🧮 algebra

1. Problem: Evaluate the absolute value function $|x|$ at $x=-3,0,3,100,-100$ and explain the piecewise definition and graph. 2. Recall the definition of absolute value.

1. Masalah yang diberikan melibatkan fungsi kubik $$y = x^3 - 4x$$ yang menggambarkan taman yang terbagi menjadi tiga daerah oleh kurva tersebut. 2. Pertama, kita cari titik potong

1. **State the problem:** We need to evaluate the limit $$\lim_{x \to -2} \frac{x^{2} + 4x + 4}{x^{2} - 2x - 8}$$. 2. **Factor numerator and denominator:**

1. Problem: Simplify the expression $\dfrac{125m x^{-4}}{\dfrac{x^2 \cdot x \cdot \sqrt{x^4}}{25}}$. 2. Note that $\sqrt{x^4}=x^2$ for $x\ge 0$.

1. Let's start by stating what logarithmic equations are: equations that involve the logarithm of a variable. 2. A common form is $\log_a(x) = b$, which means $x = a^b$.

1. Algebra is a branch of mathematics dealing with symbols and the rules for manipulating these symbols. 2. The fundamental concept is to solve equations where variables represent

1. **Simplify** the expression $$\sqrt[3]{\frac{125 \times x^{-4}}{x^2}} \times \sqrt{\frac{x^4}{25}}$$. 2. Apply laws of exponents inside the cube root:

1. **State the problem:** Solve the equation $$ \sqrt{27g + 513} = 3g + 3 $$ to find the value(s) of $g$. 2. **Isolate and square both sides:** To eliminate the square root, square

1. Solve $17x + 12 = 54 - 4x$. Add $4x$ and subtract $12$: $$17x + 4x = 54 - 12$$

1. **State the problem:** Solve the equation $$\sqrt{8f + 5} = \sqrt{4f + 8}$$. 2. **Square both sides** to eliminate the square roots: $$\left(\sqrt{8f + 5}\right)^2 = \left(\sqrt

1. **State the problem:** Solve the equation $$\sqrt{6w + 5} = \sqrt{2w + 8}$$. 2. **Square both sides** to eliminate the square roots:

1. The problem is to solve the equation $3\sqrt[n]{x}w + 1 = 1$ for $x$. 2. Start by subtracting 1 from both sides to isolate the term with $x$:

1. Stating the problem: We need to solve for $j$ in the equation $$\sqrt[3]{4j + 4} = 5$$. 2. To eliminate the cube root, cube both sides of the equation:

1. **State the Problem:** Given the line equation $$6y - 8x - 10 = 0$$, find: I. The slope and intercept of line L₁.

1. لنفترض أن لدينا قطعة مستقيمة ذات نهايتين بنقطتين $A(x_1,y_1)$ و $B(x_2,y_2)$. 2. **الميل** للقطعة هو معدل التغير في الإحداثيات الرأسية إلى الأفقية ويمكن حسابه باستخدام الصيغة:

1. সমস্যা: একজন ব্যক্তি ২৫,০০০ টাকা ব্যবসায় বিনিয়োগ করেন। তিনি কয়েক টাকা ৪ বছর এবং বাদবাকি ৩ বছরের জন্য বিনিয়োগ করেন। সমগ্র মুনাফা ৯,৯০০ টাকা এবং মুনাফার হার প্রথম ক্ষেত্রে দ্ব

1. Let's clarify the question: "what about 0" can refer to different contexts in math. 2. If you're asking about properties of the number 0, here are some key points:

1. The problem is to evaluate each mathematical expression and then list the results from lowest to greatest. 2. Evaluate each expression step-by-step:

1. Let's clarify the problem: it seems you want to solve an equation or expression involving a logarithm. 2. Recall the main properties of logarithms: for example, $\log_b(xy) = \l

1. **Stating the problem:** We are given several mathematical expressions and asked to list them from lowest value to greatest value. 2. **Evaluate each expression:**

1. **State the problem:** We are given a 3x3 grid of expressions: \[\sum_{i=2}^3 i, \quad e^3, \quad 6! \\