🧮 algebra

1. **State the problem:** Find the area of the region enclosed by the curves given by the function $y = (2x - 1)(2x + 1)$. 2. **Rewrite the function:** Expand the product to get a

1. **State the problem:** We want to find an explicit formula for the sequence $a_n$ defined by the recurrence relation $$a_n - 8a_{n-1} + 15a_{n-2} = n5^n, \quad n \geq 2$$

1. **State the problem:** Find the area of the region enclosed by the curve $y=(2x-1)(2x+1)$ and the x-axis. 2. **Rewrite the function:** Expand the product:

1. **State the problem:** We need to solve the system of inequalities:

1. **State the problem:** We are given two equations:

1. The problem asks to find the value of the sum $$1 + i + i^2 + i^3 + i^4 + \cdots + i^{16}$$ where $i$ is the imaginary unit with the property $i^2 = -1$. 2. Important property:

1. The problem involves a piecewise function: $$f(x) = \begin{cases} x^2 & \text{if } x > 10 \\ 3x + 1 & \text{if } x \leq 10 \end{cases}$$

1. **State the problem:** Find the Highest Common Factor (HCF) of 40 and 50. 2. **Formula and rules:** The HCF of two numbers is the largest number that divides both without leavin

1. **State the problem:** Find the least common multiple (LCM) of 10 and 4. 2. **Formula and rules:** The LCM of two numbers is the smallest positive integer that is divisible by b

1. The problem is to find the least common multiple (LCM) of 8 and 4. 2. The LCM of two numbers is the smallest positive integer that is divisible by both numbers.

1. **State the problem:** Find the least common multiple (LCM) of 8 and 4. 2. **Formula and rules:** The LCM of two numbers is the smallest positive integer that is divisible by bo

1. Muammo: Kumush va misdan iborat qotishmaning og’irligi 2 kg. Kumushning og’irligi mis og’irligining $\frac{7}{9}$ qismini tashkil etadi. Kumushning og’irligini toping. Formulala

1. **State the problem:** We are given a graph of a function $f$ and need to find the values $f(-14)$, $f(0)$, and $f(-7)$ from the graph. 2. **Analyze the graph:** The graph is a

1. Muammo: Qotishmaning 60% misdan iborat va mis qo’rg’oshindan 2 kg ko’p. Qotishmada qancha mis bor? Formulalar:

1. Bir ishchi buyurtmani 6 soatda, boshqasi esa 10 soatda bajaradi. Ular birgalikda 3 soat ishlaganglaridan keyin ishning qancha qismi bajarilmay qoladi? Ishchi 1 soatda ishning $\

1. Masala: Anvarning o'ziga suv 20 kunga, uksagiga 60 kunga yetadi. Ikkalasi birga necha kunga yetadi? Formulasi: Ikkala odamning bir kunda ishlatadigan suv miqdori qo'shiladi, key

1. Probleem: teisendada protsent kümnendmurruks, säilitades 4 kohta pärast koma. 2. Valem protsendi teisendamiseks kümnendmurruks on $$\text{kümnendmurd} = \frac{\text{protsent}}{1

1. **Problem:** Evaluate the expression $$\frac{0.13 \times 0.3 - 0.003}{0.09}$$ without using a calculator or tables. 2. **Formula and rules:** We use basic arithmetic operations

1. **Problem:** Evaluate the expression $$\frac{0.13 \times 0.3 - 0.003}{0.09}$$ without using a calculator or tables. 2. **Formula and rules:** Multiplication and subtraction of d

1. **State the problem:** We are given the function $f(x) = -\left(\frac{5}{2}\right)^x$ and want to understand its behavior and graph. 2. **Formula and rules:** This is an exponen

1. **State the problem:** We need to graph the exponential function $$f(x) = - \left(\frac{3}{5}\right)^{-x}$$ and plot five points on its graph, as well as draw the horizontal asy