🧮 algebra

1. Problem: If $\frac{x}{7} = \frac{y}{15} = 1$, find the values of $x$ and $y$. Step 1: Since both fractions equal 1, set each fraction equal to 1.

1. The problem asks to find the total number of tourists in a group if 13500 tourists represent 12% of that group. 2. Let $x$ be the total number of tourists in the group.

1. **Stating the Problem** We will learn about arithmetic sequences and series, understand their formulas, and then solve 5 example problems of varying difficulty with detailed ste

1. نبدأ بتعريف موضوع السؤال: \"ترتيب العمليات على الأعداد النسبية\" يعني معرفة الترتيب الصحيح لتنفيذ العمليات الحسابية (الجمع والطرح والضرب والقسمة والقوى) عند التعامل مع الأعداد ا

1. هذه أسئلة في الرياضيات للصف الثاني المتوسط - الشهر الأول - الفصل الأول من المنهج العراقي 2025. 2. السؤال الأول: حل المعادلة $$3x+5=20$$

1. **Problem Statement:** Show that SO(2, \mathbb{Q}) is a subgroup of GL(2, \mathbb{Q}). SO(2, \mathbb{Q}) is defined as the set of all 2\times 2 orthogonal matrices with rational

1. The problem asks for the square of the fraction \(\frac{25}{9}\). 2. To square a fraction, we square both the numerator and the denominator separately.

1. The problem is to convert the decimal 0.90 into a fraction. 2. Write 0.90 as $\frac{90}{100}$ because 0.90 means 90 hundredths.

1. The phrase "In fraction" is ambiguous. It might refer to understanding fractions, converting numbers to fractions, or operations involving fractions. 2. If you want to express a

1. Problem: Find the average of given sets of numbers. 2. Recall: The average of $n$ numbers $x_1, x_2, ..., x_n$ is calculated using the formula:

1. Let's understand the problem: You want to know why when multiplying both sides of an equation by 2, the term $2x - 3$ does not change. 2. Suppose we have an equation involving $

1. State the problem: Given the equation $$\frac{2x - 3}{2} = k - 1$$ and the value $$k = 5$$, find the value of $$2x$$. 2. Substitute $$k = 5$$ into the equation:

1. **Problem statement:** Given a quadratic equation $ax^2+bx+c=0$ whose roots are $\cos \theta$ and $\sin \theta$, show that $$a^2-b^2+2ac=0.$$\n\n2. **Recall Vieta's formulas:**

1. Let's start by stating the problem: Solve the equation $x + \frac{9}{5} + 2 + \frac{x}{2} = 0$ for $x$. 2. First, combine the constant terms: $\frac{9}{5} + 2 = \frac{9}{5} + \f

1. The problem is to solve the equation $x + \frac{9}{5} + 2 + \frac{x}{2} = 0$ for $x$.\n\n2. First, combine the constant terms $\frac{9}{5}$ and $2$. Convert $2$ to a fraction wi

1. State the problem: Solve the equation $$\frac{r}{2} = \frac{1}{2} + \frac{2r}{5}$$ for $r$. 2. Eliminate the denominators by multiplying both sides of the equation by the least

1. Exercice n°01: Problème: Soit $A(x) = (x^2 -1) - (x-1)(4x-4)$ et $B(x) = (x-1)(2x-3)$.

1. The problem is to simplify the expression $\sqrt{75}$.\n2. Begin by factoring 75 into its prime factors: $75 = 25 \times 3$.\n3. Since $25 = 5^2$, we can rewrite $\sqrt{75}$ as

1. The problem is to simplify the nested radical expression $$\sqrt{75 - 3\sqrt{27 + \sqrt{49}}}$$. 2. Start with the innermost radical: \(\sqrt{49} = 7\).

1. The problem is to simplify the square root expression $\sqrt{75}$.\n\n2. Factorize 75 into its prime factors: $75 = 25 \times 3 = 5^2 \times 3$.\n\n3. Use the property of square

1. The problem is to understand the expression $\sqrt[n]{x}$, which denotes the $n$-th root of $x$. 2. This means we want to find a number which when raised to the power $n$ equals