🧮 algebra

1. **Problem statement:** We need to find an exponential depreciation model of the form $$V(t) = V(0) e^{-rt}$$ where $V(t)$ is the value at time $t$, $V(0)$ is the initial value,

1. **State the problem:** We need to find a linear depreciation model for the value of a car over time, given its initial value and current value after 3 years. 2. **Formula:** The

1. ปัญหาคือการวิเคราะห์ฟังก์ชัน $f(x) = 3e^{2x}$ และค่าคงที่ $B = 0.7$ ซึ่งอาจใช้ในการคำนวณหรือเปรียบเทียบ 2. ฟังก์ชันนี้เป็นฟังก์ชันเลขชี้กำลังที่มีรูปแบบทั่วไปคือ $f(x) = ae^{bx}

1. **State the problem:** We need to analyze the rational function $$y=\frac{-3x^2+1}{2x^2-4x-5}$$. 2. **Recall the formula and rules:** This is a rational function, which is a rat

1. **State the problem:** Solve the equation $$\frac{21}{5x} = 2$$ for $x$. 2. **Formula and rules:** To solve for $x$, we need to isolate $x$ on one side of the equation. We can d

1. **State the problem:** Solve the equation $$\frac{72}{2h} = 4$$ for $h$. 2. **Understand the equation:** The equation means that 72 divided by $2h$ equals 4.

1. **Problem statement:** Find the 9th term $a_9$ of the recursive sequence defined by: $$a_1 = a_2 = 1, \quad a_n = a_{n - \lfloor n/2 \rfloor} + a_{n - \lfloor n/2 \rfloor},$$

1. The problem asks to find the sum of the series: $1595 + ... + 190 + 11 + 3$ and determine which option matches the result. 2. We need to clarify the series. It appears to be a d

1. **Stating the problem:** We are given the weights of Cindi, Dania, and Eva with the following conditions:

1. The problem is to find the fourth root of 654, which is written as $\sqrt[4]{654}$. 2. The fourth root of a number $x$ is a value $y$ such that $y^4 = x$.

1. The problem is to simplify the expression $$\frac{4}{\sqrt{5} + 1}$$ by rationalising the denominator. 2. To rationalise the denominator, multiply both numerator and denominator

1. **State the problem:** We need to find the values of $x$ for which the expression $$\frac{(x - 2)(x + 2)}{(x + 1)(x + 3)}$$ is undefined.

1. **State the problem:** We are given the function $F(x) = x^3 - 12x^2 + 36x$ and we want to analyze or solve it. 2. **Formula and rules:** This is a cubic polynomial function. To

1. **State the problem:** Simplify the function $F(x) = x^2 - 12x^2 + 36x - 1$. 2. **Combine like terms:** The terms $x^2$ and $-12x^2$ are like terms.

1. Problem: The user asks to "Susstavi neka budu," which translates to "Make some equations" or "Set some to be." Since the request is vague, let's create a simple algebraic equati

1. Problem: Pronaći dva broja gdje je aritmetička sredina jednaka 185, a veći broj podijeljen manjim daje količnik 2 i ostatak 40. 2. Definirajmo brojeve: neka su to $x$ (veći broj

1. The problem asks to find 56% of 234. 2. To find a percentage of a number, use the formula: $$\text{Percentage of a number} = \frac{\text{percentage}}{100} \times \text{number}$$

1. **State the problem:** Solve the inequality $5 - \frac{2}{x} < 1$ for $x$. 2. **Rewrite the inequality:**

1. **Stating the problem:** We need to perform operations or solve a problem involving matrices. Since the exact question is not specified, let's assume a common matrix problem: mu

1. **Problem statement:** Calculate how many monthly instalments must be paid if the deposit is 69 and each instalment is 28.5, with a total hire purchase price of 354.

1. **Stating the problem:** We are given four mathematical statements and asked which pairs are correct. 2. **Analyze each statement:**