🧮 algebra

1. **State the problem:** We need to subtract the two rational expressions: $$\frac{x}{2x - 3} - \frac{x + 6}{3x}$$

1. **State the problem:** Simplify the expression $$\sqrt{75v^{14}}$$. 2. **Recall the formula:** The square root of a product is the product of the square roots: $$\sqrt{ab} = \sq

1. **State the problem:** Solve the equation $$x^2 - 7x = 0$$ by factoring. 2. **Write the equation:** $$x^2 - 7x = 0$$

1. **State the problem:** Solve the equation $$x^2 - 16x = 0$$ by factoring. 2. **Factor the equation:**

1. **State the problem:** We need to determine which values of $x$ satisfy the inequality $$\frac{11}{100} < x < \frac{\pi}{23}$$. 2. **Convert the bounds to decimal approximations

1. **Problem 8:** Find the exponent in the scientific notation of the wavelength $0.00000062$ meters. 2. To write a number in scientific notation, express it as $$a \times 10^n$$ w

1. **Problema 515:** Calcolare $$\frac{[(−4)^2]^6}{[(+2)^4]^3} − (−8)^3 \cdot (−2)^3$$. 2. **Passo 1:** Calcolare le potenze all'interno delle parentesi.

1. **State the problem:** Factor the greatest common factor (GCF) from the expression $$ht^2 - t^2 + 4ht^3$$. 2. **Identify the terms:** The terms are $$ht^2$$, $$-t^2$$, and $$4ht

1. **State the problem:** We need to solve the system of equations: $$y = x^2 - x - 20$$

1. **Problemstellung:** Gegeben sind Geraden mit Steigungen, die durch Steigungsdreiecke bestimmt wurden. Ziel ist es, die Steigung zu bestätigen und die Funktionsgleichungen der G

1. **Problem Statement:** We are given a function $m(x)$ and asked to find its domain. 2. **Understanding the Domain:** The domain of a function is the set of all possible input va

1. **State the problem:** Simplify the polynomial expression $$t^3(8 + 9t) - (t^2 + 4)(t^2 - 3t)$$ and determine which statements about the simplified expression are true. 2. **Exp

1. **State the problem:** We need to find if the income from furniture sales was higher or lower in 2020 compared to 2019. 2. **Identify given data:** The problem does not provide

1. **State the problem:** Solve the equation $$x - 4.25 = 7.5$$ using inverse operations and analyze Ozzy's solution. 2. **Formula and rule:** To isolate $$x$$, add $$4.25$$ to bot

1. **State the problem:** Solve the equation $$f - 9 = 22$$ using inverse operations. 2. **Recall the rule:** To isolate the variable $$f$$, perform the inverse operation of subtra

1. **State the problem:** Solve the quadratic inequality $$2x^2 - 4x - 6 < 0$$ using the quadratic formula and test values $-3$, $0$, and $4$. 2. **Recall the quadratic formula:**

1. **State the problem:** Solve the linear equation $$12x - 2 = 2x + 18$$. 2. **Write down the formula and rules:** To solve a linear equation, we isolate the variable $x$ by perfo

1. **Problem:** Solve by completing the square: $x^2 + 7 = 0$ 2. **Formula:** To complete the square for $x^2 + bx + c = 0$, rewrite as $(x + d)^2 = e$ where $d$ and $e$ are consta

1. **State the problem:** We are given a function $f$ with values at certain $x$ points and a transformed function $g$ defined by $g(x) = f(x - 4)$. We need to create a table for $

1. We start with the first equation: $$7x + 3 = 4(x + 2) - 2$$ 2. Apply the distributive property on the right side: $$7x + 3 = 4x + 8 - 2$$

1. **State the problem:** We are given three exponential functions: $$y=2^x$$, $$y=3^x$$, and $$y=4^x$$.