🧮 algebra

1. Diketahui elips dengan sumbu panjang 12 dan eksentrisitas $e=\frac{2}{3}$, serta titik apinya pada sumbu X dan simetris terhadap titik O. 2. Tentukan persamaan elips tersebut.

1. **State the problem:** We are given the progression 81, 54, 36 and asked to find the sum of its terms. 2. **Identify the type of progression:** The terms decrease and the ratio

1. نبدأ بكتابة التعبير المعطى: $$\frac{4y^0}{630} + \frac{2}{5} \times \frac{3}{4}$$ 2. نعلم أن أي عدد مرفوع للأس صفر يساوي 1، إذن: $$y^0 = 1$$

1. **State the problem:** Solve the equation $$\frac{\pi}{2} + \frac{x}{2} = \frac{3\pi}{4}$$ for $x$. 2. **Isolate the term with $x$:** Subtract $$\frac{\pi}{2}$$ from both sides:

1. **Énoncé du problème** : Trouver l'ensemble des solutions du système linéaire représenté par la matrice augmentée $$\begin{bmatrix} 1 & 1 & 0 & | & 5 \\ 0 & 2 & 1 & | & 3 \\ 0 &

1. **State the problem:** We have a binary operation defined as $a*b = \frac{a}{b} + \frac{b}{a}$ for real numbers $a$ and $b$. 2. We are given the equation $((\sqrt{x})+1)*((\sqrt

1. لنحسب القاسم المشترك الأكبر (PGCD) للعددين 490 و 630. 2. نبدأ بتحليل كل عدد إلى عوامله الأولية:

1. **State the problem:** We are given the 4th and 5th terms of a geometric progression (G.P.) as $-13.5$ and $40.5$ respectively, and we need to find the first term $a$. 2. **Reca

1. Let's clarify the problem you are solving. It seems you have an expression or equation involving $\frac{7x-13}{x-2}$.\n\n2. If you want to simplify or verify this expression, no

1. **Problem statement:** Solve the system of equations using the substitution method: $$\begin{cases} y = 2x + 3 \\ 3x - y = 7 \end{cases}$$

1. **State the problem:** Simplify the expression $$6 + \frac{\frac{x + 5}{x^2 + 3x - 10}}{x - 1}$$ and show it can be written as $$\frac{ax - b}{cx - d}$$ where $a,b,c,d$ are inte

1. Write each expression as a single logarithm in the form $\log k$: - $g:\quad g \log 20 + \log(0.2) = \log(20^g) + \log(0.2) = \log(20^g \times 0.2)$

1. The problem defines a binary operation $*$ on real numbers such that for any real numbers $a$ and $b$, $$a * b = \frac{a}{b} + \frac{b}{a}$$

1. **Stating the problem:** Simplify the expressions: - $5 \times 3 = \frac{490}{630} + \frac{2}{5} \times \frac{3}{4}$

1. The problem is to simplify the expression $(2\sqrt{3}-3)(2\sqrt{3}+3)$.\n\n2. Recognize this as a product of conjugates of the form $(a-b)(a+b) = a^2 - b^2$. Here, $a = 2\sqrt{3

1. **Stating the problem:** We want to understand how logarithms with any base $b$ can be expressed using the natural logarithm base $e$. 2. **Formula:** The change of base formula

1. The problem is to understand and represent the inequalities on a number line: $x < 2$, $2 < x < 3$, $3 < x < 4$, and $x > 4$. 2. These inequalities divide the number line into f

1. Stating the problem: Simplify the expression $$(2\sqrt{3}-3)(2\sqrt{3}+3)$$. 2. Recognize this as a difference of squares pattern: $$(a-b)(a+b) = a^2 - b^2$$ where $a = 2\sqrt{3

1. The problem involves evaluating inequalities and expressions given as: - $x7 - 4$

1. Solve for $x$: 1.1.1 Solve $x^2 - 5x = 0$:

1. The problem is to simplify the expression $4x^2 + 12xy$. 2. Identify the common factors in both terms. Both terms have a factor of $4x$.