🧮 algebra

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

1. **State the problems:** Solve the quadratic equation $9x^2 - 3x + 1 = 0$ and then prove that $$81\left(x^4 + \frac{1}{6561x^4}\right) = 1.$$

1. **Problem:** Calculate the time Mofenvl took to travel from his cattle post at 23:10 to his village at 01:08 the following day. 2. We notice the arrival time is past midnight, s

1. لنفترض أن الدالة الأصلية هي دالة $y=f(x)$، حيث يجب عليك تحديد شكل الدالة الأصلية لتتمكن من رسم الدالة العكسية. 2. لحساب الدالة العكسية $f^{-1}(x)$، يجب حل المعادلة $y=f(x)$ بالن

1. **Problem statement:** We need to graph two functions using the point plotting method for integer values of $x$ from $-3$ to $3$.

1. **المشكلة الأولى:** لدينا التابع $f: \mathbb{R}^+ \to \mathbb{R}^+, f(x) = (x + 3)^2$. المطلوب هو: 1.1 أوجد التابع العكسي $f^{-1}(x)$.

1. Solve the equation $5x - 1 = 8x + 1$. Step 1: Subtract $5x$ from both sides:

1. **State the problem:** Solve for $x$ in the equation $$3x + x + x + x - 3 - 2 = 7 + x + x$$. 2. **Combine like terms on the left side:** $$3x + x + x + x = 6x$$ and $$-3 - 2 = -