🧮 algebra

1. Stating the problem: Solve the equation $$\frac{3p}{12pq+4q} = \frac{8p^2}{6p^2 + 2pq}$$ and solve for $x$ in $$2x = \frac{2y^2 - 3z}{2}$$. 2. Simplify the first equation:

1. Énonçons le problème : Simplifier l'expression $$\left(\sqrt[\sqrt{b^{16d}}]{\ }\right)^{-2} \left(\sqrt[\sqrt{b^{-24d}}]{\ }\right)^{-3}$$ en utilisant les lois des exposants.

1. Énonçons le problème : Simplifier l'expression $$\left(\frac{a^4}{\sqrt{a^{10}}}\right)^4 \left(\frac{\sqrt{a^{20}}}{a^8}\right)^{-2}$$ en utilisant les lois des exposants. 2. S

1. Énonçons le problème : Simplifier l'expression $$\left( \frac{2a^{2}b^{2}}{3a^{-1}b^{2}}\right)^{-3} \left(\frac{3ab^{3}}{2a^{2}b}\right)^{-2}$$ en utilisant les lois des exposa

1. Problem: Zuordnen der grünen Terme zu den äquivalenten blauen Termen ohne Taschenrechner. 2. Vereinfachung der grünen Terme:

1. **Problem Statement:** Alia hired a taxi with a fixed charge of 1500 plus 450 per 30 minutes.

1. The problem is to simplify the expression $$16^{\frac{3}{4}}$$ and verify the equality $$16^{\frac{3}{4}} = 2^{4 \cdot \frac{3}{4}}$$. 2. Start by expressing 16 as a power of 2:

1. The problem is to find the sum of the series $$1 + i + i^2 + i^3 + i^4 + \cdots + i^{2021}$$ where $i$ is the imaginary unit with the property $i^2 = -1$. 2. Recall the powers o

1. **Problem statement:** Solve the polynomial equation $$2x^4 + 8x^3 + 3x^3 + 4x + 1 = 0$$ given that the sum of two of the roots is zero. 2. **Simplify the polynomial:** Combine

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