🧮 algebra

1. **State the problem:** A factory needs to produce a batch of pens using 12 machines in 20 days. Due to a fault, only 3 machines worked for the first 8 days, then all 12 machines

1. **Stating the problem:** We have two types of printers, old and new, producing batches of comic books. We know the time taken by a certain number of printers to produce one batc

1. **State the problem:** We are given a vector $\mathbf{v} = \begin{pmatrix} -2 \\ 7 \end{pmatrix}$ and need to find its modulus (magnitude) $|\mathbf{v}|$. 2. **Formula:** The mo

1. **State the problem:** We are given the vector $\overrightarrow{AB} = \begin{pmatrix} -10 \\ 2 \end{pmatrix}$ and asked to find $8 \overrightarrow{BA}$ as a column vector. 2. **

1. The problem is to solve the equation and analyze its graph. 2. Since no specific equation was given, let's consider a common example: solve and graph the quadratic equation $$y

1. **State the problem:** We are given membership numbers of the Church of Jesus Christ of Latter-day Saints at five-year intervals from 2000 to 2015. We want to find the average n

1. **Problem Statement:** We are given a graph showing the cost to rent a moving truck for one day, depending on the distance driven in miles. The cost increases by the same amount

1. **State the problem:** Given $a=1$, $b=3$, and $c=5$, evaluate the expression $$(a=b)^2 - (b+c)^2$$. 2. **Clarify the expression:** The notation $a=b$ usually means equality, bu

1. **State the problem:** Simplify the expression $$\frac{\frac{1}{a^{2}} - \frac{1}{b^{2}}}{\frac{1}{a^{3}} + \frac{1}{b^{3}}}$$

1. **State the problem:** A wire of length $\frac{7}{8}$ meter broke into two pieces. One piece is $\frac{1}{4}$ meter long. We need to find the length of the other piece. 2. **For

1. **State the problem:** Simplify the expression $$\frac{1 + \frac{3}{x+2}}{1 + \frac{6}{x-1}}$$ and analyze its structure. 2. **Rewrite the expression:** To simplify, write numer

1. **State the problem:** We need to find the volume of a cuboid with side lengths given as $6r^2$, $6p$, and $7q^2$. 2. **Formula for volume of a cuboid:** The volume $V$ is given

1. **Problem Statement:** We have two clubs: Music and Mathematics.

1. **State the problem:** Solve the system of equations: $$y = -2x + 3$$

1. **Problem Statement:** We have two clubs: Music and Mathematics. Each originally has $x$ members.

1. **Problem Statement:** A trader buys 50 kg of type q groundnuts at 130 per kg and 75 kg of type r groundnuts at 180 per kg, then mixes them.

1. **Problem Statement:** We have two clubs: Music and Mathematics. Each originally has $x$ members.

1. **Stating the problem:** We need to solve the algebraic expression or equation provided by the user. Since no specific problem was given, please provide the problem statement fo

1. Let's clarify the problem: you want to find the degree of two functions, say $f$ and $d$. 2. The degree of a polynomial function is the highest power of the variable in the poly

1. Diketahui suku ke-3 ($a_3$) dan suku ke-10 ($a_{10}$) dari barisan aritmetika adalah 11 dan 67. 2. Rumus suku ke-n barisan aritmetika adalah $$a_n = a_1 + (n-1)d$$ di mana $a_1$

1. **Problem Statement:** Determine if equation D, $\frac{1}{2}x = x + \frac{1}{2}$, has one solution. 2. **Write the equation:**