🧮 algebra

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

1. **State the problem:** Marion thinks of a number less than 15. She multiplies it by 3, subtracts 4, then divides the result by 5, and the final answer is 7. 2. **Set up the equa

1. The problem is to calculate the product of two fractions: $\frac{5}{8} \times \frac{2}{3}$ and simplify the result. 2. The formula for multiplying fractions is:

1. The problem is to multiply two fractions: $\frac{7}{8} \times \frac{5}{2}$.\n\n2. The formula for multiplying fractions is:\n$$\frac{a}{b} \times \frac{c}{d} = \frac{a \times c}

1. **Problem Statement:** We need to define a piecewise function $f(x)$ representing the cost of electricity for up to 700 units, where the cost per unit changes based on the numbe

1. The problem is to solve the equation or expression given by the user, but since no specific equation or expression was provided, I cannot solve a particular problem. 2. Please p

1. **Stating the problem:** We want to find the expression for $\tan^{-1}(\sqrt{x-3})$ or understand its behavior. 2. **Understanding the function:** The function is the inverse ta

1. The problem is to solve a GCSE level algebra question. Since no specific problem was given, let's consider a common example: Solve for $x$ in the equation $2x + 3 = 11$. 2. The

1. **Problem Statement:** Given the ratio $$(x - 2y + 8z) : (y - 3z + 4w) : (4x + 5z - 7w) = 3 : 4 : 7,$$

1. **Stating the problem:** Given the ratio $$ (x - 2y + 8z) : (y - 3z + 4w) : (4x + 5z - 7w) = 3 : 4 : 7 $$