🧮 algebra

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 $5$.

1. **State the problem:** We are given the system of equations: $$2x + 3y = 7$$

1. **Énoncé du problème :** Calculer l'aire $A$ sous la courbe $C_f$ de la fonction $f(x) = 18\left(-\frac{1}{x} + 1 + a \ln(x)\right)$ entre $x=1$ et $x=3$, avec $a$ une constante

1. The problem is to simplify the fraction $\frac{2}{6}$. 2. The formula to simplify a fraction is to divide the numerator and denominator by their greatest common divisor (GCD).

1. You asked if the graph is correct, but you did not provide the graph or the function it represents. 2. To verify if a graph is correct, we need the function or equation it is su

1. The problem asks to find the graph of the inverse function $y = f^{-1}(x)$ given the graph of $y = f(x)$. 2. The inverse function $f^{-1}$ swaps the roles of $x$ and $y$, so the

1. **Stating the problem:** We have a square sheet of cardboard with side length 10 units. Squares of side length $x$ units are cut from each corner, and the sheet is folded to for