🧮 algebra

1. **Stating the problem:** We have a sequence of tile patterns where the first two patterns have 21 and 33 tiles respectively. We need to find the number of tiles for the first fi

1. **Problem Statement:** Find the equation of line N passing through points $(-2,0)$ and $(0,20)$ in the form $y = mx + c$. 2. **Formula:** The equation of a line is $y = mx + c$,

1. State the problem: Solve the quadratic equation $x^2 - 5x + 6 = 0$. 2. Use the quadratic formula: $$x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}$$ where $a=1$, $b=-5$, and $c=6$.

1. Solve the linear equation $4x + 3 = 2x + 9$. Subtract $2x$ from both sides: $4x - 2x + 3 = 9$.

1. The problem is to find the $x$ and $y$ values of the function $g(x)$. 2. To analyze $g(x)$, we need the explicit formula or expression for $g(x)$, which is not provided in the q

1. **Problem Statement:** Identify the transformations from the graph of $f(x) = x^4$ to $g(x) = 5(x + 2)^4 - 4$ and describe how $g$ relates to $f$. 2. **General Transformation Fo

1. The problem is to understand how the numbers 8 and 1000 relate in binary and decimal systems. 2. The number 8 in decimal is represented in binary as $1000$.

1. Let's consider the problem: Simplify the expression $$\sqrt{50} + \sqrt{18} - \sqrt{8}$$. 2. First, recall the rule for simplifying square roots: $$\sqrt{a \times b} = \sqrt{a}

1. **State the problem:** Simplify the expression $6x+2$ multiplied by $5x+1$. 2. **Formula used:** To multiply two binomials, use the distributive property (also known as FOIL met

1. Diketahui determinan matriks pertama adalah $$\begin{bmatrix} a & b & c \\ d & e & f \\ g & h & i \end{bmatrix} = 3$$

1. Diketahui matriks 3x3 pertama adalah \(\begin{bmatrix} a & b & c \\ d & e & f \\ g & h & i \end{bmatrix}\) dengan determinan \(3\). 2. Matriks kedua adalah \(\begin{bmatrix} 2a

1. Problem 1: Number of tourists difference between 1993 and 2000. The number of tourists decreases by 10% per year starting from 1990 with 12000 tourists.

1. **مشكلة:** الفرق بين التعبيرات الجبرية التالية: - $x^2 + 1^2$

1. **Problem 301:** Given the initial number of people with internet access is 3.2 million in 2017, growing at 18% per year, find the expression for the number of people $y$ after

1. **Solve the equation** $3x(x - 2)(4x + 7) = 0$. The product of factors equals zero if any factor is zero.

1. The problem is to subtract 13 from 1, which is written as $1 - 13$. 2. The subtraction of a larger number from a smaller number results in a negative number.

1. **State the problems:** We need to solve two expressions involving fractions and mixed numbers:

1. مسئله اول: یافتن ضابطهٔ وارون تابع $$f(x) = \frac{x^2 - x - 6}{x - 3}$$ که به صورت $$f^{-1}(x) = \frac{(x - a)(x - b)}{x - b}$$ داده شده است و مقدار $$20 - b$$ را می‌خواهیم. 2.

1. **State the problem:** Simplify the expression $f = b - (a - 1) - [b - (-a - 1)] + (a + 6)$. 2. **Recall the rules:** When simplifying expressions, remove parentheses by distrib

1. **Problem 1:** Simplify and evaluate $$f(x) = \frac{\tan x \cos^2 x}{1 + \tan^2 x}$$ at given points. 2. **Recall the identity:** $$1 + \tan^2 x = \sec^2 x$$.

1. **Simplify the expression:** $5(-8 + 12) + 7 + 6^2 \times (4 \div 2)$ - First, simplify inside the parentheses: $-8 + 12 = 4$