🧮 algebra

1. The problem is to evaluate the expression $8 \times e^8$ where $e$ is the base of the natural logarithm, approximately equal to 2.71828. 2. The formula used here is simple multi

1. **Énoncé du problème :** Une entreprise vend des poutres métalliques à 2,3 milliers d'euros la tonne. Le coût de production en milliers d'euros est donné par la fonction $$C(x)

1. The problem is to solve the inequality $y > 3$. 2. This inequality means we are looking for all values of $y$ that are strictly greater than 3.

1. **State the problem:** We need to graph the inequality $$y \leq \frac{2}{3}x - 5$$. 2. **Formula and rules:** The inequality is in slope-intercept form $$y = mx + b$$ where $$m

1. **State the problem:** Simplify the expression \(\frac{(x^3)(x + 5)}{x - 9} \cdot \frac{(x - 9)(x + 8)}{3x^3}\). 2. **Write the formula and rules:** When multiplying fractions,

1. The problem asks: What is the percentage of 2 in 17? 2. To find the percentage of a number $a$ in another number $b$, we use the formula:

1. **State the problem:** Solve the exponential equation algebraically. 2. **General approach:** For an equation of the form $$a^{x} = b^{x}$$ or $$a^{f(x)} = b^{g(x)}$$, we use pr

1. **State the problem:** Solve the exponential equation $$5^{x^x} = 5^x + 26$$. 2. **Analyze the equation:** The equation involves an exponential expression with a variable expone

1. Das Problem: Du möchtest wissen, wie man den Wert von $k$ findet. 2. Allgemein hängt die Methode zur Bestimmung von $k$ vom Kontext ab, z.B. ob $k$ eine Konstante in einer Gleic

1. Das Problem besteht darin, den Wert von $k$ zu bestimmen, wobei die offizielle Lösung $k=11$ ist. 2. Um $k$ zu finden, müssen wir die gegebene Gleichung oder den Zusammenhang ke

1. **Stating the problem:** Risolvi l'equazione \(9x - 4 + 3x - 5 = 1 - 4(x - 4) + 6\). 2. **Formula and rules:** Per risolvere un'equazione lineare, si raccolgono i termini simili

1. Problem: Polynomdivision a) Dividieren Sie $$\frac{5x^3 - 16x^2 + 58x - 11}{x^2 - 3x + 11}$$ 2. Formel: Bei der Polynomdivision dividieren wir den höchsten Grad des Dividenden d

1. **Stel het probleem vast:** We moeten de waarde van $x$ vinden die voldoet aan de vergelijking: $$(x-30) \times 29302 + 46046 \times (x-60) + 29302 \times (x-35) + 50 \times (x-

1. **State the problem:** Solve the system of linear equations: $$3x - y = -4$$

1. **State the problem:** We are given the quadratic function $f(x) = x^2 + 4x + 5$ and want to analyze it. 2. **Formula and rules:** The general form of a quadratic function is $f

1. **State the problem:** Solve the quadratic equation $$x^2 + 6x - 7 = 0$$ using the method of completing the square. 2. **Rewrite the equation:** Move the constant term to the ri

1. **State the problem:** We have a rectangular pool 20 feet wide and 50 feet long, surrounded by a deck of uniform width. The deck's total area is 456 square feet. We need to find

1. The problem asks us to find which factorization correctly identifies the real zeros of the quadratic function $$f(x) = -20x^2 + 23x - 6$$. 2. To find the real zeros, we need to

1. **Problema 1:** Semplificare $$\left( \frac{2x-1}{x+1} - 2 \right)^2 : \left( \frac{4}{(x+1)^2} - \frac{2}{x+1} \right) - \frac{1}{x-1}$$. 2. **Formula e regole importanti:**

1. **State the problem:** Simplify or analyze the expression $3\frac{6}{25} x^2 - \frac{9}{16} y^2$. 2. **Convert mixed number to improper fraction:**

1. **State the problem:** We want to express the rational function $$\frac{4x^3 - 5x^2 + 3x - 14}{x^2 + 2x - 1}$$ in the form $$Ax + B + \frac{Cx + D}{x^2 + 2x - 1}$$ and find cons