🧮 algebra

1. Let's denote Paige's weekly salary as $S$. 2. She spends a quarter of her salary on food: $$\frac{1}{4}S$$.

1. Let's consider a simple algebra problem: Solve for $x$ in the equation $$2x + 3 = 11.$$ 2. To isolate $x$, subtract 3 from both sides: $$2x + 3 - 3 = 11 - 3$$ which simplifies t

1. The problem is to simplify and solve the expression $$x = \frac{-(-5) + \sqrt{(-5)^2 - 4(2)(6)}}{2(2)}$$. 2. First, simplify the numerator's components:

1. **State the problem:** Solve the system of equations: $$2x - y = 53$$

1. **State the problem:** Solve the system of equations: $$2x - y = 53$$

1. **State the problem:** Solve the system of equations: $$4x + 3y = 10$$

1. **State the problem:** Solve the system of equations: $$4x + 3y = 10$$

1. **State the problem:** Solve the simultaneous equations: $$x + 2y = 73$$

1. The problem is to evaluate the sum $$\sum_{i=1}^n 1^i$$. 2. Notice that for any integer $i$, $1^i = 1$ because any number to the power of $i$ is itself, and $1$ raised to any po

1. The problem is to evaluate the sum of squares from $i=1$ to $n$, which is written as $\sum_{i=1}^n i^2$. 2. The formula for the sum of the first $n$ squares is:

1. The problem is to find the domain, range, and asymptotes of a function. Since the function is not specified, let's consider a general rational function example: $$f(x) = \frac{1

1. The problem is to analyze the function $y=2\times10^x$. 2. This is an exponential function where the base is 10 and it is multiplied by 2.

1. Let's analyze the function $y=2\ln x$. - The domain of $\ln x$ is $x>0$, so the domain of $y=2\ln x$ is also $x>0$.

1. **State the problem:** Simplify the expression $$\frac{e^{\ln 5}}{e^{\ln 6}}$$. 2. **Recall properties of logarithms and exponents:** For any positive number $a$, $e^{\ln a} = a

1. نبدأ بتحديد الفترات الزمنية لوصول القطارات إلى كل رصيف: - القطار على الرصيف 1 يصل كل 4 دقائق.

1. نلاحظ الأعداد المعطاة: 3، 8، 18، 38، 78. 2. نحسب الفروق بين الأعداد المتتالية:

1. Let's start by stating the problem: We want to understand and apply common algebraic identities. 2. The most common algebraic identities are:

1. **Énoncé du problème :** Calculer \((\sqrt{6} - \sqrt{5})^{2024} \times (\sqrt{6} - \sqrt{5})^{2024}\) et \(\left( \frac{\sqrt{3}}{\sqrt{3} - 2} \right)^{-2} + \left( \frac{\sqr

1. The laws of exponents are rules that describe how to simplify expressions involving powers of the same base. 2. **Product rule:** When multiplying powers with the same base, add

1. Problem a) Simplify $$(\sqrt{a} - 1 - \sqrt{a} + 1)(\sqrt{a} + 1 + \sqrt{a} - 1)$$ Step 1: Simplify inside each parenthesis:

1. **State the problem:** We need to simplify the expression $$\frac{x^3+6x^2+11x+6}{x+1}$$ by performing polynomial division. 2. **Set up the division:** Divide the cubic polynomi