🧮 algebra

1. **Stating the problem:** The question asks to solve the last problem involving $ \pi$ (pi) and specifically wants the answer expressed using $\pi$ rather than a decimal approxim

1. We are given a quadratic function and asked to analyze its characteristics and solve it if needed. 2. Assume the problem is to find the roots of $y = ax^2 + bx + c$ and analyze

1. Let's state the problem: We want to find the power $n$ such that $2^n = 32$. 2. We know that 32 can be expressed as a power of 2: $32 = 2^5$.

1. We are asked to simplify the expression $\frac{1}{4}(2^n - 2^{n+2})$. 2. Start by factoring out the common term $2^n$ inside the parentheses:

1. The problem asks us to find the value of the expression $\frac{2 + 2 + 2 + 2}{4}$. 2. First, calculate the sum inside the numerator: $2 + 2 + 2 + 2 = 8$.

1. Stated problem: Solve the equation $$ (x + 3) \times \frac{2}{3} \times (4 - x) \times \frac{4}{9} = \frac{27}{8} $$ for $x$. 2. Simplify the left side by combining the fraction

1. State the problem: Simplify the given expression for $S_n$: $$S_n=3\left[1-\left(\frac{1}{3}\right)^{n}+\frac{1}{2\cdot 3}\right]$$ 2. Simplify the term inside the brackets step

1. The problem appears incomplete because no equation or expression is given to find solutions for. 2. To help you, please provide the full equation or problem statement you want t

1. The problem is to calculate $2 \times 10^{100} - 2 \times 10^{98}$ and express the answer in standard form. 2. First, factor out the common factor $2 \times 10^{98}$ from both t

1. **Stating the Problem:** We want to find out which petrol option offers better value for money and then calculate the cost of 30 litres from the cheaper option. 2. **Calculate p

1. **State the problem:** We want to write down the inequalities defining the feasible region, identify the corner points of this region, and then find the maximum and minimum valu

1. **Stating the problem:** Calculate the values of the logarithmic expressions: a) $4\log 35$

1. The problem is to analyze the function $$y = \frac{1}{2}x^2 \cdot \sqrt{16 - x^2}$$. 2. First, understand the domain: since there is a square root $$\sqrt{16 - x^2}$$, we requir

1. The problem is to simplify the expression referred to as "question Q". 2. Since the exact expression for question Q is not provided, I cannot perform simplification directly.

1. **Rewrite each expression in negative index form:** (a) $\frac{1}{6^2} = 6^{-2}$

1. **State the problem:** Simplify the expression $\frac{-1}{8} \times (12 - \sqrt{16} - \sqrt{12})$. 2. **Calculate the square roots:**

1. **Problem 17:** Find the exact value of $8^{\frac{2}{3}} \times 49^{-\frac{1}{2}}$. 2. First, simplify each term separately.

1. The problem is to simplify the expression $$2.1 \times 10^p + 2.1 \times 10^{p-1}$$ and express the answer in standard form. 2. Factor out the common term $$2.1 \times 10^{p-1}$

1. **State the problem:** Evaluate the expression $$0.25^{-3} + \left(\frac{5}{4}\right)^{-2} + 38 \left(\left(-\frac{2}{3}\right)^{-1} - 0.125^{-1}\right)^{-1}$$

1. 问题：求函数 $y=-5x+3$ 与 $x$ 轴交点坐标。\n 方法：交点是 $y=0$ 的点，\n 解方程：$0 = -5x + 3$ \n 解得：$5x = 3 \Rightarrow x = \frac{3}{5}$。\n 交点坐标为 $\left(\frac{3}{5}, 0\right)$。\n\n2. 问题：判断哪个点在函数

1. The problem is to make solving algebraic expressions easier by simplifying the process. 2. Start by identifying like terms and combine them to reduce complexity.