🧮 algebra

1. **State the problem:** Find all functions $f:\mathbb{R} \to \mathbb{R}$ such that for every $x,y \in \mathbb{R}$, the equation $$1 + f(xy) = f(x + f(y)) + (y - 1)f(x - 1)$$

1. **Problem:** Find the cube root of each of the following numbers: 0, 27, 729, 1728, 6859, and \(\left(\frac{1}{2}\right)^3\). 2. **Formula:** The cube root of a number \(a\) is

1. **Problem Statement:** Find the difference between the temperatures of Lahore and Muree. 2. **Given:** Temperature of Lahore = 24°C, Temperature of Muree = -10°C.

1. **State the problem:** Calculate the total gross income in PHP for a 5-day/4-night group tour to Israel for six adults, given airfare, hotel, and ancillary service costs with ag

1. **State the problem:** Calculate the total gross income in PHP for a 5-day/4-night group tour to Israel for six adults, given airfare, hotel, and ancillary service costs with ag

1. **State the problem:** Simplify the expression $$[(24 - 6) \div 3 - 5] \times (-2)$$. 2. **Apply the order of operations (PEMDAS/BODMAS):**

1. **Problem Statement:** Solve for $x$ in the equation $8x + 4 = 3(x - 1) + 7$. 2. **Formula and Rules:** To solve linear equations, we use the rule of balancing both sides by per

1. **State the problem:** We want to solve the equation $$\sin(0.5t) + 0.3t = 1$$ for $$0 \leq t \leq 1$$. 2. **Understand the equation:** This is a transcendental equation involvi

1. Simplify the expression $x^3 \cdot x^{-5}$. 2. Simplify the expression $\frac{m^{-4}}{m^{-2}}$.

1. The problem is to solve the equation $$\sin(0.5t) + 0.3t = 1$$ for the variable $t$. 2. This is a transcendental equation because it involves both a trigonometric function and a

1. The problem asks to find the sum of the integers from 1 to 5. 2. We use the formula for the sum of the first $n$ natural numbers: $$S = \frac{n(n+1)}{2}$$ where $n$ is the last

1. **State the problem:** Simplify the expression $4x + 7x - 2y + 5y$. 2. **Formula and rules:** To simplify algebraic expressions, combine like terms. Like terms have the same var

1. Diberikan sistem persamaan linear: $$4y - 9x = 34$$

1. Diberikan sistem persamaan: $$4y + 9x = 34$$

1. Masalah: Susun angka-angka berikut ke dalam sebuah matriks. 2. Angka yang diberikan adalah: $-0.0322$, $0.0000196$, $-10.0715$, $-0.000039$, $0.8876$, $-0.00127$.

1. Diberikan fungsi $f(x)=3x^5-5x^3+1$. Kita diminta menentukan interval di mana fungsi meningkat, menurun, konkaf ke atas, konkaf ke bawah, serta titik maksimum lokal/global, mini

1. The problem involves finding the sum of two fractions: $\frac{1}{2}$ and $\frac{1}{3}$.\n\n2. To add fractions, we need a common denominator. The denominators are 2 and 3, so th

1. The problem is to calculate the total work done when 15 workers work for 28 days. 2. The formula used here is: $$\text{Work} = \text{Number of workers} \times \text{Number of da

1. Masalah: Selesaikan persamaan $x^2 - 11 = 0$ menggunakan metode Interval Bagi-Dua dengan interval awal $x_0 = 1$ dan $x_1 = 3$. 2. Metode Interval Bagi-Dua (Metode Bisection) di

1. The problem is to solve the equation $x - 12 = 7$ using the unitary method. 2. The unitary method involves finding the value of one unit and then using it to find the value of t

1. **Nyatakan masalah:** Kita diminta mencari nilai $y_2$ dari persamaan berikut: $$30.84 = 1 \times \left(\frac{26.01 + 38.01}{2} \times \frac{38.01 + 2y_2}{2}\right)^{\frac{5}{3}