🧮 algebra

1. **Problem statement:** (a)(i) A furniture salesman earned 36200 last year and paid 22% tax. Find how much was left after tax.

1. Stating the problem: Solve the equation $8x + 3x = 12 \times 2x$ for $x$. 2. Combine like terms on the left side: $8x + 3x = 11x$.

1. The problem asks to solve part c from the previous context, but since the previous parts are not provided, I will assume part c involves solving an algebraic expression or equat

1. **State the problem:** We need to compute $\log_{\frac{1}{8}} 6$ using the change of base formula and round the answer to the nearest thousandth. 2. **Recall the change of base

1. **Problem Statement:** Find the canonical equations of the straight line defined by the system of planes: $$\begin{cases} 3x + y + z - 2 = 0 \\ 2x - y - 3z + 6 = 0 \end{cases}$$

1. The problem asks to rewrite the mixed number \(1 \frac{1}{4}\) as an improper fraction. 2. A mixed number consists of a whole number and a fraction. To convert it to an improper

1. The problem is to calculate $\frac{15}{32} \times 4$. 2. The formula for multiplying a fraction by a whole number is:

1. **Stating the problem:** A box contains 4 bags of sugar. We want to find the total amount of sugar in the box if each bag contains a certain amount of sugar. 2. **Formula used:*

1. The problem asks to solve for each of the ratios mentioned in the data inside the link. Since the link data is not provided, I will explain how to solve for ratios generally. 2.

1. **State the problem:** Solve the equation $\tan x + 1 = 0$ using the Regula Falsi method. 2. **Rewrite the equation:** We want to find $x$ such that $f(x) = \tan x + 1 = 0$.

1. The problem states that $x = 0.999999\ldots$ and asks about the equality $0.999999\ldots = \frac{9}{9}$ and whether $\frac{9}{9} = 1$.\n\n2. First, note that $\frac{9}{9} = 1$ b

1. **State the problem:** We are given the function $f(x) = 3x^{2} - 6x$ and want to analyze it. 2. **Formula and rules:** This is a quadratic function of the form $ax^{2} + bx + c

1. Énonçons le problème : Résoudre l'exercice 14 (sans détails supplémentaires, supposons qu'il s'agit d'une équation algébrique classique). 2. Formule et règles importantes : Pour

1. **Énoncé du problème :** Montrer que la famille $B = (u_1, u_2, u_3)$ avec $u_1 = (1,0,1)$, $u_2 = (0,1,1)$, $u_3 = (1,1,0)$ est une base de $\mathbb{R}^3$. 2. **Rappel de la dé

1. **Énoncé du problème :** Dans $\mathbb{R}^3$ muni de la base canonique $B = (e_1, e_2, e_3)$, on définit $u_1 = (1,0,1)$, $u_2 = (0,1,1)$ et $u_3 = (1,1,0)$. Montrer que $B' = (

1. **State the problem:** Find the value of $$\left(\sqrt{\frac{6.231}{242.7}}\right)^3$$ using logarithm tables. 2. **Rewrite the expression:** Let $$x = \frac{6.231}{242.7}$$. Th

1. The problem is to find the square root of a number. 2. The square root of a number $x$ is a value $y$ such that $$y^2 = x$$.

1. **State the problem:** Calculate $\frac{6.231}{(242.7)^3}$ using logarithm tables. 2. **Formula and rules:** Using logarithms, division and powers can be transformed into subtra

1. **Problem statement:** The sum of the first two terms of an arithmetic series is 47, and the thirtieth term is -62. Find: a) The first term and the common difference.

1. **State the problem:** Factorize the expression $x^2 + 25y^2$. 2. **Recall the formula:** The sum of squares $a^2 + b^2$ generally cannot be factorized over the real numbers int

1. **State the problem:** Solve the quadratic equation $$3x - 15x + 18 = 0$$. 2. **Simplify the equation:** Combine like terms: