🧮 algebra

1. **State the problem:** Solve the exponential equation $$2^{3x - 2} = 8^{\frac{1}{2x}}.$$\n\n2. **Rewrite the bases:** Note that 8 can be written as a power of 2: $$8 = 2^3.$$ So

1. **State the problem:** Calculate the value of $$\left(\frac{30 \times 10^{-3} \text{ m}}{1.2 \times 10^{7} \text{ m/s}}\right)^2$$. 2. **Formula and rules:** We are squaring a f

1. The problem is to understand the inequality $n > 50$. 2. This inequality means that the variable $n$ must be greater than 50.

1. **Problem Statement:** Simplify the expression $$\frac{3^5 \times 3^{-11}}{2^{-1} \times 5^0}$$. 2. **Formula and Rules:** When multiplying powers with the same base, add the ex

1. **Stating the problem:** We need to calculate the value of $$K = \frac{748.200 \times (748.200 \times 735.493 - 2 \times (735.493 \times 748.200) + 748.200 \times 760.607)}{735.

1. **State the problem:** Mokaya bought and sold a cow twice at different prices. We need to find the total profit he made. 2. **Identify the transactions:**

1. Problem: Determine the nature of the solution for the system of equations: $$2x - 5y = 3$$

1. Let's clarify the problem: You are asking why you need to divide by 4 and 2 separately when you already divided by 8. 2. The key is understanding that dividing by 8 is the same

1. **State the problem:** We need to sketch the graph of the function $$y=\frac{x^2 + 3x + 2}{x^2 - 1}$$ and understand its behavior. 2. **Identify the function and domain:** The f

1. Let's start by stating the problem: You are trying to complete the square and simplify the quadratic expression $$y = 2x^2 - 8x + \_ + 6$$ to the form $$y = (x - 4)^2 - 26$$. 2.

1. The problem is to evaluate the expression $5^{34}$. 2. The expression $5^{34}$ means multiplying 5 by itself 34 times.

1. Diberikan fungsi pertumbuhan populasi $P(t) = 735.493e^{0,0167t}$. 2. Kita akan menghitung nilai $P(t)$ untuk $t = 0,1,2,3,4,5,6,7,8,9,10$.

1. **Problem:** Find the terms of the sequence $\{a_n\}$ where $a_n = 2 \cdot (-3)^n + 5^n$ for the following values: a) $a_0$, b) $a_1$, c) $a_4$, d) $a_5$. 2. **Formula:** The ge

1. Problem a: Solve the inequality $2x^2 + 5x + 2 > 0$. 2. Use the quadratic formula to find roots of $2x^2 + 5x + 2 = 0$:

1. **State the problem:** Solve the equation $0.5x + 12960 = (50406 - x) \times \frac{5}{8} \times 11.2$ for $x$. 2. **Write the equation clearly:**

1. **State the problem:** Solve for $x$ in the equation $0.5 + 12960 = (50406 - x) \times \frac{5}{8} \times 11.2$. 2. **Rewrite the equation:**

1. The problem states that the average temperature of Temuco, Chile in July is $7\degree \text{C}$. We need to determine which statements about this temperature relative to $0\degr

1. Stating the problem: Simplify the expression $$C = \sqrt{x^2 + 2x + 1} - \sqrt{x^2 - 2x + c}$$ where $c$ is a constant. 2. Recognize that $x^2 + 2x + 1$ is a perfect square trin

1. **Problem Statement:** We have a parabola with vertex at $(9, -14)$ and it intersects the x-axis at two points. The parabola's equation is $y = ax^2 + bx + c$. We need to find w

1. Problem 26: Solve the equation $$36 - \frac{96 - x}{5} \cdot \frac{12}{18} = 24$$ for $x$. 2. Use the order of operations and simplify step-by-step.

1. The problem involves plotting points, graphing equations, matching viewing rectangles, analyzing tables, and determining intercepts from graphs. 2. For plotting points, each poi