🧮 algebra

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.

1. Masalah: Seorang peternak memiliki pakan untuk 30 ekor sapi yang cukup untuk 20 hari. Jika peternak menjual 5 ekor sapi, berapa lama pakan tersebut akan habis? 2. Rumus yang dig

1. **State the problem:** Evaluate the expression $-3(-11+2\times4)^2$. 2. **Apply order of operations:** First, calculate inside the parentheses and perform multiplication before

1. **State the problem:** Find the coordinates of points A and B where the curve $y = \sqrt{3x - 2}$ intersects the line $y = \frac{1}{2}x + 1$. 2. **Set the equations equal to fin

1. The problem is to understand when a graph represents a relation that is also a function. 2. The key rule is the Vertical Line Test: A graph represents a function if and only if

1. **State the problem:** Evaluate the expression $a + \frac{a b^2}{c}$ for $a=3$, $b=4$, and $c=6$. 2. **Write the formula:** The expression is given by

1. El problema es encontrar el límite $$\lim_{x \to 3} \frac{x^2 - 9}{x - 3}$$. 2. La fórmula para límites que resultan en una indeterminación $$\frac{0}{0}$$ es factorizar el nume

1. **State the problem:** Solve the equation $\frac{4}{3} = \frac{6}{4.5}$ and check if it is true. 2. **Recall the rule:** Two fractions $\frac{a}{b}$ and $\frac{c}{d}$ are equal

1. **Stating the problem:** We want to multiply the scalar $\sqrt{x}$ by the matrix $\begin{bmatrix}a & b \\ c & d\end{bmatrix}$.

1. **State the problem:** Solve the equation $$\frac{9}{4}y - 12 = \frac{1}{4}y - 4$$ for $y$. 2. **Write down the equation:** $$\frac{9}{4}y - 12 = \frac{1}{4}y - 4$$