🧮 algebra

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

1. **State the problem:** Simplify and solve the expression involving products and powers of binomials and polynomials given as: $$\left(\frac{(a+2)(a+1)}{(a+2)(a-1)}\right)^3 = \f

1. **Problem 4:** Determine the equation in vertex form for the parabola given the vertex and a point. 2. The vertex form of a parabola is given by:

1. **State the problem:** Write the quadratic equation $y = -x^2 - 4x + 5$ in vertex form, identify the axis of symmetry, extrema, and zeros. 2. **Recall vertex form:** The vertex

1. **State the problem:** Solve for $x$ in the equation $y = f(x)$ where $f(x) = -5x + 1$.

1. **State the problem:** Solve the equation $$x |x - 8| = 24x + 4$$ for $x$ and identify which solutions are roots or extraneous. 2. **Understand the absolute value:** The express

1. The question asks whether the mathematical constant $e$ should be written with a positive exponent. 2. The constant $e$ is approximately equal to 2.71828 and is the base of natu

1. **State the problem:** Sarah’s Pet Store has at most 16 cats and dogs combined, and at most 9 cats. 2. **Define variables:** Let $x$ be the number of cats and $y$ be the number

1. **State the problem:** We have a model rocket launched from a deck, and its height $A$ in meters after $t$ seconds is given by the quadratic function $$A = -5t^2 + 100t + 15.$$

1. **State the problem:** We want to find the year when women made up 30% of the labor force using the function $$f(x) = \frac{68.35}{1 + 0.036e^{-0.117x}}$$

1. **State the problem:** We have the function $$f(x) = \frac{68.35}{1 + 0.036e^{-0.117x}}$$ modeling the percent of women in the labor force, where $x$ is years since 1950. 2. **P