🧮 algebra

1. **Problem Statement:** Draw addition ⊕ and multiplication ⊗ tables for the set {2, 4, 6, 8} modulo 9.

1. Planteamos el problema: Tenemos una maquinaria con valor depreciado linealmente, con valor S/24000 a los 4 años y S/18000 a los 10 años. 2. La fórmula para depreciación lineal e

1. **State the problem:** We need to determine the feasible region and vertices for the system of inequalities: $$4x - 2y < 2$$

1. **State the problem:** We need to find the number that should be added to $\frac{3}{32}$ to get $\frac{53}{96}$. 2. **Set up the equation:** Let the unknown number be $x$. Then,

1. The problem asks which method is used to solve a linear system by multiplying one or both equations by appropriate numbers so that one variable has the same coefficient with opp

1. **State the problem:** Find the y-intercept of the line given by the standard equation $$2x - 3y = 4$$. 2. **Recall the formula for y-intercept:** The y-intercept occurs where $

1. **State the problem:** We need to find the number that should be added to $\frac{3}{32}$ to get $\frac{53}{96}$. 2. **Set up the equation:** Let the number to be added be $x$. T

1. **State the problem:** Solve the system of equations for $x$, $y$, and $z$ given by: $$\begin{cases} y + 2 = 5 \\ 2x - y = 45 \\ 3y - 4z = 12 \end{cases}$$

1. Masalah: Diberi dua titik (5, m) dan (n, 9) yang memuaskan fungsi $$y = \frac{20}{x} + 4$$. Cari nilai $$m - n$$. 2. Formula fungsi yang diberikan adalah $$y = \frac{20}{x} + 4$

1. **Problem Statement:** We are working with a multiplication operation \(\otimes\) modulo 8 on the set \(\{3,5,7\}\).

1. Masalah: Diberi dua titik (5, m) dan (n, 9) yang memuaskan fungsi $$y = \frac{20}{x} + 4$$, cari nilai $$m - n$$. 2. Formula fungsi yang diberikan adalah $$y = \frac{20}{x} + 4$

1. Evaluate $12 - \left(\frac{8}{5} + 3 \div \frac{2}{3}\right)$. - First, calculate $3 \div \frac{2}{3} = 3 \times \frac{3}{2} = \frac{9}{2}$.

1. **State the problem:** Solve the equation $$|4x - 5| = |x - 1|$$ for $x$. 2. **Recall the property of absolute values:** For any real numbers $A$ and $B$, if $$|A| = |B|,$$ then

1. **Problem:** Calculate $12 - \left(\frac{8}{5} + 3 \div \frac{2}{3}\right)$ using BODMAS rules. 2. **Step 1:** Understand BODMAS (Brackets, Orders, Division/Multiplication, Addi

1. The problem is to simplify the expression $12 - \left( \frac{8}{5} + 3 \div \frac{2}{3} \right)$. 2. Recall the order of operations: parentheses first, then division and multipl

1. The problem is to simplify the expression $5x^2 + 5x$. 2. We use the distributive property which states that $a(b + c) = ab + ac$.

1. **State the problem:** Expand and simplify the expression $5x(x+1)$. 2. **Formula used:** Use the distributive property $a(b+c) = ab + ac$.

1. **State the problem:** Expand and solve the equation $5x(x-1) = 0$. 2. **Expand the expression:** Use the distributive property $a(b+c) = ab + ac$.

1. The problem involves understanding the correct direction of operations for four machines that transform input values to output values. 2. Machine 1 adds 8 to the input to get th

1. **Problem Statement:** A toy is sold for 220 with a profit rate of 10% on the cost price. We need to find the cost price. 2. **Formula:** Profit percentage is given by

1. The problem is to simplify the expression $5x - 5x$. 2. The formula used here is the distributive property and combining like terms: $a x - a x = (a - a) x = 0 \cdot x = 0$.