🧮 algebra

1. **Understanding Numbers** Numbers are the basic building blocks in math. They can be classified into different types: natural numbers ($1, 2, 3, \ldots$), whole numbers ($0, 1,

1. **Problem:** A boat travels at 15 km/hr in still water and the stream speed is 5 km/hr. Find the time to travel 60 km downstream. 2. **Formula:** Downstream speed = speed of boa

1. **State the problem:** Arrange the fractions $\frac{3}{2}$, $\frac{3}{9}$, and $\frac{3}{4}$ from largest to smallest. 2. **Recall the rule:** To compare fractions with the same

1. **Problem 9:** Casey and Jane bought turkeys and hams with different weights and total costs. We need to find the cost per pound of turkey and ham. 2. Let $t$ be the cost per po

1. **Stating the problem:** Arrange the fractions $\frac{3}{7}$, $\frac{5}{7}$, and $\frac{4}{7}$ from largest to smallest. 2. **Understanding the fractions:** All fractions have t

1. The problem is to arrange fractions from largest to smallest. 2. To compare fractions, we find a common denominator or convert them to decimals.

1. The problem is to find the value of $\sqrt{17}$, which means the square root of 17. 2. The square root of a number $x$ is a value that, when multiplied by itself, gives $x$. So,

1. **Problem statement:** We are given a geometric series where the sum of the first 3 terms is $\frac{19}{9}$ and the sum of the first 6 terms is $\frac{2179}{243}$. We need to fi

1. **State the problem:** Find the x-intercept and y-intercept of the linear equation $$7x + 7y = 21$$. 2. **Recall the intercept rules:**

1. **Problem Statement:** Find the x- and y-intercepts of the graph of the equation $$9x + y = 25$$. 2. **Formula and Rules:**

1. **State the problem:** Find the x- and y-intercepts of the line given by the equation $$-3x + 2y = 28$$. 2. **Recall the intercept definitions:**

1. **Problem 42: Calculate the total number of females and males given mature counts and percentages.** Given:

1. **State the problem:** Find the x- and y-intercepts of the line given by the equation $x + 10y = 20$. 2. **Recall the intercept rules:**

1. **State the problem:** Find the x- and y-intercepts of the line given by the equation $$x - y = 17$$. 2. **Recall the intercept rules:**

1. **Stating the problem:** Solve the inequality $5x + 3y > -15$ for $y$ in terms of $x$. 2. **Formula and rules:** To isolate $y$, we use basic algebraic operations: addition, sub

1. The problem is to find a function $f(x)$ such that $f(0)=7$, $f(1)=4$, and $f(2)=3$. 2. We can try to find a polynomial function that fits these points. Since we have three poin

1. **Stating the problem:** We have a scatter plot with points (1,7), (2,4), and (3,2) representing input-output pairs (Entrée, Sortie). We want to find the table of values and an

1. **Problem statement:** Find the number of pairs of natural numbers $(x,y)$ such that $$7x + 13y \leq 1000.$$ 2. **Understanding the problem:** We want to count all pairs $(x,y)$

1. **State the problem:** Solve the system of linear equations: $$3x - 2y = 7$$

1. **Problem Statement:** Find the Highest Common Factor (HCF) and Least Common Multiple (LCM) of the numbers 378, 180, and 420. 2. **Formula and Rules:**

1. **Stating the problem:** Find the Highest Common Factor (HCF) and Least Common Multiple (LCM) of the numbers 12, 21, and 15. 2. **Formula and rules:**