📘 algebra and geometry

1. حل المعادلة 3(x - 2) = 0 نبدأ بكتابة المعادلة:

1. **Problem 1: Choose the correct answers for each expression.** (1) Factorize $x^2 - ax + bx - ab$.

1. Problem 32(a): An arithmetic progression (AP) has $n$ terms, the $n^{th}$ term is 4, and the common difference $d=2$. The sum of $n$ terms $S_n = -14$. Find $n$ and the sum of t

1. **Problem 6:** Given that $y$ varies directly as the square of $(x+1)$, and $y=200$ when $x=-4$, find the equation connecting $y$ and $x$. 2. **Step 1:** Write the variation equ

1. Problem 6: Given that $y$ varies directly as the square of $(x+1)$, we write the variation as: $$y = k(x+1)^2$$

1. **Determine the height of the plant after 4 weeks using** $H(t) = 2t^3 - 5t^2 + 3t + 1$. Substitute $t=4$:

1. **Problem 1:** Solve the equation $4x + 5(2x - 7) = 7$. 2. Expand the expression:

1. **Problem 1: Determine the truth of each statement for any nonzero rational number $a$.** a. The product $4a$ is negative.

1. **Statement of the problem:** We have three exercises involving algebraic expressions and geometry.

1. **Calculate** $-\frac{12}{5} + \frac{7}{8} - \frac{4}{9} + \frac{3}{5}$. Find common denominator, which is $\mathrm{lcm}(5,8,9) = 360$.

1. The term with number without variable is called the **Constant Term**. 2. The function $y = x^4 + 1$ is a **Quartic Function** because the highest power of $x$ is 4.

1. The problem asks to find $x$ given the determinant equation: $$\begin{vmatrix} 2 & 6 \\ 3 & x \end{vmatrix} = 0.$$ 2. Calculate the determinant using the formula for a 2x2 matri

1. The unit of area is the square meter, represented as $m^2$. 2. A quadrilateral having each angle equal to 90° is called a Rectangle.

1. Problem: Two contiguous square lots have a total area of 4703 m² and require 282 m of fence to enclose them as a six-sided figure. Find the side length of the larger lot. Step 1

1. Problem 1: Find $\sqrt{11001_2}$ and express the answer in base two.\n\n2. First, convert $11001_2$ (binary) to decimal:\n$$11001_2 = 1\times 2^4 + 1\times 2^3 + 0\times 2^2 + 0