🧮 algebra

1. **State the problem:** Find the value of $2^3 \times 2^0$. 2. **Recall the exponent rule:** When multiplying powers with the same base, add the exponents: $a^m \times a^n = a^{m

1. **State the problem:** We need to find the sum of the fractions $\frac{3}{5} + \frac{9}{10} + \frac{13}{15}$.\n\n2. **Find a common denominator:** The denominators are 5, 10, an

1. The problem is to factor the expression $x^2$. 2. Factoring means expressing the expression as a product of simpler expressions.

1. **State the problem:** Simplify the expression $6 \div 2(1+2)$. 2. **Evaluate inside the parentheses:** Calculate $1+2=3$. Now the expression is $6 \div 2(3)$.

1. **State the problem:** Simplify the expression $$\frac{x^2-25}{x^2+5x} \div \frac{xy+6x-5y-30}{5x-15}$$. 2. **Recall the division of fractions rule:** Dividing by a fraction is

1. **State the problem:** We have three equations based on images: - Red apple + banana bunch + banana bunch = 18

1. Let's solve an example problem involving fractions: Simplify the fraction $\frac{12}{16}$.\n\n2. The formula to simplify a fraction is to divide both the numerator and denominat

1. **State the problem:** We want to find the positive integer value of $x$ such that the expression $3x + 9$ is a multiple of 7. 2. **Formula and rule:** An expression is a multip

1. Het probleem is om te begrijpen wat de notatie $35,(\ldots)$ betekent. 2. De komma met haakjes geeft aan dat het getal een repeterende decimale breuk is, bijvoorbeeld $35,\overl

1. Het probleem is om de waarde van $x$ te berekenen, maar er is geen vergelijking gegeven. 2. Om $x$ te berekenen, hebben we een vergelijking nodig waarin $x$ voorkomt, bijvoorbee

1. **State the problem:** Simplify the expression $$\frac{35x + 37(100 - x)}{100}$$. 2. **Apply the distributive property:** Expand the numerator.

1. **State the problem:** You sold 400 products last week and 600 products this week. We want to find the percentage improvement in sales. 2. **Formula:** The percentage improvemen

1. **State the problem:** We need to find 3% of 600. 2. **Formula:** To find a percentage of a number, use the formula:

1. **Problema:** Resolver la ecuación exponencial $$7^{2x+8} = 1$$. 2. **Fórmula y regla:** Sabemos que $$a^0 = 1$$ para cualquier base $$a > 0$$ y $$a \neq 1$$.

1. **Problem:** Solve the exponential equation $$7^{2x+8} = 1$$. 2. **Formula and rules:** Recall that for any base $a > 0$, $a \neq 1$, the equation $a^y = 1$ holds if and only if

1. **State the problem:** Solve the compound inequality $$-3x + 4 < x + 7 < 2x + 5$$. 2. **Understand the compound inequality:** This means both inequalities must be true simultane

1. The problem is to simplify the quadratic expression $x^2 - 9x + 14$. 2. We use factoring to simplify quadratic expressions of the form $ax^2 + bx + c$ by finding two numbers tha

1. Problem: Given midpoint M(3,4) and point A(5,7), find coordinates of point B. 2. Formula: Midpoint M of segment AB is given by $$M=\left(\frac{x_A+x_B}{2}, \frac{y_A+y_B}{2}\rig

1. **Énoncé du problème :** Calculer la moyenne arithmétique de deux nombres, ici les coordonnées des points A(-6 ; 3) et B(2 ; 7). 2. **Formule de la moyenne arithmétique :**

1. **State the problem:** Solve the equation $\frac{5y - 15}{5} = 3$ for $y$. 2. **Formula and rules:** To solve for $y$, we need to isolate $y$ on one side of the equation. We can

1. Das Problem lautet: Löse die Gleichung $2x + 3 = 11$ nach $x$ auf. 2. Die verwendete Formel ist die Umkehrung der Addition und Multiplikation, um $x$ zu isolieren. Wichtig ist,