🧮 algebra

1. Problem: Ziehe die Wurzel, sofern möglich, von den gegebenen Ausdrücken. 2. a) $$\sqrt{a^2 + 6ab + 9b^2}$$

1. **State the problem:** We need to find the slope of the line passing through the points approximately (-1, -6) and (1, 6). 2. **Recall the slope formula:** The slope $m$ of a li

1. The problem is to evaluate the expression $i^{100}$, where $i$ is the imaginary unit with the property $i^2 = -1$. 2. Recall the powers of $i$ cycle every 4 steps:

1. **Stating the problem:** Solve the cubic equation $$3x^3 - 26x^2 + 52x - 24 = 0$$ given that the roots are in geometric progression. 2. **Let the roots be:** $$a, ar, ar^2$$ whe

1. Le problème consiste à rendre le dénominateur entier pour les expressions suivantes : - $\frac{2}{\sqrt{11}}$

1. Énonçons le problème : Simplifier l'expression $a = (\sqrt{3} + \sqrt{6})(1 - \sqrt{2})$. 2. Appliquons la distributivité :

1. **State the problem:** Convert the quadratic function $y = x^2 + 6x$ from standard form to vertex form and find the vertex coordinates. 2. **Recall vertex form:** The vertex for

1. **State the problem:** Convert the quadratic function $y = x^2 + 12x + 32$ from standard form to vertex form and find the vertex coordinates. 2. **Recall vertex form:** The vert

1. The problem is to simplify and analyze the equation given: $x \times y = -xy + x + 2y + 3$. 2. Start by rewriting the equation clearly:

1. Stated problem: Solve the equation $x(7y) = xy + 2x + 2y + 2$ for $x$ and $y$. 2. Rewrite the left side: $x(7y) = 7xy$.

1. The problem is to analyze the quadratic function given by the equation $y = 4x^2 - 8x - 4$. 2. First, we rewrite the quadratic in vertex form by completing the square.

1. **State the problem:** Rewrite the quadratic function $y = -7x^2 + 84x - 251$ in vertex form by completing the square. 2. **Factor out the coefficient of $x^2$ from the first tw

1. **State the problem:** We need to find values of $a$ for which the system $$\begin{cases} x + 2y - 3z = 4 \\ 3x - y + 5z = 2 \\ 4x + y + (a^2 - 14)z = a + 2 \end{cases}$$

1. Énonçons le problème : résoudre l'inéquation $f(x) > g(x)$ avec $f(x) = x^2 - 6x - 27$ et

1. The problem asks to factorize the quadratic equation $$4x^2 - 12x + 9$$ and solve for $$x$$. 2. Recognize that the equation is of the form $$(a - b)^2 = a^2 - 2ab + b^2$$.

1. The problem is to define and graph a piecewise function \(f(x)\) with three parts: - \(f(x) = \log_2(x)\) for \(a < x < b\)

1. Let's clarify the context of step 3 where division by 4000 occurs. 2. Typically, dividing by 4000 in a problem might be related to converting units, normalizing a value, or calc

1. **Énoncé du problème :** Nous avons une fonction linéaire qui convertit une valeur $X$ en dollars en une autre valeur $Y$ selon la formule $$Y = 1.005 \times X.$$

1. **State the problem:** X, Y, and Z invested 12000, 8000, and 10000 respectively in a business. Z received 2500 as his share of the profit. We need to find X's and Y's shares of

1. **State the problem:** Solve for $x$ in the equation $$6x + 5 = -6x - 9$$. 2. **Combine like terms:** Add $6x$ to both sides to get all $x$ terms on one side:

1. The problem asks to calculate the value of $951$ raised to the power of $\frac{2}{3}$. 2. Recall that raising a number to the power of $\frac{2}{3}$ means taking the cube root o