📘 algebra, geometry

1. نبدأ بحل المعادلة: $$0 = 3(x - 2)$$ 2. نوزع 3 على القوس: $$0 = 3x - 6$$

1) **حل المسألة الأولى: العمليات على المجموعات باستخدام خط الأعداد** ① لدينا المجموعتين $[-1,4]$ و $[2,5]$ ونريد اتحادهما $[-1,4] \cup [2,5]$.

1. **Problem 1: Find the median length of the leaves given the frequency distribution.** We have the length intervals and the number of leaves in each interval:

1. **Stating the problem:** Simplify and evaluate the expressions for $X$, $Y$, $A$, $B$, and $C$, and solve the geometric problem involving triangle $ABC$ with given segment ratio

1. نبدأ بحل المعادلة الجبرية المعطاة: $$س - 3س - 1 = 0$$. 2. نجمع الحدود المتشابهة: $$س - 3س = -2س$$، إذن المعادلة تصبح:

1. Problem 65: A miller takes 1/10 of the flour he grinds as his fee. A customer has exactly one bushel left after the fee. How much flour did the miller grind? 2. Let the total am

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 direct variati

1. **Problem statement:** We have several algebraic expressions and geometric questions to solve.

1. Problem 1: The total cost of a tablet device is divided into material, labour, and overheads in the ratio 3:4:1. The cost of material is given as 315.

1. **Factorize** $25 - 16x^2$. This is a difference of squares: $a^2 - b^2 = (a - b)(a + b)$.

1. **Problem:** Identify the graph type for each polynomial function given. 2. **Step 1:** Understand the shape of polynomial graphs based on degree and leading coefficient.

1. **Convert the trapezoid dimensions to centimeters and find the area.** - Given: 1 m vertical segment, horizontal segments 2 m, 300 cm, 2 m.

1. Problem 6: A relief organization donated 240 kg of maize and 150 kg of beans to needy families. Each family received exactly the same quantity by mass of either maize or beans,

1. The problem asks for the possible values of $n$ in $f(x) = x^n$ if $f$ is a polynomial function. 2. Polynomial functions have non-negative integer exponents. So $n$ must be a wh

1. The problem asks which values of $n$ can be used in $f(x) = x^n$ for $f$ to be a polynomial function. 2. Polynomial exponents must be whole numbers (non-negative integers). So $

1. The problem asks which values of $n$ can be used in $f(x) = x^n$ if $f$ is a polynomial function. 2. A polynomial function requires $n$ to be a whole number (non-negative intege

1. **Problem 1: Find the missing numbers given median and range** We have four number cards: 1, 5, ?, ?

1. **Stating the problem:** We have several expressions to simplify and evaluate:

1. **Problem 29:** Given numbers 40 and $p$ in ratio 4:3, with prime factors shown as: - $40 = 2^3 \times 5$

1. **Problem 1: Find the area of the shaded part in the rectangle.** The rectangle is divided into three parallelograms by two diagonal parallel lines. The total length of the bott

1. **Décomposer en base p et b** Pour décomposer un nombre en base $p$ ou $b$, on exprime ce nombre comme une somme de puissances de la base multipliées par des coefficients entier