🧮 algebra

1. **Énoncé du problème :** Soit la suite $(u_n)$ définie par $u_0=1$ et $u_{n+1} = \frac{5u_n + 3}{u_n + 3}$ pour tout $n \in \mathbb{N}$.

1. **State the problem:** Factor the expression $$18m - 27n$$. 2. **Identify the greatest common factor (GCF):** The coefficients are 18 and 27. The GCF of 18 and 27 is 9.

1. **State the problem:** Factor the expression $$54x + 15y - 9$$. 2. **Identify the greatest common factor (GCF):** Look at the coefficients 54, 15, and 9. The GCF of 54, 15, and

1. **State the problem:** We need to find the cost of each item sold separately: small pizza ($x$), liter of soda ($y$), and salad ($z$). 2. **Write the system of equations from th

1. Énoncé du problème : Déterminer la nature de la fonction $f(x)=\frac{9x-10}{2x-3}$ et ses éléments caractéristiques. 2. Domaine de définition : La fonction est définie pour tous

1. **State the problem:** Solve the inequality $-2x - 76 > -66$. 2. **Isolate the variable term:** Add 76 to both sides to get rid of the constant on the left.

1. **State the problem:** Find the non-permissible values (values of $x$ that make the denominator zero) for the rational expression $$\frac{x^2 + 2}{x^2 - x - 6}$$ 2. **Formula an

1. The problem asks which inequality is true when $w = -2$. 2. We will substitute $w = -2$ into each inequality and check if the inequality holds.

1. Problema: Raskime begalinės nykstamosios geometrinės progresijos sumą, kai pirmasis narys $a_1=10$, o bendrasis vardiklis $r=\frac{1}{5}$.\n\n2. Formulė: Begalinės nykstamosios

1. Problema: Turime nurodytą nelyginės progresijos sumą $S = 20$ ir vardiklį $q = 0,8$. Reikia rasti pirmąjį narį $a_1$. 2. Formulė nelyginės progresijos sumai yra:

1. The problem asks to identify which sequence is not a convergent geometric progression. 2. A geometric progression (GP) is a sequence where each term is found by multiplying the

1. Problema: Raskime begalinės nykstamosios geometrinės progresijos 6-ąjį narį, kai pirmas narys $b_1 = 81$ ir bendrasis santykis $q = \frac{1}{3}$.\n\n2. Formulė: Geometrinės prog

1. The problem is to find the general term formula $x_n$ for the sequence: 5, $\frac{5}{2}$, $\frac{5}{4}$, ... 2. This is a geometric sequence where each term is obtained by multi

1. The problem asks to find the value of $x$ in the equation $3x - 7 = 11$. 2. The formula used here is to isolate $x$ by performing inverse operations.

1. **Problem 1: Tickets sold at the door** Tickets cost 4 in advance or 5 at the door. No tickets were sold in advance, total sales were 440. Find how many tickets were sold at the

1. **State the problem:** Solve the linear equation $$y - 42935 = 5135(x - 4200)$$ for $y$. 2. **Recall the point-slope form of a line:** $$y - y_1 = m(x - x_1)$$ where $m$ is the

1. Let's start with simplifying algebraic fractions. The problem is to simplify expressions like $$\frac{6x^2}{9x}$$. 2. The formula used is to factor numerator and denominator and

1. The problem asks to express the number 8 040 500 in scientific notation, which is in the form $a \times 10^n$ where $a$ is a number between 1 and 10, and $n$ is an integer. 2. T

1. The problem is to express the fraction 2/7 as a decimal or understand its value. 2. The fraction 2/7 means 2 divided by 7.

1. **State the problem:** Simplify the given expression step-by-step: $$\{(x,y) : x^2 - y^2\} + \{(3, 9+3) + (3, \frac{8}{3} \div \frac{1}{5})\} - 2 \{(1) \times (-1) - 6\} \div 4

1. **State the problem:** Chloe thinks of a number less than 15. She multiplies it by 2, subtracts 4, then divides the result by 3, and the final answer is 2. We need to find the o