🧮 algebra

1. **State the problem:** Solve the quadratic equation $$x^2 - 3x - 6 = 0$$. 2. **Formula used:** The quadratic formula for solving $$ax^2 + bx + c = 0$$ is $$x = \frac{-b \pm \sqr

1. **State the problem:** Solve the quadratic equation $2x^2 - 3x - 6 = 0$ by completing the square. 2. **Rewrite the equation:** Divide all terms by 2 to make the coefficient of $

1. The problem is to find the missing value of $x$ in the ordered pair $(x, -6)$ that satisfies the equation $4x + y = 10$. 2. Substitute $y = -6$ into the equation: $4x + (-6) = 1

1. Problem: Compute the matrix operations for given matrices A, B, and C. Matrices:

1. **State the problem:** Find the slope of the line given points on the graph. 2. **Recall the slope formula:** The slope $m$ of a line passing through two points $(x_1, y_1)$ and

1. The problem asks for the slope of the line given by the equation $$4x - 1 = 3y + 5$$. 2. To find the slope, we need to rewrite the equation in slope-intercept form $$y = mx + b$

1. The problem is to find the missing value of $y$ when $x = -1$ in the equation $y - 3 = 2(x + 1)$. 2. The formula given is a linear equation in point-slope form. We will substitu

1. The problem is to verify or understand the formula for the sum of squares of the first $n$ natural numbers: $$12 + 22 + 32 + \cdots + n^2 = 6n(n+1)(2n+1)$$ 2. The correct formul

1. The problem is to graph the line given by the slope-intercept form equation $$y = -\frac{1}{3}x + 5$$. 2. The slope-intercept form of a line is $$y = mx + b$$ where $m$ is the s

1. **Problem 1: Transformation of figure ABCD under ERS** Given points:

1. The problem is to simplify the expression. 2. Since no expression was provided, no simplification can be done.

1. **State the problem:** We need to graph the linear function $y = -x - 6$. 2. **Formula and rules:** This is a linear equation in slope-intercept form $y = mx + b$, where $m$ is

1. **Evaluate the following logarithms:** 1) $\log_2 32$

1. Diketahui fungsi $f(x) = 3x^2 - 4x + 6$ dan $g(x) = 2x - 1$. Kita diminta mencari nilai $x$ yang memenuhi $(f \circ g)(x) = 101$. 2. Pertama, kita hitung $(f \circ g)(x) = f(g(x

1. The problem is to understand and use the discount formula to calculate the discounted price of an item. 2. The discount formula is:

1. Misalkan masalahnya adalah menyelesaikan persamaan kuadrat $ax^2 + bx + c = 0$. 2. Gunakan rumus kuadrat: $$x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}$$

1. **Problem Statement:** Sohanlal purchased 120 reams of paper at 100 per ream. The transport cost was 480, octroi duty was 0.50 per ream, and coolie charges were 60. We need to f

1. The problem asks to find how many customers are interested in the tablet brand Hob. 2. We know the total number of customers is 165,192 and the percentage interested in Hob is 2

1. **State the problem:** Solve the equation $3a(2-2x) = -4a + x$ for $x$. 2. **Distribute the left side:** Use the distributive property $a(b+c) = ab + ac$.

1. مسئله: باید بازه‌ای را پیدا کنیم که در آن دو تابع $$f(x) = \sqrt{x - |x - 1|}$$ و $$g(x) = \sqrt[3]{x} - 1$$ برابر باشند. 2. ابتدا دامنه هر تابع را بررسی می‌کنیم:

1. **State the problem:** Solve the equation $3a(2-2x) = -4a = x$ for $x$. 2. **Analyze the equation:** The equation as given is ambiguous because it contains two equal signs. We i