🧮 algebra

1. **State the problem:** Simplify the expression $$\frac{2(2-3i)}{1+5i}$$ and then evaluate $$\left(\frac{2(2-3i)}{1+5i}\right)^8$$. 2. **Simplify the fraction:** Multiply numerat

1. **State the problem:** Rationalize the expression $$\frac{3\sqrt{3}+\sqrt{5}}{3\sqrt{3}-\sqrt{5}} \times \frac{3\sqrt{3}+\sqrt{5}}{3\sqrt{3}+\sqrt{5}}$$ 2. **Formula and rule:**

1. **State the problem:** Rationalize the expression $$\frac{3\sqrt{3}+\sqrt{5}}{3\sqrt{3}-\sqrt{5}} \times \frac{3\sqrt{3}+\sqrt{5}}{3\sqrt{3}+\sqrt{5}}$$ 2. **Understand the goal

1. **State the problem:** Given the relation $R = \{(1, 2), (2, 4), (3, 9), (4, 16)\}$, determine if $R$ is a function by definition. 2. **Definition of a function:** A relation is

1. **State the problem:** We have the arithmetic sequence $-18, -23, -28, -33, \ldots$ and need to find the recursive formula, explicit formula, and the 52nd term. 2. **Identify th

1. **State the problem:** Simplify the expression $3\sqrt{3} + \frac{4\sqrt{2}}{2\sqrt{3}}$. 2. **Recall the rules:**

1. The problem is to solve a Grade 5 level math question. Since no specific problem is given, let's consider a common Grade 5 math problem: solving a simple equation like $2x + 3 =

1. **Stating the problem:** We are given expressions involving square roots and powers with numbers 15, 6, 0, 43, and powers 2, 3, 4. The goal is to simplify or evaluate the expres

1. **State the problem:** We have an arithmetic sequence starting with 4, -1, -6, -11, ... 2. **Identify the common difference:** The difference between consecutive terms is $-1 -

1. The problem is to find the set $A = [2, \infty) \cap (-2, 5]$. 2. This means we want the intersection of the two intervals: $[2, \infty)$ and $(-2, 5]$.

1. **State the problem:** Prove by mathematical induction that for all integers $n \geq 0$, the expression $$10^n + 3 \cdot 4^{n+2} + 5$$ is divisible by 9. 2. **Base case ($n=0$):

1. **State the problem:** We have an arithmetic sequence starting with 19, 4, -1, -6, -11, ... and we need to find the recursive formula, explicit formula, and the 52nd term using

1. **Problem statement:** Given the arithmetic sequence $6, 206, 406, 606, \ldots$, write the recursive formula, explicit formula, and find the 52nd term using the explicit formula

1. **Problem:** Given $4 = ج(س) = 7$, find $س$. 2. **Understanding the problem:** The equation states that the function $ج$ evaluated at $س$ equals both 4 and 7, which is contradic

1. **Stating the problem:** We have a rational function $$f(x) = \frac{x^2 - 5x + 15}{x-2}$$ and an asymptote of the form $$f(x) = ax + b + \frac{c}{x-2}$$. We want to find the val

1. **Problem Statement:** Given the arithmetic sequence $-15, -7, 1, 9, \ldots$, write the recursive formula, explicit formula, and find the 52nd term using the explicit formula. 2

1. **Stating the problem:** We need to find the image (bayangan) of the line given by the equation $x + 2y - 1 = 0$ after a translation by the vector $T\left(-3, 2\right)$. 2. **Fo

1. **State the problem:** Simplify the fraction $\frac{14775000}{8650}$. 2. **Formula and rules:** To simplify a fraction, divide numerator and denominator by their greatest common

1. The problem is to simplify the fraction $\frac{6887500}{7250}$. 2. To simplify a fraction, we divide the numerator and denominator by their greatest common divisor (GCD).

1. Diketahui barisan aritmetika dengan suku ke-9 ($a_9$) = 11 dan suku ke-21 ($a_{21}$) = 35. 2. Rumus suku ke-n barisan aritmetika adalah $$a_n = a_1 + (n-1)d$$ dimana $a_1$ adala

1. **Stating the problem:** We want to find the value of $$\frac{8^{\frac{3}{5}} \times 94^{5}}{81^{\frac{1}{8}} \times 64^{\frac{1}{5}}}$$.