🧮 algebra

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

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 w

1. The problem involves analyzing the number of Rp100,00 coins based on the given graph points representing different individuals. 2. Each point on the graph corresponds to a pair

1. **State the problem:** Solve the system of linear equations using matrices: $$\begin{cases} 2x_1 + 3x_2 - 4x_3 = -4 \\ x_1 - x_2 + x_3 = 2 \\ x_1 + 2x_2 + 3x_3 = 14 \end{cases}$

1. Masalah: Diketahui total massa dari sembilan pemain bulu tangkis adalah 804 kg dan massa rata-rata dari enam perenang adalah 76 kg. Kita diminta mencari massa rata-rata seluruh

1. Masalah: Skor rata-rata Mayang dari tiga tes adalah 68. Ia ingin nilai rata-ratanya bertambah 2 setelah tes keempat. Berapakah nilai yang harus ia peroleh pada tes keempat? 2. R

1. **State the problem:** Solve for $x$ in the equation $$6200=12000\left(1-\frac{x}{100}\right)^6.$$\n\n2. **Formula and explanation:** This is an exponential decay type equation

1. Problem 1: Simplify the expression $\frac{1}{3}x - (8\sqrt{x} + \sqrt{18x} + \sqrt{2x})$. - Recall that $\sqrt{a} = a^{1/2}$ and simplify each term inside the parentheses.

1. **Problem statement:** Simplify each expression step-by-step. 2. **Expression 1:** $(8x) - (8\sqrt{x} + \sqrt{18x} + \sqrt{2x})$