🧮 algebra

1. **Stating the problems:** We have two main problems:

1. The problem asks us to find the missing numerator and denominator in the equivalent fractions: $$\frac{?}{8} = \frac{14}{16} = \frac{35}{?}$$

1. **State the problem:** We need to find a three-digit number where the sum of its digits is 11. 2. **Define variables:** Let the hundreds digit be $h$, the tens digit be $t$, and

1. **State the problem:** Simplify the expression $\frac{6}{2}(1+2)$. 2. **Apply the order of operations (PEMDAS/BODMAS):** Parentheses first, then multiplication and division from

1. The problem is to understand the expression $10t$. 2. In algebra, $10t$ means 10 multiplied by the variable $t$.

1. **State the problem:** We need to find a two-digit number where the tens digit is 3 less than the units digit, and the number itself is 9 more than four times the sum of its dig

1. **State the problem:** Solve the equation $x + (x-4) = 9x (x-4) + 4$ for $x$. 2. **Write the equation clearly:**

1. The problem is to find the equation of the function or solve the given expression (please provide the specific problem for detailed steps). 2. Generally, for algebraic problems,

1. **Problem Statement:** Find the slope of the lines passing through each pair of points and determine if the lines are parallel or perpendicular. 2. **Formula for slope:** The sl

1. **State the problem:** Solve the Diophantine equation $$45x + 30y = 15$$ for integers $x$ and $y$. 2. **Formula and rules:** A linear Diophantine equation in two variables $ax +

1. **Problem Statement:** Find the slope of the line passing through two points for each pair given. 2. **Formula:** The slope $m$ between two points $(x_1, y_1)$ and $(x_2, y_2)$

1. **State the problem:** Write the expression $\frac{x^4}{x^3} \times \frac{3}{4}$ as a single fraction in its simplest form. 2. **Recall the laws of exponents:** When dividing po

1. The problem asks to find the first four terms of the sequences given in parts a), b), and c). 2. For part a), the sequence is not clearly readable, but assuming it is $a_n = n$,

1. **State the problem:** We have a triangle and a rectangle with given dimensions and areas. The triangle's height is $h$ and base is $x$. The rectangle's height is $(h+2)$ and le

1. The problem is to express the number 5.1 x 10^-2 in decimal form. 2. The number is given in scientific notation, which is a way to express very large or very small numbers.

1. The problem is to express the number 2.74 x 10^{-5} in standard decimal notation. 2. The number is given in scientific notation, which is of the form $a \times 10^{n}$ where $a$

1. **Problem Statement:** In a class, 50% students passed in Maths, 55% passed in English, and 15% passed in both subjects. 60 students failed in both subjects. Find:

1. **Problem statement:** Ramon usually drives $\frac{3}{5}$ of a kilometer to pick up Joe, then they drive another $\frac{4}{5}$ of a kilometer to work. Today, Ramon drives direct

1. **State the problem:** We have three ropes with lengths in the ratio 7 : 4 : 9. The longest rope is 63 meters. We need to find the difference in length between the other two rop

1. **Problem (a):** Find the equation of the line with x-intercept 5 and passing through (6,9). - The x-intercept means the line crosses the x-axis at (5,0).

1. **Problem Statement:** Given: