🧮 algebra

1. **Problem:** Find the equation of the resulting graph $g(x)$ when $f(x) = x^2 + 2$ is vertically stretched with scale factor 2. 2. **Formula and Explanation:**

1. **State the problem:** Prove that $3\sqrt{3}$ (three times the square root of 3) is an irrational number. 2. **Recall definitions and properties:**

1. **State the problem:** We are given the distance between two cities as 17000 km, rounded to the nearest 1000 km. We want to write an inequality to show the possible limits of th

1. The problem states that 1/7 of the animals in a pet shop are gerbils. 2. We need to find the ratio of gerbils to other animals.

1. The problem states that pink paint is made by mixing red and white paint in a 2 : 3 ratio. 2. This means for every 2 parts of red paint, there are 3 parts of white paint.

1. **State the problem:** We have a cookie dough mix made up of butter, sugar, and flour. 2. **Given:** Butter is $\frac{2}{5}$ of the mix, sugar is $\frac{1}{3}$ of the mix.

1. Diketahui persamaan matriks $A = 2B^T$ dengan $$A = \begin{pmatrix} a & 4 \\ 2b & 3c \end{pmatrix}, \quad B = \begin{pmatrix} 2c - 3b & 2a + 1 \\ a & b + 7 \end{pmatrix}$$

1. The problem asks to draw the lines given by the equations $y = x$ and $x + y = 7$ on a grid. 2. The first line is $y = x$, which means for every $x$ value, $y$ is the same. This

1. **State the problem:** Solve the quadratic equation $3x^2 - 5x - 8 = 0$. 2. **Formula used:** The quadratic formula is given by

1. **State the problem:** Calculate the value of the expression $\frac{2072}{37} + (2626 - 2419) \times 27$. 2. **Apply order of operations:** According to the order of operations

1. **State the problem:** Given the equation $a^2 - ab$, multiply both sides by $a$ and follow the steps to simplify and solve for $a$. 2. **Step-by-step solution:**

1. **State the problem:** We are given integers $x$ and $y$ such that $3 < x < 7$, $4 < y < 9$, and $x + y = 13$. We need to find all possible values of $x$. 2. **Analyze the inequ

1. Problem: Find the value of the determinant $$\begin{vmatrix} x + y & x & y \\ x & x + z & z \\ y & z & y + z \end{vmatrix}$$

1. The problem is to arrange a given set of numbers in ascending order. 2. Ascending order means arranging numbers from the smallest to the largest.

1. **State the problem:** Simplify the expression $\frac{2}{5} + \frac{2}{9} + \frac{2}{11} + \frac{2}{3}$. 2. **Find a common denominator:** The denominators are 5, 9, 11, and 3.

1. لنفترض أن لدينا متراجحة نريد حلها، على سبيل المثال: $$2x - 3 > 7$$. 2. نبدأ بحل المتراجحة كما لو كانت معادلة، مع مراعاة قواعد المتراجحات، مثل:

1. نريد مقارنة بين $81^{41}$ و $55^{77}$ لمعرفة أيهما أكبر. 2. نستخدم اللوغاريتمات لتحليل المقارنة بدون آلة حاسبة. إذا كان $a^m > b^n$، فهذا يعني أن $m \log(a) > n \log(b)$.

1. The problem is to find the equation of the retrace or reflection of a given function or curve. 2. The general formula for retracing or reflecting a function $y=f(x)$ about the x

1. The problem is to simplify and understand the expression $$\frac{2 \left( \frac{2e^{2} - 1}{2ze} + Pn(2e) \right)}{(2e + 1)^{2}}$$ and then plot its curve. 2. The expression inv

1. The problem is to express the quadratic expression $x^2 + 14x + 49$ in the form $(x + a)^2$. 2. Recall the formula for a perfect square trinomial: $$(x + a)^2 = x^2 + 2ax + a^2$

1. **State the problem:** We need to evaluate the expression