🧮 algebra

1. The problem asks us to find the number of hours, denoted as $$h$$, that the gardener works on the job. 2. To solve this, we need a relationship or equation involving the number

1. **State the problem:** A taxi charges a flat rate of $10$ plus $2$ for each kilometre driven. The total cost of the ride was $100$. We need to find the number of kilometres, $k$

1. **Problem Statement:** A rectangular lawn measures 12 m by 10 m and is surrounded by a uniform walkway of width $x$ meters on all sides. The total area of the lawn plus the walk

1. **State the problem:** Solve the equation $2(x + 19) = 78$ for $x$. 2. **Recall the distributive property:** $a(b + c) = ab + ac$. This helps us expand expressions.

1. Problem 32(a): An arithmetic progression (AP) has $n$ terms with the $n$th term $a_n = 4$ and common difference $d = 2$. The sum of $n$ terms $S_n = -14$. Find $n$ and the sum o

1. **State the problem:** Factorize the expression $$a^4 + 64b^4$$. 2. **Recall the formula:** This is a sum of two fourth powers. We can use the sum of squares and difference of s

1. **State the problem:** The product of 5 and an unknown number $u$ is 40. 2. **Write the equation:** Using $u$ as the unknown number, the word statement translates to the equatio

1. The problem states: The product of 5 and an unknown number is 40. 2. Let the unknown number be $u$.

1. Tentukan daerah himpunan penyelesaian dari sistem pertidaksamaan berikut: **a.**

1. Tentukan daerah himpunan penyelesaian dari sistem pertidaksamaan berikut: $$\begin{cases} x^2 + y^2 \leq 5 \\ x^2 + y \leq 4 \\ x \geq 0 \\ y \geq 0 \\ 3x + 2y \geq 24 \\ 2x - 3

1. **Factorize the polynomial** $P(z) = 5z^2 - 14zi + 3$ into linear factors. We treat $z$ as a variable and $i$ as the imaginary unit. The polynomial is quadratic in $z$:

1. The problem is to analyze and graph the function $$y = X^{\frac{2}{3}} + \sqrt{3.3 - X^{2}} \cdot \sin(6.41 \cdot 3.14 \cdot X)$$. 2. This function combines a power term, a squa

1. **State the problem:** Solve for $x$ in the equation $$\frac{5x+2}{4} - \frac{3}{2} = \frac{7x-1}{3}.$$\n\n2. **Identify the formula and rules:** To solve for $x$, we want to is

1. **State the problem:** Find the square root of $-3.50$. 2. **Recall the rule:** The square root of a negative number is not a real number. Instead, it is an imaginary number inv

1. **State the problem:** Simplify the expression $5 + 3 (42 + 7) - 7 (2 + 32 \times 8) \times 0$. 2. **Recall order of operations:** Use PEMDAS (Parentheses, Exponents, Multiplica

1. **State the problem:** We need to find the value of $x$ in the equation $$30 = x + \frac{2^3 \cdot x}{100}.$$ 2. **Understand the equation:** The equation relates $30$ to $x$ pl

1. The problem asks if the inequality $y^2 \geq x$ is true. 2. This inequality means that for any point $(x,y)$, the square of $y$ must be greater than or equal to $x$.

1. **State the problem:** We need to analyze the inequality $Y^2 \geq x$. 2. **Understand the inequality:** This means the square of $Y$ is greater than or equal to $x$.

1. **State the problem:** Solve the equation $$\sqrt{x^2 + 3x + 20} = 0$$. 2. **Recall the property of square roots:** The square root of a number is zero if and only if the number

1. The problem is to find the square root of $-0.021$. 2. Recall that the square root of a negative number is not a real number, but an imaginary number. We use the imaginary unit

1. State the problem: Solve for $x$ in the equation $$100000 = 80000 \left(1 + \frac{x}{100}\right)^6.$$\n\n2. Formula and explanation: This is a compound growth equation where the