🧮 algebra

1. **Énoncé du problème** : Résoudre le système d'équations \(\begin{cases}-2x + 3y = -1 \\ -7x + 5y = 16 \end{cases}\) par substitution ou méthode de Gauss et vérifier graphiqueme

1. **Problem Statement:** Complete the table for the graph of $$y=\frac{3x-2}{2}$$ and draw the graph of $$y=\frac{3}{2}x - 1$$.

1. **State the problem:** We want to find how to use the numbers 4, 30, 36, 52, and 57 to get the total 119. 2. **Understand the problem:** We need to check if any combination of t

1. **State the problem:** Solve the inequality $3x - 4 < x + 10$. 2. **Write the inequality:**

1. **Stating the problem:** We are demonstrating Theorem (14) which involves expanding a 3×3 determinant using minors and cofactors. 2. **Formula used:** The determinant of a 3×3 m

1. **Problem statement:** Ein Lift darf maximal 450 kg oder 6 Personen befördern. Wieviel Gewicht wird maximal für eine Person angenommen? 2. **Formel:** Um das maximale Gewicht pr

1. **Problem:** Find the value of $x$ such that $h(x) = 2$ where $h(x) = 8 \cdot 2^x$. 2. **Formula:** We use the equation $h(x) = 8 \cdot 2^x = 2$.

1. **State the problem:** We need to find the maximum value of the quadratic function $A(x)$ modeling the area of a rectangle based on the side length $x$, given data points and a

1. **State the problem:** We are given average monthly high temperatures for certain months and a sinusoidal model predicting temperature as a function of month number $t$. We need

1. The problem involves finding the equation of a line given points and verifying or using linear functions. 2. For a linear function, the general form is $y = mx + b$, where $m$ i

1. The problem defines the set $S = \{3x - 1 \mid x \in \mathbb{N} \wedge 5 \leq x \leq 8\}$. 2. This means $S$ contains values of the expression $3x - 1$ where $x$ is a natural nu

1. **Stating the problem:** We are given three pairs of linear equations and asked to analyze their relationships and solve the first pair.

1. **State the problem:** We want to find the set $W = \{x \in \mathbb{N} \mid 2x \leq 4 \wedge x > 1\}$. 2. **Understand the conditions:** The set $W$ contains natural numbers $x$

1. **State the problem:** Solve the equation $$\log \sqrt{3x + 1} = 1 + \log \sqrt{2x - 3}$$ for $x$. 2. **Recall logarithm properties:**

1. Planteamos el problema: La maquinaria pierde el 20% de su valor cada año, y su valor inicial es 40000. 2. La fórmula para el valor después de $n$ años con una pérdida porcentual

1. **State the problem:** Simplify the expression $$(3u^2 - 3u + 8) - (5u^2 - 4u - 1) + (2u^2 + 3u + 4)$$. 2. **Remove parentheses carefully:** Remember to distribute the minus sig

1. **State the problem:** Simplify the expression $$(-5t^2 - 4t + 1) + (-3t^2 + 7)$$. 2. **Formula and rules:** When adding polynomials, combine like terms. Like terms have the sam

1. **State the problem:** We are given two functions, $f(x)$ and $g(x)$, graphed as a blue decreasing line and a red upward-opening parabola, respectively. We need to find the poin

1. The problem asks which statement is true regarding the graphed functions $f(x)$ and $g(x)$. 2. We are given that $g(x)$ is the red increasing line in the center-right of the gra

1. **State the problem:** Solve the quadratic equation $$-2x^2 + 12x - 5 = 0$$ by finding the discriminant, describing the roots, and finding the exact solutions using the quadrati

1. **State the problem:** We are given the quadratic equation $x^2 + 2x + 7 = 0$. 2. **Find the discriminant:** The discriminant $\Delta$ of a quadratic equation $ax^2 + bx + c = 0