🧮 algebra

1. Problem: Calculate the value of $l = \left|\left(\frac{8}{3} - 8\right) - \left(-\frac{8}{3} + 8\right)\right|$. 2. First, simplify inside the absolute value step by step.

1. The problem is to understand and analyze the function $y=\frac{1}{3}x^2$. 2. This is a quadratic function in the form $y=ax^2$, where $a=\frac{1}{3}$.

1. **State the problem:** Solve the system of equations: $$\frac{27^x}{81^x} + 2y = 9$$

1. **Problem:** Determine if the function $f(x) = x^4 - 5x^3 + x^2 + 12x - 5$ has a zero between 0 and 1. 2. **Method:** Use the Intermediate Value Theorem which states that if a c

1. **State the problem:** Solve the first system of linear equations for variables $f$ and $g$: $$3(3f + 2g) = 5 - f$$

1. We are given the system of equations: $$\frac{5x}{8} - \frac{y}{2} = \frac{1}{4}$$

1. **Problem:** Find the value of $$\sqrt[4]{81}^{-2}$$. 2. **Formula and rules:**

1. **State the problem:** Solve the equation $\frac{1}{2}(4g - 3) = 5g - 7$ for $g$. 2. **Use the distributive property:** Multiply both sides by 2 to eliminate the fraction.

1. **State the problem:** Mohsin’s earnings increase exponentially at a rate of 8.7% each year. In 2018, he earned 195600. We want to find how much more he earns in 2027 compared t

1. **Problem Statement:** We want to understand the formula of Newton's Binomial Theorem and how it is used to expand expressions of the form $$(a+b)^n$$ where $n$ is a non-negativ

1. Solve the inequality $\frac{2x}{3} - \frac{1}{2} < 0$. Step 1: Add $\frac{1}{2}$ to both sides:

1. **State the problem:** Solve the linear equation $4x + y = 8$ for $y$ in terms of $x$. 2. **Formula and rules:** To isolate $y$, subtract $4x$ from both sides of the equation.

1. **Problem statement:** Given the relation $$R = \{ (x,y) \in \mathbb{R}^2 \mid y^2 = 4x - x^2 \},$$ find the domain and range of $R$, determine if $R$ defines a function from $\

1. **Problem:** Solve the linear inequality $$\frac{2x}{3} - \frac{1}{2} < 0$$. 2. **Formula and rules:** To solve inequalities, isolate the variable on one side. Remember, multipl

1. **State the problem:** Simplify the expression $$(2x - 3)^2 + (2x + 3)^2$$. 2. **Recall the formula:** The square of a binomial is given by $$(a \, \pm \, b)^2 = a^2 \, \pm \, 2

1. **Problem statement:** Evaluate the sum $\sum_{r=1}^9 3^r$ to an appropriate degree of accuracy. 2. **Formula used:** This is a geometric series with first term $a = 3^1 = 3$ an

1. المشكلة هي تبسيط تعبير يحتوي على قيمة مطلقة في البسط فقط. 2. القاعدة المهمة هنا هي أن القيمة المطلقة لـ $x$ تُكتب كـ $|x|$ وتعني المسافة بين $x$ والصفر على خط الأعداد، وهي دائما

1. المشكلة: لدينا تعبير رياضي ونريد إضافة القيمة المطلقة له. 2. القاعدة: القيمة المطلقة لعدد $x$ تُكتب $|x|$ وتعني المسافة بين $x$ والصفر على خط الأعداد، وهي دائماً غير سالبة.

1. Let's solve the first problem: $\frac{4}{10} = \frac{\_}{60}$. We want to find the missing number in the numerator. 2. To find the missing number, we use the rule that if two fr

1. **State the problem:** We need to find the equation of a line parallel to line A that passes through point P. 2. **Identify the slope of line A:** Line A passes through points (

1. المشكلة: لدينا معادلة تحتوي على قيمة مطلقة في المتغير $x$. 2. القاعدة الأساسية: القيمة المطلقة $|x|$ تعني أن الناتج دائمًا غير سالب، أي $|x|=x$ إذا كان $x \geq 0$ و$|x|=-x$ إذا