🧮 algebra

1. The problem asks for the best approximation of $\sqrt{91}$.\n\n2. We note the perfect squares near 91: $81 = 9^2$ and $100 = 10^2$.\n\n3. Since $91$ is between $81$ and $100$, i

1. The problem asks to solve an equation or expression using decomposition, but the specific problem is missing. 2. Decomposition generally means breaking down a complex expression

1. **State the problem:** Simplify the expression $$\frac{3(6-x)}{x^3+27} + \frac{x-3}{x^2-3x+9} - \frac{1}{x+3}.$$\n\n2. **Factor denominators where possible:**\n- $x^3+27$ is a s

1. **Problem Statement:** Factor the cubic polynomial $$6x^3 + 33x^2 + 45x$$. 2. **Identify the greatest common factor (GCF):** The coefficients 6, 33, and 45 share a common factor

1. **State the problem:** Find the factors of 324 that add up to 15. 2. **Find the factors of 324:**

1. Let's restate the problem: Find a factor of 300 such that when the factor and some other number are added, the sum equals -65. 2. First, list the factors of 300. Since 300 = $2^

1. **State the problem:** Determine on which intervals the function $f(x) = |9 - x^2|$ is decreasing. 2. **Analyze the function:** Inside the absolute value, we have the quadratic

1. **Stating the problem:** We have a cubic function $$y = ax^3 + bx^2 + cx + d$$ that passes through points $(3,0)$ and $(0,6)$, and has a critical point at $(2,2)$. 2. **Using gi

1. Kita diminta menentukan banyaknya bilangan bulat $a$ dengan $0 \leq a \leq 10$ sehingga $$\frac{a(a^2-1)}{3}$$ merupakan bilangan asli. 2. Bentuk tersebut dapat ditulis ulang se

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: $$\frac{3}{7}(2, 8a - 2, 1) - \frac{1}{9}(2, 7a - 3, 6)$$