🧮 algebra

1. **State the problem:** You sold hot dogs and sodas. Each hot dog costs $1.50 and each soda costs $0.50. The total money made is 78.50, and the total number of items sold (hot do

1. The problem is to graph the equation $$y = |x + 2| - 2$$. 2. This is an absolute value function shifted horizontally and vertically.

1. The problem is to graph the equation $$y = |x + 3| + 4$$. 2. This is an absolute value function, which creates a V-shaped graph.

1. **State the problem:** Calculate the summation $$\sum_{i=1}^4 i$$ which means adding all integers from 1 to 4. 2. **Formula used:** The sum of the first $n$ natural numbers is g

1. Il problema chiede di trovare l'equazione della parabola sapendo che il vertice è $V(0;3)$ e passa per il punto $P(1;2)$. 2. L'equazione generale di una parabola con vertice in

1. **State the problem:** Graph the equation $y = |x - 2| - 4$. 2. **Recall the absolute value function:** The graph of $y = |x|$ is a V-shaped graph with vertex at the origin $(0,

1. **Stating the problem:** We need to solve the expression $\frac{3}{-4} - \left(-\frac{2}{5}\right)$ and the product $\frac{3}{-4} \cdot \left(-\frac{2}{5}\right)$.

1. **Stel het probleem vast:** We moeten de uitdrukking $3\sqrt{3} \cdot \sqrt{12} \cdot 2\sqrt{8}$ herleiden. 2. **Gebruik de regels voor wortels en vermenigvuldiging:**

1. **State the problem:** We need to solve for $n(t)$ in the equation:

1. The problem asks to express each fraction as a decimal. 2. The formula to convert a fraction to a decimal is to divide the numerator by the denominator: $$\text{Decimal} = \frac

1. **State the problem:** We are given that 730 ml of water is used for 950 grams of flour. We need to find how much water is used for 1000 grams of flour. 2. **Formula used:** Thi

1. Il problema chiede di trovare l'intersezione con l'asse x di una funzione, cioè i punti in cui la funzione si annulla (y=0). 2. La formula generale per trovare l'intersezione co

1. The problem is to convert the equation $y = -\frac{3}{4}x - 3$ into the form $3x + 4y = 4$ and verify the solution. 2. Start with the given equation:

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 $i = \sqrt{-1}$.