🧮 algebra

1. The problem appears to involve calculating percentages or proportional values based on given numbers and amounts. 2. To find a percentage, the formula is: $$\text{Percentage} =

1. The problem is to simplify the expression $$4d^7 - (5q)^{\frac{3}{5}}$$ without further simplification or evaluation. 2. The expression consists of two terms: the first term is

1. The problem states that Millie truncates the number $N$ to 1 digit and the result is 8. 2. Truncating to 1 digit means keeping only the integer part of $N$ and discarding all di

1. **State the problem:** Rewrite the expression $$4(d)^{2/7} - (5q)^{3/5}$$ using radicals instead of fractional exponents.

1. **State the problem:** Solve the equation $\frac{x-5}{3} - 5 = \frac{x-9}{5}$ for $x$. 2. **Write down the equation:**

1. **State the problem:** Solve the equation $$\frac{x-2}{4} - 3 = \frac{x-4}{5}$$ for $x$. 2. **Identify the formula and rules:** To solve equations with fractions, first eliminat

1. **State the problem:** Solve the equation $\frac{x-2}{4} - 3 = \frac{x-4}{5}$ for $x$. 2. **Formula and rules:** To solve equations with fractions, first eliminate the denominat

1. The problem involves solving for $x$ given the equation $x = 23$ and other expressions involving $x$. 2. The first expression is $x = \frac{45}{23}$, which is a fraction represe

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 $$\begin{vmatrix} x + y & x & y \\ x & x + z & z \\ y & z & y + z \end{vmatrix}$$