🧮 algebra

1. **State the problem:** We want to find the cost of 1 fruit cake and 4 muffins given two purchase scenarios. 2. **Define variables:** Let $x$ be the cost of 1 fruit cake and $y$

1. **State the problem:** We need to find the minimum total price for a school trip for 100 students to a museum where each group can have a maximum of 25 people including at least

1. **State the problem:** Simplify the expression $-2x \cdot 2y - xy \cdot (-2x)$. 2. **Recall the rules:** Multiplication is distributive and associative. Also, multiplying two ne

1. **Problem statement:** Two real numbers $a$ and $b$ satisfy the inequality $$(a - b)^2 > a^2 + b^2.$$ We want to determine which of the given statements always holds: - $a = 0$

1. **Problem statement:** Find the value of the sequence terms $U_0$ to $U_4$ given $U_0=0$ and $U_1=\sqrt{U_0 + 12}$.

1. **State the problem:** Evaluate the function $f(x) = 3 - \frac{x}{10}$ at $x = -\frac{1}{2}$. 2. **Write the formula:**

1. **Problem Statement:** Given two matrices \( A = \begin{bmatrix} 2 & x \\ 3 & 4 \end{bmatrix} \) and \( B = \begin{bmatrix} y & 5 \\ 3 & z \end{bmatrix} \), find the values of \

1. **State the problem:** Solve the inequality $ (x - 4)(x - 2) > 0 $. 2. **Recall the rule:** A product of two factors is positive if both factors are positive or both are negativ

1. The problem is to understand what turning points are in the context of graphs, especially for IGCSE 10th grade. 2. A turning point on a graph is a point where the graph changes

1. The problem is to explain turning points in the context of IGCSE mathematics. 2. A turning point on a graph is where the curve changes direction from increasing to decreasing or

1. **State the problem:** Simplify the expression $35 - 45 \times 67$. 2. **Recall the order of operations:** Multiplication must be done before subtraction.

1. **State the problem:** Solve the equation exactly. 2. **Identify the equation:** Since the user did not specify the exact equation, please provide the equation to solve.

1. The problem is to solve for the expression or equation given values $a=0$ and $b=1.3$. However, the exact equation or expression to solve is not provided. 2. Please provide the

1. **State the problem:** We are given the function $f(x) = 6x^5 + 3x^3 - 2x - 8$ and we want to analyze or work with it as needed. 2. **Identify the function type:** This is a pol

1. **State the problem:** We are given values $a=0$ and $b=1.3$. The problem is to understand or solve for these values as given. 2. **Interpretation:** Since $a$ and $b$ are const

1. Stating the problem: Simplify the expression $$(x-1)^2 - 4x^2$$. 2. Use the formula for the square of a binomial: $$(a-b)^2 = a^2 - 2ab + b^2$$.

1. **Problem:** Factorise the expression $25x^2 - 36$. 2. **Formula:** Use the difference of squares formula: $$a^2 - b^2 = (a - b)(a + b)$$

1. **State the problem:** Simplify the expression $$9x^9 \div \left(\frac{x^3}{3}\right)$$. 2. **Rewrite the division by a fraction as multiplication:** Dividing by a fraction is t

1. **State the problem:** Solve the quadratic equation $$x^2 + 2x - 8 = 0$$. 2. **Recall the formula:** For a quadratic equation $$ax^2 + bx + c = 0$$, the solutions are given by t

1. **State the problem:** The number of dance steps performed varies directly with the length of the music played. Given that 120 steps are performed in 3 minutes, we want to find

1. **State the problem:** Simplify the expression $$\frac{3}{2x + 5} - \frac{5}{3x + 2}$$. 2. **Find a common denominator:** The denominators are $2x + 5$ and $3x + 2$. The common