🧮 algebra

1. **State the problem:** We have three types of tickets sold for a concert: adult, child, and student. We know the total tickets sold, total money collected, and the relationship

1. **Problem statement:** Given the system of equations: $$n + h = 12$$

1. **Problem statement:** We need to determine if it is possible to create a mango orchard where the length is twice the width and the area is 800 m². If possible, find the length

1. The problem is to understand and analyze the function $y = x^2$. 2. This is a quadratic function, which generally has the form $y = ax^2 + bx + c$. Here, $a=1$, $b=0$, and $c=0$

1. Let's start with a simple algebra problem: Solve for $x$ in the equation $2x + 3 = 7$. 2. The formula to isolate $x$ is to get $x$ alone on one side of the equation. We do this

1. The problem asks to find the next term in the sequence (16): 7, 14, 23, 34, 47, ... 2. Let's analyze the differences between consecutive terms:

1. **State the problem:** Simplify the expression $ax^2 + bx^2 - bx - ax + a + b$. 2. **Group like terms:** Group terms with $x^2$, terms with $x$, and constant terms:

1. Let's state the problem: Verify if the expression $ax^2 - bx^2 - bx + ax - a + b$ equals $(ax - bx)(x + 1) - a + b$. 2. Start by simplifying the left-hand side (LHS):

1. **State the problem:** We are given the equation relating $r$ and $\theta$ as $$r = \frac{1}{\theta}$$ and we want to understand this relationship. 2. **Formula and explanation:

1. The problem is to understand what \( \ln \) means. 2. \( \ln \) stands for the natural logarithm, which is the logarithm to the base \( e \), where \( e \approx 2.71828 \).

1. The problem asks to determine whether each given statement is true or false. 2. Let's analyze each statement one by one:

1. Solve the equation $2x + 3 = 7$. 2. Subtract 3 from both sides: $2x = 7 - 3$

1. **State the problem:** Simplify the expression $2x^2 - 8$. 2. **Identify the formula and rules:** We can factor out the greatest common factor (GCF) from the terms.

1. **State the problem:** Convert the quadratic expression $2x^2 + 4x + 1$ into its completing the square form. 2. **Recall the formula:** To complete the square for a quadratic ex

1. The problem is to find the missing number represented by $??$ in the given sequence of numbers arranged in rows. 2. Let's analyze the pattern row by row and column by column to

1. **State the problem:** We want to find the value of $x$ when $y = 7000$ in the linear equation $y = -23.04x + 6223.44$. 2. **Given equation:**

1. نبدأ بكتابة المعادلة المعطاة: $$\frac{x^3}{4} = \frac{y}{z}$$. 2. الهدف هو التعبير عن $y$ بدلالة $x$ و $z$.

1. نبدأ بكتابة المعادلة المعطاة: $$x^{\frac{3}{4}} = y^{\frac{1}{2}}$$ وهي تعني أن الجذر التربيعي لـ $y$ يساوي $x$ مرفوعًا للقوة $\frac{3}{4}$. 2. نعلم أن $y^{\frac{1}{2}} = \sqrt{

1. **Problem statement:** Given the polynomial $$f(x) = x^{4} - 2x^{3} - 2x^{2} + a$$ and that it is divisible by $$x^{2} - 4x + 4$$, find the value of $$a$$ and show that $$f(x)$$

1. The problem is to evaluate an expression by substituting numbers without multiplying them. 2. Normally, substitution means replacing variables with numbers and then performing o

1. **Problem:** Factorise the expression $$x^2 - y^2 + yz - zx - 4x + 2y + z + 3$$. 2. **Formula and rules:** We use factoring techniques such as grouping, difference of squares, a