🧮 algebra

1. The problem asks to calculate the product of $-12$ and $-12$. 2. Multiplying two negative numbers produces a positive result because the negatives cancel each other out.

1. Stating the problem: Calculate $(-9) + (-9)$. 2. Explanation: Adding two negative numbers means combining their absolute values and keeping the negative sign.

1. Mari kita tetapkan persamaannya: $$8^{2x-1} = \sqrt{4^{2x+3}}$$ 2. Karena $$\sqrt{4^{2x+3}} = (4^{2x+3})^{\frac{1}{2}} = 4^{\frac{2x+3}{2}}$$, persamaan menjadi $$8^{2x-1} = 4^{

1. ප‍්‍රශ්නය පවසන්නේ: $a, b, c \in \mathbb{R}$ නම්, $$3x^2 - 2(a+b+c)x + bc + ac + ab = 0$$

1. Stating the problem: Simplify the expression $$7C(x + 4) - 2C(x - 3 + x)$$. 2. Start by simplifying the terms inside the parentheses:

1. **State the problem:** Simplify the expression $$7GC + 4) - 2 [Cx - 3C + X]$$ where mixing of variables and constants is present. 2. **Rewrite the expression clearly:** $$7GC +

1. Stating the problem: Simplify the expression $$4 (x + 15) - 2 [Cx - 3 C (25)]$$ where C is a constant. 2. Distribute outside the parentheses and brackets:

1. Määritellään lukujonot: $$a_n = 3n - 16$$

1. Stating the problem: Solve the equation $$x + \frac{1}{2} - \frac{11}{20} = \frac{5x + 1}{4}$$ for $x$. 2. Find a common denominator to combine fractions on the left side. The d

1. The equation given is $pqm = psm$. 2. We want to isolate the variables to understand the relationship. To do this, first note that $p$ appears on both sides of the equation.

1. Kita diberi fungsi $m(x) = x^2 - 4x + 3$ dengan domain $x \geq p$ dan harus mencari nilai $p$ agar fungsi ini mempunyai songsang. 2. Fungsi $m(x)$ adalah fungsi kuadratik dan un

1. **State the problem:** We need to find the smallest positive integer $n$ such that there exists a positive integer $k$ where the inequality $$\frac{7}{13} < \frac{n}{n+k} < \fra

1. **State the problem:** Simplify the expression $$\sqrt{3 + 2\sqrt{2}} + \sqrt{3 - 2\sqrt{2}}$$. 2. **Analyze each term:** The expressions inside the square roots involve nested

1. We are given the function $$f(n) = \frac{(\frac{100}{3})^n}{n!}$$

1. **Problem statement:** Find positive integers $a$ and $b$ with $a \leq b$ satisfying $$a^2 + b^2 + 3ab = 719$$

1. **State the problem:** Find the value of $$\frac{300^2}{253^2 - 247^2}$$. 2. **Recognize the denominator as a difference of squares:**

1. Define the concepts: (i) Domain is the set of all possible input values (x-values) for which the function is defined.

1. The problem is to simplify each given fraction expression step-by-step. 2. For expression 1: $\frac{a}{b} + \frac{c}{d}$, find common denominator $bd$, then write $$\frac{ad}{bd

1. Sederhanakan bentuk berikut dan selesaikan: (a) $4^5 \times 4^3 \times 4^{-6} = 4^{5+3-6} = 4^{2} = 16$

1. **State the problem:** Calculate the sum of $6 \times 10^{1}$ and $9 \times 10^{1}$.\n\n2. **Evaluate each term:**\n\n- $6 \times 10^{1} = 6 \times 10 = 60$.\n\n- $9 \times 10^{

1. **State the problem:** We need to add two numbers given in scientific notation: $5.2 \times 10^7$ and $3.01 \times 10^4$. 2. **Rewrite the numbers with the same power of 10:** T