🧮 algebra

1. **State the problem:** We want to decompose the rational expression \( \frac{4x + 1}{(x - 3)(x + 2)^2} \) into partial fractions. 2. **Set up the partial fractions:** Since the

1. Problem 1: Find the least 6-digit number which is a perfect square. - The smallest 6-digit number is 100000.

1. **State the problem:** We are given the equation $x = \frac{4}{5}(x + 10)$ and need to solve for $x$. 2. **Distribute the fraction:** Multiply $\frac{4}{5}$ by each term inside

1. **State the problem:** Find the range of values of $x$ such that $$\frac{x^2 - 12}{x} > 1.$$\n\n2. **Rewrite the inequality:** Multiply both sides by $x$, but remember to consid

1. State the problem: Simplify the expression $$\frac{9}{16} \times \frac{4}{12} + \frac{9}{16} \times \frac{3}{-9}$$. 2. Multiply the fractions in each term:

1. **State the problem:** Find the range of values for which $$x^2 - \frac{12}{x} > 1$$. 2. **Rewrite the inequality:** Move all terms to one side to get a single inequality:

1. The problem asks to find the function \( f(x) \) for a line passing through points (-4, -1), (0, 1), and (4, 3).\n\n2. To find the function of a line, we use the slope-intercept

1. **State the problem:** We need to find the equation of line B, which passes through point P(2, 5) and is parallel to line A. 2. **Find the slope of line A:** Line A passes throu

1. The problem is to simplify the fraction $\frac{0.0044}{0.0404}$. 2. Convert the decimals to fractions or use division directly.

1. Masalah: Diberikan fungsi produksi senyawa $$f(x) = \frac{4000x^3 + x + 3}{20x^2 + 1} (10x + 2)$$ gram, tentukan banyak senyawa saat waktu $$x$$ sangat besar (limit saat $$x \to

1. Masalah: Diberikan fungsi produksi senyawa $$f(t) = (20t^2 + 1)(100t + 2)$$ gram, kita diminta untuk menyederhanakan fungsi ini. 2. Langkah pertama adalah mengalikan kedua fakto

1. **State the problem:** Find the range of values for which $x+5 < |2x + 1|$. 2. **Understand the absolute value:** The inequality involves an absolute value, so we consider two c

1. The problem is to solve the product of two numbers: $0.004 \times 0.0004$. 2. Convert the decimals to scientific notation for easier multiplication:

1. Diberikan fungsi produksi senyawa: $$f(t) = 4(t+1)^2 - 3(2t^2 - 1)(t^2 + 2)$$

1. **State the problem:** Find the range of values for $x$ such that $$\frac{3x - 10}{x - 4} < 2.$$\n\n2. **Rewrite the inequality:** Subtract 2 from both sides to get a single rat

1. The problem states that after a 10% discount, the article is sold for 360. 2. Let the original price be $x$.

1. **State the problem:** A shopkeeper buys 48 radios for a total cost of 7200. We need to find the selling price per radio to make a 15% profit on the total cost. 2. **Calculate t

1. **State the problem:** We need to divide $1 \frac{3}{4}$ by $\frac{1}{5}$.\n\n2. **Convert mixed number to improper fraction:** $1 \frac{3}{4} = \frac{4 \times 1 + 3}{4} = \frac

1. **State the problem:** We need to calculate $\frac{1}{5}$ divided by $1 \frac{3}{4}$. 2. **Convert mixed number to improper fraction:** $1 \frac{3}{4} = \frac{7}{4}$.

1. **State the problem:** Gail's hourly pay increases from 15 to 18. We need to find the percent increase in her pay. 2. **Calculate the increase in pay:**

1. Given the equations: $$\sqrt{a} + \sqrt{b} = 5$$