🧮 algebra

1. The problem states we have a quadratic sequence with a general term involving 7, but the exact formula is unclear. Typically, a quadratic sequence has a general term of the form

1. **Stating the problem:** We have a quadratic sequence with a general term formula involving $n$, and we want to find the explicit formula or understand its properties given some

1. **State the problem:** Simplify the expression $$7\left(-12 + \frac{2}{7}\right) + 4 \begin{pmatrix} -5 & -1 \\ 2 & -1 \end{pmatrix}$$. 2. **Simplify inside the parentheses:** C

1. نبدأ بكتابة المسألة: \( \frac{\sqrt{83}}{32\sqrt{6}} \). 2. القاعدة المهمة هنا هي أن \( \frac{\sqrt{a}}{\sqrt{b}} = \sqrt{\frac{a}{b}} \).

1. **State the problem:** Solve the equation $$|7(\alpha + \beta) + 4(\gamma + \delta)| = 7 \left| -12 + \frac{2}{7} + \left(-\frac{5}{2} - 1\right) \right|$$ for the expression in

1. We are given a function $f: X \to Y$ with $X = \{a,b,c,d\}$ and $Y = \{1,2,3\}$, and the mappings $f(a) = 1$, $f(b) = 2$, $f(c) = 3$, $f(d) = 3$. 2. The problem asks to find val

1. Bài toán yêu cầu giải phương trình sau: a) \((3x - 2)(4x + 5) = 0\)

1. Het probleem: We willen weten hoe je een verticale asymptoot van een functie kunt berekenen. 2. Definitie: Een verticale asymptoot is een verticale lijn $x = a$ waar de functie

1. مسئله را بیان می‌کنیم: عددی داریم که اختلاف مربع عدد قبلش از مربع عدد بعدش برابر با آن عدد است. می‌خواهیم بدانیم این عدد از مربع کامل چند واحد کمتر است. 2. فرض کنیم عدد مورد نظر

1. Diberikan fungsi $f(x) = 2x + 3$. Kita diminta mencari nilai $f(-2)$. 2. Substitusikan $x = -2$ ke dalam fungsi:

1. **Problem b:** Evaluate $$\frac{-\sqrt{38}}{\text{trunc}(1.3) \times | -1.53 | \times \sqrt{1}}$$. 2. **Step 1:** Calculate each component.

1. The problem seems to involve verifying or calculating a value, possibly related to a previous question where the answer was suggested as 1.11852. 2. Without the original problem

1. **Problem b:** Evaluate $$\frac{| -\sqrt{38} |}{\text{trunc}(1.3) | -1.53 | \sqrt{|1|}}$$ 2. **Step 1:** Calculate the numerator:

1. The problem is to solve the first question from the provided document link. Since the link is inaccessible, I will solve a common algebra problem as an example. 2. Let's solve t

1. समस्या: हमें एक सरल समीकरण हल करना है। 2. नियम: समीकरण को हल करने के लिए, हम दोनों पक्षों में समान क्रियाएं करेंगे ताकि समीकरण संतुलित रहे।

1. **State the problem:** Solve the equation $$\frac{2x - 4}{3} - \frac{3x + 2}{4} = \frac{x - 5}{6} - 3$$ given $x = 12$. 2. **Substitute $x = 12$ into the equation:**

1. The problem gives three quadratic functions: $$J = x^2 + 6x + 9$$, $$K = 5x^2 - 2\sqrt{5} x + 1$$, and $$L = 7x^2 - 1$$. We are asked to analyze their shapes and properties. 2.

1. **State the problem:** Find the equation of the ellipse with axes along the coordinate axes, vertices at $(\pm 5, 0)$, and foci at $(\pm 4, 0)$.\n\n2. **Recall the standard form

1. Problem: A bookworm bores horizontally from the first page of Volume 1 to the last page of Volume 3. Each volume is 1 inch thick without covers, and each cover is \frac{1}{16} i

1. **Problem statement:** Find the length of the major and minor axes, coordinates of foci and vertices, and eccentricity for the ellipses: (i) $16x^2 + 25y^2 = 400$

1. **Problem:** A shopkeeper earns a profit of 70 for every 3 bags of wheat sold. How many bags must be sold to make a profit of 1400? 2. **Formula:** Profit per bag = \frac{70}{3}