🧮 algebra

1. نبدأ بحل التعبير الجبري المعطى: $1 - 8 \times 2 + 4 + 5 - 3$ 2. نطبق قاعدة ترتيب العمليات: نبدأ بالضرب ثم الجمع والطرح من اليسار إلى اليمين.

1. The problem asks for the slope of the line given by the equation $y = -5x + 8$. 2. Recall that the slope-intercept form of a line is $y = mx + b$, where $m$ is the slope and $b$

1. **State the problem:** Convert the equation $y - 5 = 3(x - 2)$ to slope-intercept form, which is $y = mx + b$ where $m$ is the slope and $b$ is the y-intercept. 2. **Recall the

1. **Stating the problem:** We need to identify which situation is NOT a direct variation. 2. **Understanding direct variation:** Direct variation means two quantities are related

1. **Problem Statement:** We analyze the quadratic height function of a bungee jumper given by $$h(t) = -0.5t^2 + v_0 t + h_0$$ with $$v_0 = 0$$ and $$h_0 = 210$$ meters. 2. **Doma

1. **State the problem:** Solve for the variable in the proportion $\frac{20}{7} = \frac{6}{m}$. 2. **Formula used:** In a proportion $\frac{a}{b} = \frac{c}{d}$, the cross product

1. **Problem:** Find the root: $5\sqrt{32a^5 b^{10}}$ 2. **Formula and rules:** The $n$th root of a product is the product of the $n$th roots:

**Exercice 1** 1. Calculer :

1. Énoncé du problème : Calculer et simplifier les expressions suivantes : $$A = \frac{1}{7} \times \left(\frac{4}{7} - \frac{3}{7}\right), \quad B = \left(-\frac{5}{-3}\right) \ti

1. **Calculer les expressions données :** A = \sqrt{2} + \sqrt{49} = \sqrt{2} + 7

1. **Problem Statement:** Given a line with intercepts $a$ and $b$ on the x-axis and y-axis respectively, and $p$ as the length of the perpendicular from the origin to this line, s

1. The problem is to understand and work with matrices, which are rectangular arrays of numbers arranged in rows and columns. 2. A matrix is usually denoted by a capital letter, fo

1. **Énoncé du problème :** Calculer les puissances suivantes : $(-1)^{2022}$, $1^{3099}$, $0^{1990}$, $\left(-\frac{1}{3}\right)^1$, $10^{-6}$, $(-4)^2$, $\left(\frac{3}{2}\right)

1. The problem is to find an alternative solution to a previously solved problem that yields the same answer. 2. Since the original problem is not specified, let's consider a commo

1. **State the problem:** We need to find the ratio of the lengths of the purple, green, and orange sections of the pole. 2. **Given lengths:**

1. **State the problem:** We need to find the ratio of glass to cardboard in a recycling bin, where the glass weighs 2 kg and the cardboard weighs 500 g. 2. **Convert units to be c

1. **Problem Statement:** Given a line with intercepts $a$ and $b$ on the coordinate axes, and $p$ as the length of the perpendicular from the origin to this line, show that $$\fra

1. **State the problem:** We have 50 fish in total. Among them, 15 are tench. Of the remaining fish, 1/5 are minnows and the rest are goldfish. We need to find the ratio of tench t

1. **State the problem:** A motorist takes 2 hours to travel from one town to another and 1 hour 40 minutes to travel back. We need to calculate the percentage change in the speed

1. The problem is to understand the logarithm function and how to work with it. 2. The logarithm function is defined as the inverse of the exponential function. For a base $b > 0$,

1. The user asked to "show examples," which is a general request without a specific math problem. 2. Since no specific math problem is given, I will provide a simple example of sol