🧮 algebra

1. **State the problem:** Solve the simultaneous equations: $$2xy=45$$

1. **State the problem:** We need to find an angle $x$ such that the sum of its complementary and supplementary angles is 200 degrees. 2. **Recall definitions:**

1. **Problem Statement:** Find the sum of the largest and smallest 5-digit numbers formed by the digits 2, 0, 6, 1, 9. 2. **Important Rule:** A 5-digit number cannot start with 0 b

1. **Problem:** Given points (-2,-6), (0,2), (2,5), (3,9), (4,26), (5,35) representing (x,y), find constants $a$ and $b$ such that $y = a \times x + b$ fits the data. 2. **Formula:

1. The problem is to simplify the expression $$\frac{ab + b}{b}$$ and verify if it equals $$a$$. 2. The formula used here is the property of division over addition: $$\frac{x + y}{

1. **Problem statement:** A football team plays 30 matches. Each win gives 5 points, each draw gives 2 points, and each loss deducts 1 point. The team scored a total of 108 points.

1. **State the problem:** Find the sum of the largest and smallest 5-digit numbers formed using the digits 3, 0, 4, 1, 9. 2. **Important rule:** A 5-digit number cannot start with

1. **Problem statement:** Given the quadratic equation $$12a^2 - 30a - 1 = 0,$$ find the value of $$4a^2 + \frac{1}{36a^2}.$$\n\n2. **Step 1: Understand the problem and what is ask

1. **State the problem:** Evaluate the expression $$\left(\frac{1}{3} + \frac{2}{9}\right)^9 + \frac{\left(\frac{3}{4}\right)^2 / 9}{\frac{9}{4} \times (-4)}$$ and determine which

1. **State the problem:** Solve the equation $$Z^{5} + Z^{3} + Z = 0$$ for $Z$. 2. **Use the factoring technique:** Notice that each term contains a factor of $Z$, so factor it out

1. The problem asks for the function of $g^n(x)$ in terms of $n$ and $x$. 2. Here, $g^n(x)$ denotes the $n$-th iterate of the function $g$, meaning applying $g$ to $x$ repeatedly $

1. The problem asks to find $g^2(x)$ when $g(x) = x - 3$. 2. The notation $g^2(x)$ means the function $g$ composed with itself: $g(g(x))$.

1. The problem is to understand and describe the graph of the function $y = x^x$. 2. The function $y = x^x$ is defined for $x > 0$ because for real numbers, raising a negative numb

1. **State the problem:** Simplify the expression $$\frac{x^2 - 4x}{x^2 - 9}$$. 2. **Recall the formulas and rules:**

1. State the problem: Compute $1\sqrt{126}$.\n2. Formula and rules: Use the product rule for square roots $\sqrt{ab}=\sqrt{a}\sqrt{b}$.\n3. Factor 126 into primes: $126=2\cdot3^2\c

1. **State the problem:** Simplify the expression $$\frac{x^2 - 4x}{x^2 - 9}$$. 2. **Recall the formulas and rules:**

1. **Stating the problem:** Aqiela travels 7 km to school using an online motorcycle taxi (ojek). We need to find the total round-trip cost (to school and back) based on the given

1. **State the problem:** We need to find the missing transaction $N$ on Dec 1 such that the account balance becomes zero after all transactions. 2. **List all transactions:**

1. The problem involves understanding the relationship between values X, Y, and M given in two number lines and a sequence of numbers. 2. From the first part, we have:

1. **State the problem:** Solve the equation $2x + 3 = 7$ for $x$. 2. **Formula and rules:** To solve for $x$, isolate $x$ by performing inverse operations. Subtract 3 from both si

1. The problem is to generate a simple math puzzle. 2. A common simple puzzle is to find the value of $x$ in a basic algebraic equation.