🧮 algebra

1. **State the problem:** We need to find the percentage increase when a company's sales increase from 250 to 300. 2. **Formula for percentage increase:**

1. **Problem statement:** A can finish the entire task alone in 12 hours. We need to determine if A can finish half the task in 6 hours. 2. **Formula and concept:** The work rate o

1. **Problem statement:** Two persons start walking from the same point in opposite directions. One walks at 4 km/hr and the other at an unknown speed $x$ km/hr. We need to find th

1. The problem states that $3A = 2B = 6C$. We need to find the ratio $A : B : C$. 2. Let the common value be $k$, so:

1. **State the problem:** Solve the inequality $\frac{x}{2} + 1 \leq 5$. 2. **Formula and rules:** To solve inequalities, we isolate the variable on one side. Remember, when multip

1. **مقارنة العددين $2\sqrt{7}$ و $7\sqrt{2}$** نبدأ بحساب قيمة كل عدد تقريبا:

1. **Problem Statement:** We need to find the total number of 4-digit numbers between 1000 and 3000 that are divisible by 4, formed using the digits 1, 2, 3, 4, 5, and 6 without re

1. The problem states: For the quadratic equation $$3.089\cdot 2x^1 - (1 - 3b)x + 5b = 0$$ one root is $b$. We need to find the value of $b$. 2. The general form of a quadratic equ

1. **State the problem:** Solve the inequality $\frac{x}{3} > 4$. 2. **Formula and rules:** To solve inequalities involving division or multiplication by a positive number, you can

1. **State the problem:** We are given the system of inequalities: $$3x + y \geq 3$$

1. **State the problem:** We are given the system of inequalities:

1. **Stating the problem:** We are given the number of students in each grade category and the corresponding sector angles in a pie chart. We need to identify which grade's sector

1. **State the problem:** Anna inputs the same number $x$ into two different function machines, and the outputs are equal. We need to find the value of $x$. 2. **Write the expressi

1. **State the problem:** Solve the equation $$\frac{45 - x}{x} = 4$$ for $x$. 2. **Formula and rules:** This is a rational equation where the variable $x$ is in the denominator. T

1. **Stating the problem:** We need to solve the expression $$h^2 = (2 m^2 + 3)(4 m - 10)$$ for $h^2$ in terms of $m$. 2. **Formula and rules:** To simplify, we use the distributiv

1. The problem is to find the value, but the expression or equation to evaluate is missing. 2. To solve any problem, we need a clear mathematical expression or equation.

1. The problem is to find the reciprocal of an expression involving indices (exponents). 2. The reciprocal of a number or expression $a$ is $\frac{1}{a}$.

1. **State the problem:** Simplify the expression $$\frac{16^{\frac{3}{4}n}}{8^{\frac{5}{3}}} \times 4^{n-1}$$. 2. **Recall the rules:**

1. **State the problem:** The price of apples increased by $0.75$ per pound. Sam bought $3$ pounds at the new price, paying a total of $5.88$. We need to find the original price pe

1. **State the problem:** Fabio scored 31 points in the last game. Fabio had 7 points less than 2 times as many points as Carlos. We need to find how many points Carlos scored, den

1. **State the problem:** We need to find a fraction where the denominator is 3 less than the numerator. 2. **Define variables:** Let the numerator be $x$. Then the denominator is