🧮 algebra

1. Problem 7a: Duota, kad $a, b, c$ yra trys vienas po kito einantys aritmetinės progresijos nariai, taigi galime rašyti:

1. The problem asks to convert observations into a Total column and fill each row's cell based on weightage, rounding values with no decimals. 2. To solve this, we use the formula

1. Problema: Turime tris vienas po kito einančius geometrinės progresijos narius $a$, $b$, $c$, kurių suma lygi $-6$. Taip pat skaičiai $a$, $b$, $c+18$ yra aritmetinės progresijos

1. Problema: Verificăm dacă mulțimea M = {0,1,2,3,4,5} este parte stabilă a mulțimii Z în raport cu legea de compoziție dată. Partea stabilă înseamnă că pentru orice $x,y \in M$, r

1. **Problem:** Solve the system of equations: $$3x + 5y = 24$$

1. **Problem statement:** Given a charity association contributed $\frac{5}{12}$ of the total amount, the municipality contributed $\frac{2}{4}$, and the rest was contributed by a

1. **State the problem:** We have investment values $V(n)$ at different years $n$ and want to find an exponential regression model of the form $$V(n) = a \cdot b^n$$ where $a$ is t

1. **Stating the problem:** We are given the objective function $$Z = 18x + 10y$$ with a value of $$Z = 134$$ and several points and constraints:

1. **State the problem:** We are given two functions $f(x) = x + 3$ and $g(x) = x - 1$. We need to find the composite function $(fg)(x)$, which means $f(g(x))$. 2. **Formula and ex

1. **State the problem:** We are given two functions $f(x) = x + 3$ and $g(x) = x - 1$. We need to find the product of these functions, denoted as $(f \cdot g)(x)$, and simplify th

1. **State the problem:** We are given two functions $f(x) = x + 3$ and $g(x) = x - 1$. We need to find the function $(f - g)(x)$ and simplify it. 2. **Formula used:** The differen

1. **Énoncé du problème :** Soit $x$ un nombre réel tel que $x < 3$. Montrer que $2x + 3 > -5$ et $\sqrt{x + 13} < 4$.

1. **State the problem:** We are given three expressions involving exponents and asked to find values of $m$ and $n$, and to simplify an expression.

1. **Problem:** Simplify the expression $x^5 \times x^7$ and find the value of $m$ such that $x^5 \times x^7 = x^m$. 2. **Formula:** When multiplying powers with the same base, add

1. The problem is to evaluate the expression $14 - 2 \times 4 + 12$. 2. According to the order of operations (PEMDAS/BODMAS), multiplication is performed before addition and subtra

1. **State the problem:** We have a rectangular garden with an area of 40 m². The length and width are whole numbers, and we want to find the smallest possible perimeter. 2. **Form

1. **State the problem:** Find the value of $f(0)$ and find $x$ such that $f(x) = -5$ for the function $f : x \to \frac{1}{2}x - 1$.

1. **Stating the problem:** George takes out a loan with compound interest. We have the loan values at the start, after 1 year, and after 2 years. We need to find: a) The annual in

1. **Stating the problem:** George takes out a loan of £7500 that gathers compound interest. We are given the loan values after 1 and 2 years and need to find:

1. **Problem statement:** There are 1225 students arranged in rows such that the number of rows equals the number of students in each row. We need to find how many students are in

1. **State the problem:** Prove the inequality $$(a+1)(a+2)(a+3)(a+6) > 96a^2.$$\n\n2. **Rewrite the inequality:** We want to show that the product of these four linear terms is gr