🧮 algebra

1. The problem states the determinant of the 3x3 matrix: $$\begin{vmatrix} a+x & b+x & c+x \\ a+y & b+y & c+y \\ a^2 & b^2 & c^2 \end{vmatrix} = (a - b)(b - c)(c - a)(x)$$

1. State the problem: We are given two functions $f(x) = x^2 + 1$ and $g(x) = x - 5$. We need to solve the equation $f(g(x)) = g(f(x))$. 2. Find $f(g(x))$: Substitute $g(x)$ into $

1. مسئله: باید مقدار $m$ را از تساوی $$\frac{5}{4} \times \frac{6}{5} \times \frac{7}{6} \times \cdots \times \frac{m+1}{m} = 1$$

1. The problem states an equation involving a product of fractions: $1 \cdot 11 = \frac{m}{1+m} \times \times \times \times \times \frac{p}{q}$. 2. First, interpret the left side:

1. The problem is to simplify the expression $\frac{-1}{-1}$.\n\n2. Recall the rule that dividing two negative numbers results in a positive number.\n\n3. Here, both numerator and

1. The problem is to solve Exercise 1.1, Question 2 from Class 10, Chapter 1. 2. Usually, this question involves basic algebraic expressions or equations. Let's assume the question

1. Calculate the GST for the $100 item: $100 \times 0.05 = 5$. Total cost = $100 + 5 = 105$.

1. Problem (a): Simplify the expression $\frac{4a + 13}{5} - \frac{2a + 3}{3}$. 2. To combine the two fractions, find the common denominator, which is the least common multiple of

1. **Stating the problem:** Simplify the expression $+2 - 4$. 2. **Step 1:** The plus sign before 2 simply means positive 2, so this is equivalent to $2 - 4$.

1. Stated problem: Simplify the expression $2 - \frac{2}{5}$.\n\n2. Rewrite $2$ as a fraction with denominator $5$: $$2 = \frac{10}{5}.$$\n\n3. Subtract the fractions: $$\frac{10}{

1. Problème : Simplifier l'expression $a - 2a + 3a$. Étapes :

1. The problem states: Multiply both sides by $x$ given the equation $y = - \frac{1}{\sqrt{3}} x$. 2. The equation is already expressed as $y = - \frac{1}{\sqrt{3}} x$, which means

1. Given the problem: Identify the type of graphs represented by the equations: a) $2x + y = 8$

1. We are given the equation \( \frac{b}{3} + \frac{3c}{4} = 2a \) and need to make \(b\) the subject. 2. Start by isolating the term with \(b\) on one side. Subtract \( \frac{3c}{

1. Let's state the problem: find the value(s) of $k$ such that the quadratic equation $$x^2 + 3x - k = 0$$ has one repeated root. 2. A quadratic equation has one repeated root when

1. Problem statement: Factorize the given expressions: - $C = x^2 - 9$

1. Stating the problem: Solve the system of linear equations using the Gauss-Jordan method. Given:

1. **Problem statement:** A man is 12 miles south of a straight beach and wants to reach a point 20 miles east along the shore. He can travel by boat at 20 mph by paying 2 dollars

1. The previous problem solved was not specified to include a function, so here I explain how to graph a generic function $y = f(x)$.\n2. To graph $y = f(x)$, select values of $x$

1. The problem involves matching each polynomial function to its described graph characteristics. 2. For $f(x) = -x^3 - 2x^2 - 1$:

1. **State the problem:** Find the x- and y-intercepts of the line given by the equation $$x - 2y = 6$$. 2. **Find the x-intercept:** To find the x-intercept, set $$y = 0$$ and sol