $f(x)$ is invertible and asks to find $f^{-1}(-3)$. 2. By definition, the inverse function $f^{-1}(y)$ gives the value of $x$ such that $f(x

1. **State the problem:** Solve the linear equation $3x - y = 0$ for $y$ in terms of $x$. 2. **Formula and rules:** To solve for $y$, isolate $y$ on one side of the equation by per

1. The problem asks to find the inverse function value $f^{-1}(-10)$ given that $f(x)$ is invertible. 2. By definition, $f^{-1}(y)$ gives the $x$ such that $f(x) = y$.

1. **State the problem:** Simplify the expression $$(6\sqrt{3} - 5)(2\sqrt{5} + 4\sqrt{2})$$. 2. **Formula used:** Use the distributive property (FOIL method) for multiplying two b

1. **State the problem:** Simplify the expression $5. (6\sqrt{3} - 5)(2\sqrt{5} + 4\sqrt{2})$. 2. **Use the distributive property (FOIL) to expand:**

1. **State the problem:** Simplify the expression by combining like terms: $$-9m + 5.5n - 3n - 4.7m^2 + 6m - 8.1n$$ 2. **Identify like terms:** Like terms have the same variable an

1. **State the problem:** Solve the system of equations using substitution: $$-x + y = 4$$

1. The problem is to solve the equation $x^2 - 5x + 6 = 0$ for $x$. 2. We use the quadratic equation formula or factorization method. Here, factorization is simpler.

1. **Énoncé du problème :** On considère la fonction $f$ définie sur $[0;20]$ par

1. **Problem:** Analyze the function $$f(x) = \frac{x^2 - 16}{x^2 + 10x + 24}$$ to find its x-intercepts, vertical asymptotes (VA), horizontal asymptote (HA), holes, domain, and ra

1. **Stating the problem:** Los op de vergelijking $$\sqrt{x + 11} = x - 1$$.

1. **State the problem:** We need to find the equation of a line given its graph. 2. **Analyze the graph:** The line crosses the y-axis at $-2$ and the x-axis at $5$.