🧮 algebra

1. **Problem 1(a)(i):** Find $s$ when $t=26.5$, $u=104.3$, and $a=-2.2$ using the formula $s = ut + \frac{1}{2}at^2$. 2. Substitute values:

1. لنبدأ بحساب \( \frac{144}{\sqrt{4}} \).\n\n2. نعلم أن \( \sqrt{4} = 2 \).\n\n3. إذن، \( \frac{144}{\sqrt{4}} = \frac{144}{2} = 72 \).\n\n4. الآن نحسب \( \sqrt{\frac{4}{81}} \cdo

1. The problem involves understanding how the fraction $\frac{4}{5}$ was obtained after dividing both sides of an equation by 625. 2. Suppose the original equation was $625x = 500$

1. Problem: Express $2x^2 - 8x + 1$ in the form $a(x+b)^2 + c$ where $a$ and $b$ are integers. Step 1: Factor out the coefficient of $x^2$ from the first two terms:

1. Let's first clarify the problem you are working on in Q4 to understand step 5 better. 2. Please provide the exact problem statement or the steps leading up to step 5.

1. The problem asks to find the value of $x$ that satisfies the equation $$\frac{2x+3}{4} = 5.$$\n\n2. To solve for $x$, first eliminate the denominator by multiplying both sides o

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

1. **State the problem:** Rationalize the denominator and simplify the expression $$\sqrt[4]{\frac{7}{8}}$$. 2. **Rewrite the expression:** We have $$\sqrt[4]{\frac{7}{8}} = \frac{

1. **State the problem:** Simplify the expression $$(2\sqrt{3} - 3)(2\sqrt{3} + 3).$$ 2. **Recognize the pattern:** This is a product of conjugates of the form $(a - b)(a + b) = a^

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 $\log k$: - $g:\quad g \log 20 + \log(0.2) = \log(20^g) + \log(0.2) = \log(20^g \times 0.2)$