🧮 algebra

1. Problem: Calculate $\sqrt{0.12} \cdot \sqrt{12}$. Step 1: Use the property of square roots: $\sqrt{a} \cdot \sqrt{b} = \sqrt{a \cdot b}$.

1. **State the problem:** We need to find the number of tiles required to cover a rectangular bathroom wall. 2. **Given:**

1. **State the problem:** Solve for $x$ in the equation $5^x = \frac{1}{125}$.\n\n2. **Rewrite the right side:** Note that $125 = 5^3$, so $\frac{1}{125} = 5^{-3}$.\n\n3. **Set the

1. সমস্যাটি হলো: একটি সংখ্যা থেকে ১৭ শতাংশ নেওয়া হয়েছে এবং ফলাফল ৫ পাওয়া গেছে। সংখ্যাটি কত? 2. ধরা যাক সংখ্যাটি $x$। তাহলে ১৭ শতাংশ মানে $\frac{17}{100} \times x$।

1. **State the problem:** A school has admitted 480 senior one students divided into four classes A, B, C, and D. Class A has 80 students.

1. Stating the problem: Simplify the expression $$\frac{7+\sqrt{3}}{7-\sqrt{3}} + \frac{7-\sqrt{3}}{7+\sqrt{3}}$$ using the least common multiple (LCM) method. 2. Identify the deno

1. **State the problem:** Simplify the expression $$\frac{7+\sqrt{3}}{7-\sqrt{3}} + \frac{7-\sqrt{3}}{7+\sqrt{3}}.$$\n\n2. **Rationalize each fraction:** Multiply numerator and den

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