🧮 algebra

1. **State the problem:** Calculate the product of the two binomials $(-1 - 11)$ and $(13 - 5)$. 2. **Simplify each binomial:**

1. **State the problem:** Solve for $w$ in the equation $$-4(w+1) = -24$$. 2. **Use the distributive property:** Multiply $-4$ by each term inside the parentheses:

1. **State the problem:** Solve for $h$ in the equation $$\frac{h}{6} - 1 = -3$$. 2. **Add 1 to both sides** to isolate the term with $h$:

1. **State the problem:** Subtract the rational expressions $$\frac{9x^2 + 3}{14x^2 - 9} - \frac{-3x^2 + 11}{14x^2 - 9}$$. 2. **Identify the common denominator:** Both expressions

1. The problem is to simplify the function $f(x) = x + 2 - 2\sqrt{x - 1}$.\n\n2. We start by recognizing that the function contains a square root term $\sqrt{x - 1}$. The domain of

1. Menyatakan masalah: Selesaikan persamaan kuadrat $2x^2 - 3x - 5 = 0$.

1. **State the problem:** We are given the system of equations: $$x + 13 + y = 0$$

1. **State the problem:** We are given two linear equations and a value for $x$: $$x + 13 + y = 0$$

1. **State the problem:** Solve the equation $X + 13 + y = 0$ for one variable in terms of the other. 2. **Rewrite the equation:** The equation is $X + 13 + y = 0$.

1. The problem is to solve the quadratic equation $2x^2 - 5x + 3 = 0$. 2. We use the quadratic formula to solve equations of the form $ax^2 + bx + c = 0$:

1. مسئله را بیان می‌کنیم: تابع داده شده است $f(x) = a - 2 \sin^2\left(\frac{\pi}{b} x\right)$ و چهارضلعی $OABC$ مربع است. باید مقدار $f\left(\frac{1}{3}\right)$ را پیدا کنیم. 2. چو

1. **State the problem:** We are given the function $$y = 3 \sqrt[3]{x^5}$$ and want to understand its shape and behavior. 2. **Rewrite the function using exponent rules:** The cub

1. **Menjelaskan masalah:** Pak Andi memiliki tiga anak perempuan: Ani (anak termuda), Tina, dan Lisa (anak tertua). Rasio usia Ani terhadap Tina adalah 2:3, dan rasio usia Tina te

1. Masalah: Diberikan perbandingan usia Adi, Budi, dan Coki adalah 3 : 4 : 7 dan selisih usia Adi dan Coki adalah 20 tahun. 2. Kita misalkan usia Adi, Budi, dan Coki berturut-turut

1. **Problem statement:** The amount of a medicinal drug in the body $t$ hours after injection is given by $$D(t) = 23(0.85)^t, \quad t \geq 0,$$ with zero amount before injection.

1. **State the problem:** We are given the amount of a medicinal drug in the body at time $t$ hours after injection as $$D(t) = 23(0.85)^t, \quad t \geq 0.$$ We need to find:

1. **State the problem:** We are given a system of linear equations:

1. The problem is to evaluate the expression involving matrices and fractions given as: $$11^3 - \begin{bmatrix}-5 & 3 & 1 \\ 8 & 2 & 8\end{bmatrix} = \begin{bmatrix}1 & 3 \\ 2 & 4

1. **Stating the problem:** We are given a polynomial expression with variables $g, k, a, c, d, e, t, r$ and a system of equations relating these variables. The goal is to simplify

1. Diberikan fungsi $f(x) = \frac{2x - 1}{4x - 5}$. Kita diminta mencari fungsi inversnya, yaitu $f^{-1}(x)$. 2. Untuk mencari fungsi invers, kita mulai dengan mengganti $f(x)$ men

1. The problem is to analyze the function $f(x) = 2x - 1$. 2. This is a linear function of the form $f(x) = mx + b$, where $m$ is the slope and $b$ is the y-intercept.