🧮 algebra

1. **State the problem:** We know that 730 ml of water is needed for 900 grams of flour. We want to find out how much water is needed for 1000 grams of flour. 2. **Set up the propo

1. **State the problem:** Simplify the expression \((4x^2 - 5x + 7) - (3x^2 + 2x - 5) + (2x^2 - x - 10)\). 2. **Write the expression clearly:**

1. **Énoncé du problème :** Soient $n \in \mathbb{N}^*$ et $M \in M_n(\mathbb{R})$. On définit les ensembles

1. **State the problem:** Solve the equation $2x - 5 = 5$ for $x$. 2. **Add 5 to both sides:** To isolate the term with $x$, add 5 to both sides:

1. **Problem:** Calculate the sum $2x + 8x$. 2. **Formula:** When adding like terms, add their coefficients and keep the variable the same.

1. **Énoncé du problème :** Décomposer en produit de facteurs irréductibles sur $\mathbb{R}[X]$ et $\mathbb{C}[X]$ les polynômes suivants : $$P_1 = X^3 - 2\sqrt{2}, \quad P_2 = X^5

1. **State the problem:** Simplify fully the expression $$\left( \frac{9x^4}{16y^{10}} \right)^{-\frac{1}{2}}$$. 2. **Recall the rule for negative fractional exponents:** For any n

1. The problem asks to rewrite the expression $7 - \sqrt{-55}$ as a complex number and simplify all radicals. 2. Recall that the imaginary unit $i$ is defined as $i = \sqrt{-1}$.

1. Das Problem lautet: Löse die Gleichung $2x + 3 = 11$ nach $x$ auf. 2. Die verwendete Formel ist die lineare Gleichung $ax + b = c$, wobei $a$, $b$ und $c$ Konstanten sind. Um $x

1. The problem is to graph the function $f(x) = 4\sqrt{x} - 7$. 2. The formula used is $f(x) = 4\sqrt{x} - 7$, where $\sqrt{x}$ is the square root of $x$.

1. Problem: Lukas hat die Parabel f mit f(x) = x^2 gezeichnet. Beschreibe den Fehler. 2. Die Funktion f(x) = x^2 ist die Grundparabel mit Scheitelpunkt im Ursprung (0,0).

1. **Stating the problem:** We want to understand how to factor algebraic expressions, which means rewriting them as products of simpler expressions. 2. **Common factoring:** This

1. **State the problem:** Solve the inequality $3^x + 1 > 1$ and the equation $3^x = 1$. 2. **Solve the inequality $3^x + 1 > 1$: **

1. **Problem:** Identify the pattern and continue the sequence starting with 112, 100, 88. 2. **Step 1:** Observe the differences between terms: $100 - 112 = -12$, $88 - 100 = -12$

1. Énoncé du problème : Trouver la nature de $k$ dans la fonction $f(x) = x^2 - 6x + 11$. 2. Rappel : Pour une fonction quadratique $f(x) = ax^2 + bx + c$, le sommet (ou le point c

1. **State the problem:** Simplify the expression $$-2\sqrt{294m^{16}n^{7}}$$. 2. **Recall the rule for square roots:** $$\sqrt{a \cdot b} = \sqrt{a} \cdot \sqrt{b}$$ and $$\sqrt{x

1. The problem is to simplify the expression given by the user. 2. Since the user did not provide a specific expression, let's consider a general approach to simplification: combin

1. **State the problem:** We have a ratio of flour to water in an art paste and a table showing some values. We need to find the missing values in the table and specifically answer

1. **Stating the problem:** We have 10 rows, each with a sequence of three numbers followed by nine empty squares. We need to find the next nine numbers in each sequence. 2. **Unde

1. The problem asks whether the terms solution, root, x-intercept, and zero mean the same thing in math. 2. Let's define each term:

1. The problem asks to identify what the green dots on the graph represent. 2. The green dots are located where the parabolas intersect the x-axis.