🧮 algebra

1. Masalah yang diberikan adalah mencari banyaknya bilangan bulat $a$ dengan $0 \leq a \leq 10$ sehingga $$\frac{a(a^2-1)}{e}$$ selalu merupakan bilangan asli. 2. Kita perhatikan t

1. **Énoncé:** Donner 1 monocle sur 1 oains, égaux à 9 dont la démonstration implique à 91 - 19. Cette phrase semble très confuse et peut contenir des erreurs ou être mal traduite.

1. **State the problem:** We need to find the value of $F$ given the formula $$F = \frac{2(v^2 - u^2)}{3}$$ and values $u = -8$, $v = -5$. 2. **Substitute the values:**

1. The problem is to sketch the curve given by the quadratic function $$y = x^2 - 6x + 8$$. 2. First, identify the key features of the quadratic: the vertex, axis of symmetry, and

1. **State the problem:** Factorize the quadratic expression $$4b^2 + 4b + 1$$. 2. **Look for a perfect square:** Note that $$4b^2 = (2b)^2$$ and $$1 = 1^2$$.

1. **State the problem:** Find the turning point (vertex) of the curve given by the quadratic function $$y = x^2 - 6x + 8$$ by completing the square. 2. **Rewrite the quadratic exp

1. We are asked to evaluate the expression $2 + \sqrt{x+4}$ for values of $x$ between $-3$ and $12$ inclusive. 2. First, check the expression inside the square root: $$x+4$$ It mus

1. The problem is to find the greatest length of a wooden scale which can measure 540 cm and 360 cm exactly. 2. This means the scale length must be the greatest common divisor (GCD

1. Problem: Find the greatest length of a wooden scale which can be used to measure 540 cm and 360 cm exactly. Step 1: We need to find the Greatest Common Divisor (GCD) of 540 and

1. **Stating the problem:** We want to factorize the expression $$x^4 + 4y^4$$. 2. Notice that $$x^4 + 4y^4$$ is a sum of squares: $$x^4 + (2y^2)^2$$.

1. State the problem: We want to factorize the expression $14x^{2} - 49x^{2}$. 2. Combine like terms: Since both terms have $x^{2}$, subtract the coefficients:

1. The problem involves subtracting two scalar multiples of vectors: $$\frac{3}{7}(2, 8a - 2, 1) - \frac{1}{9}(2, 7a - 3, 6)$$

1. **State the problem:** We need to factorize the quadratic expression $x^2 + 14x + 49$. 2. **Identify coefficients:** The quadratic is in the form $ax^2 + bx + c$ where $a=1$, $b

1. Énoncer les définitions du cours : 1) Une valeur propre \(\lambda\) d'un endomorphisme \(f\) est un scalaire tel qu'il existe un vecteur non nul \(v\) vérifiant \(f(v) = \lambda

1. Muammoni tushuntirish: berilgan ifodalar ustida amallarni bajarish kerak: 28. $1 \tfrac{3}{7} (2.8a - 2.1) - 1 \tfrac{1}{9} (2.7a - 3.6)$ ni hisoblaymiz.

1. Let's start by writing the expression clearly: $$\sqrt{2 - \frac{\sqrt{3}}{2}} \times \sqrt{2 + \frac{\sqrt{3}}{2}}$$ 2. We can use the property of square roots that $$\sqrt{a}

1. **State the problem**: Simplify the expression $$\sqrt{2 - \frac{\sqrt{3}}{2}} \times \sqrt{2 + \frac{\sqrt{3}}{2}}.$$\n\n2. **Recall the property of radicals**: The product of

1. The problem involves calculating simple interest, which is given by the formula $$SI = \frac{P \times R \times T}{100}$$ where $P$ is the principal, $R$ is the rate per annum, a

1. Stating the problem: We have a geometric progression (GP) where the third term is $\frac{9}{2}$ and the fifth term is $\frac{81}{8}$. We need to find: A. The common ratio $r$

1. We are given a geometric progression with terms $2$, $x$, $y$, and $250$. 2. In a geometric progression, the ratio between consecutive terms is constant. Let this common ratio b

1. The problem asks to find the product of 1 and \(\pi\).\n2. Recall that multiplying any number by 1 results in the same number.\n3. Therefore, \(1 \times \pi = \pi\).\n\nFinal an