🧮 algebra

1. The problem is to simplify the expression $x + \frac{1}{x}$. 2. Since $x$ and $\frac{1}{x}$ are unlike terms (one is $x$ and the other is its reciprocal), they cannot be combine

1. The problem is to simplify or analyze the expression $x + \frac{1}{x}$. 2. This expression is a sum of a variable $x$ and its reciprocal $\frac{1}{x}$.

1. The problem asks us to find the value of $c$ in the equation $$3^{15} \div 3 = 3^c.$$\n\n2. Recall the property of exponents: when dividing powers with the same base, subtract t

1. **State the problem:** Simplify the expression $$\frac{7d^3 f h^2}{21 d^5 h}$$. 2. **Simplify the coefficients:** $$\frac{7}{21} = \frac{1}{3}$$.

1. **Énoncé du problème :** Étudier la fonction $f(x) = x^2 - 4x + 3$ définie sur $\mathbb{R}$.

1. **State the problem:** Calculate the value of the expression $\frac{40000}{100} \times 12 \times \frac{12}{10}$.\n\n2. **Simplify step-by-step:**\n- First, simplify $\frac{40000

1. **Étudier les variations des fonctions f et g** - Pour $f(x) = x^2 - 2x$ :

1. The problem asks to calculate the value of $[V1 + V4] - [V2 - V3]$ based on the directed graph. 2. From the graph, the known edge weights are:

1. Evaluate the expression $$\frac{11}{22}x^{-22} + \frac{11}{33}x^{-33} + \frac{11}{22}x^{-44}$$ for given options. Step 1: Simplify each term.

1. **State the problem:** Simplify the expression $1\pi \sqrt{\pi^2} (2-1)(2+1)$. 2. **Simplify inside the square root:** $\sqrt{\pi^2} = \pi$ because the square root of a square i

1. **State the problem:** Simplify the expression $\frac{1}{\pi} \cdot \frac{\sqrt{\pi}}{(2-1)(2+1)}$. 2. **Simplify the denominator:** Calculate $(2-1)(2+1) = 1 \times 3 = 3$.

1. **State the problem:** Simplify the expression $$\sqrt{\frac{\pi^2}{(\sqrt{2} - 1)(\sqrt{2} + 1)}}$$. 2. **Simplify the denominator:** Notice that $$(\sqrt{2} - 1)(\sqrt{2} + 1)

1. **State the problem:** Simplify the expression $$\frac{1}{\pi} \quad \text{and} \quad \sqrt{\frac{\pi^2}{(\sqrt{2} - 1)(\sqrt{2} + 1)}}.$$\n\n2. **Simplify the denominator insid

1. **State the problem:** We are given the population of a town in 2010 as $1.8 \times 10^{6}$ and in 2012 as $9 \times 10^{3}$. We need to find how many times the population in 20

1. **State the problem:** Find the value of $m$ such that $$(-3)^{m(m+1)} \times (-3)^5 = (-3)^7.$$\n\n2. **Use the property of exponents:** When multiplying powers with the same b

1. **State the problem:** Evaluate the expression $$(5^{-1} \times 2^{-1}) \times 6^{-1}$$. 2. **Recall the meaning of negative exponents:** For any nonzero number $a$, $a^{-1} = \

1. The problem asks to express the size of a plant cell, given as 0.00001275 m, in standard form. 2. Standard form means writing the number as a product of a number between 1 and 1

1. **State the problem:** We are given the function $f(x) = 2x + 3$ and need to find the values of $f(4)$, $f(-6)$, $f(\frac{1}{2})$, and $f(0)$. 2. **Calculate $f(4)$:** Substitut

1. Problem 23: Find the equation of a hyperbola given the latus rectum $l = 10$. The latus rectum of a hyperbola $\frac{x^2}{a^2} - \frac{y^2}{b^2} = 1$ is given by $l = \frac{2b^2

1. The equation given is $$-3x^2 + 7y^2 = -1$$. To identify the conic, rewrite it as $$3x^2 - 7y^2 = 1$$ by multiplying both sides by -1.

1. The problem is to analyze the system of equations: $$x + y = 4$$