🧮 algebra

1. **State the problem:** We are given an arithmetic progression (A.P.) with the first few terms 72, 68, 64, 60, … and we need to find which term is zero. 2. **Recall the formula f

1. The problem is to solve the equation or expression given previously, but now using a different method. 2. Since the original problem is not restated, let's assume it involves so

1. **State the problem:** Find the 19th term of the arithmetic progression (AP) 54, 51, 48, ... 2. **Formula used:** The $n$th term of an AP is given by $$a_n = a_1 + (n-1)d$$ wher

1. The problem is to determine if the 19th term of a given sequence is 0. 2. To solve this, we need the explicit formula or rule for the sequence to find the 19th term.

1. **State the problem:** We have an arithmetic progression (A.P.) with first term $a_1 = 54$, common difference $d = 51 - 54 = -3$, and we want to find the number of terms $n$ suc

1. Masalah yang diberikan adalah menyelesaikan pertidaksamaan $$|2x - 1| \leq |x + 3|$$. 2. Kita gunakan definisi nilai mutlak dan sifat pertidaksamaan: $$|A| \leq |B| \iff -|B| \l

1. Diberikan pertidaksamaan $$\sqrt{x} + 1 > 3 - x$$. 2. Tujuan kita adalah mencari nilai $x$ yang memenuhi pertidaksamaan ini.

1. **Problem statement:** Given a binary operation $*$ on real numbers defined by $a * b = a + b + \frac{2ab}{5}$, evaluate (i) $3 * 2$, (ii) $2 * (4 * 5)$. 2. **Formula and rules:

1. **State the problem:** Solve the quadratic equation $x^2 + 18x - 360 = 0$. 2. **Formula used:** The quadratic formula is given by $$x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}$$ wher

1. **Problem:** Find the value of $a$ such that the lines $L_1: 3x - ay - 2 = 0$ and $L_2: 6x - 4y + 3 = 0$ are parallel. 2. **Formula and rule:** Two lines $Ax + By + C = 0$ and $

1. **State the problem:** Simplify the expression $$(x-2y)(y-3x)+(x-y)(x-3y)-(y-3x)(4x-5y).$$ 2. **Use the distributive property (FOIL) to expand each product:**

1. **State the problem:** Simplify the expression $$(x-2y)(y-3x)+(x-y)(x-3y)-(y-3x)(4x-5y).$$ 2. **Recall the distributive property:** To simplify, we expand each product using $$(

1. **Stating the problem:** We are given a pattern of equations: $1 + 4 = 5$

1. **Stating the problem:** We are given the equation $0 = 5k_n$ and need to find the value of $k_n$. 2. **Formula and rules:** The equation is a simple linear equation. To solve f

1. **State the problem:** Simplify the expression $$\frac{x^{2} - 16}{x^{2} - 8x + 16} - \frac{x^{2}}{x^{2} + 4x} = \lambda$$ and express it in simplest form. 2. **Factor all polyn

1. **State the problem:** Solve the system of linear equations: $$3kx - 4y = 2$$

1. The problem is to understand the expression "it is not d/a b/c or q/b?" and clarify its meaning. 2. This looks like a question about fractions or ratios, possibly comparing or c

1. مسئله: حل معادله $$|2x+3| = -1$$. 2. قانون مهم: مقدار قدر مطلق $$|a|$$ همیشه بزرگتر یا مساوی صفر است، یعنی $$|a| \geq 0$$ برای هر عدد حقیقی $$a$$.

1. The problem is to analyze the ellipse given by the equation $$\frac{(x+5)^2}{100} + \frac{(y-5)^2}{49} = 1.$$\n\n2. This is the standard form of an ellipse centered at $(-5, 5)$

1. **State the problem:** We are given the ellipse equation $$\frac{(x + 11)^2}{25} + \frac{(y - 2)^2}{9} = 1$$ and need to analyze its properties.

1. The problem is to find the domain and range of a function. 2. The domain of a function is the set of all possible input values (x-values) for which the function is defined.