🧮 algebra

1. **Stating the problem:** Simplify each expression using index laws. 2. **Recall the index laws:**

1. **Problem statement:** The usual profit made by a jeweller on a watch is 35%. During a sale, 20% is taken off the market price. The watch was sold for 3672 during the sale. Find

1. **State the problem:** Simplify or analyze the quadratic expression $x^2 + 5x + 10$. 2. **Recall the quadratic formula:** To find roots of $ax^2 + bx + c = 0$, use $$x = \frac{-

1. **State the problem:** Simplify the expression $$3 - \frac{x - 1}{\frac{x^2 - 1}{3x + 2}}$$ and write it in the form $$\frac{a}{x + b}$$ where $a$ and $b$ are integers. 2. **Rew

1. **Problem statement:** For the function $f(x) = 9 - 2x$ with domain $x = \{-3, 0, 1, 7\}$, find the range values. 2. **Formula and rules:** To find the range, substitute each do

1. Problema: Calculați radicalul din 300. 2. Formula: Radicalul pătrat al unui număr $a$ este notat $\sqrt{a}$ și reprezintă numărul care, înmulțit cu el însuși, dă $a$.

1. **State the problem:** We are given the equation of a line $$y + 4 = 6x + 11$$ and asked to find the y-intercept of the line. 2. **Rewrite the equation in slope-intercept form:*

1. Diberikan fungsi polinomial derajat tiga: $$y = ax^3 + bx^2 + cx + d$$ 2. Kita tahu nilai fungsi pada beberapa titik:

1. **State the problem:** Simplify the expression $$\frac{5(2x - 3) + 6(3y + 4)}{30}$$. 2. **Apply the distributive property:** Multiply inside the parentheses:

1. **State the problem:** Simplify the expression $$\frac{3x}{15} + \frac{4x}{5}$$. 2. **Find a common denominator:** The denominators are 15 and 5. The least common denominator (L

1. **Problem statement:** Given functions $f(x) = x^2 - 4$ and $g(x) = x + 2$, find the composite function $(f \circ g)(x)$, determine its domain and range, and investigate its mon

1. Let's consider the problem: Solve the equation $$2x + 3 = 11$$ for $x$. 2. The formula to solve a linear equation like this is to isolate $x$ by performing inverse operations.

1. **State the problem:** Calculate the values of \((-6)^2\) and \((-6)^3\). 2. **Recall the rules:**

1. The problem asks us to find the 8th term of the sequence defined by the formula $$T(n) = \frac{n - 2}{n^2 - 2}$$. 2. To find the 8th term, substitute $n = 8$ into the formula:

1. Problem 49: Solve the inequality \(\log_3(x - 1) - 2\log_9(2x - 3) < 0\). 2. Use the change of base and log properties: \(\log_9 y = \log_3 y / 2\), so rewrite as \(\log_3(x - 1

1. **State the problem:** Find the solution set of the equation $$x + \frac{4}{x+3} = 2$$. 2. **Rewrite the equation:** To solve for $x$, first eliminate the fraction by multiplyin

1. **State the problem:** Make $k$ the subject of the equation $$\frac{3k}{2} + \frac{h - 8k}{6} = a.$$\n\n2. **Combine the terms with $k$:** To combine the fractions, find a commo

1. Problem: Solve for $x$ in the equation $$y - \sqrt{5}x - 4 = 0$$. 2. Rearrange the equation to isolate $x$:

1. Problem 40: Solve the inequality $|\log_3 x| - \log_3 x - 3 < 0$. Step 1: Let $y = \log_3 x$. The inequality becomes $|y| - y - 3 < 0$.

1. **Problem Statement:** Solve the system of linear equations: $$8x + 5y = 9$$

1. Bài toán yêu cầu tìm giá trị của $x$ và $y$ thỏa mãn phương trình $$x^2 + 4y^2 - 6x + 99y + 130 = 0.$$\n\n2. Ta sẽ sử dụng phương pháp hoàn thành bình phương để biến đổi phương