🧮 algebra

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

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

1. **State the problem:** We are given several fractions and asked to analyze their equivalence. The reference fraction is $$\frac{4x - 28}{6x - 42}$$ and the other fractions are $

1. **State the problem:** Simplify the expression $$\frac{21y + 28}{15y^2 + 20y}$$. 2. **Factor numerator and denominator:**

1. **State the problem:** Simplify the fraction $$\frac{(3p)^2}{72pr}$$. 2. **Apply the exponent:** Recall that $ (ab)^2 = a^2 b^2 $. So,