🧮 algebra

1. **State the problem:** We have a logistic growth model for the cat population given by $$P(t) = \frac{84}{1 + 11 e^{-0.07t}}$$

1. დავიწყოთ ამოცანის დასმით: იპოვეთ ფუნქციის $y=6-5x$ უდიდესი მნიშვნელობა ინტერვალზე $[1;3]$. 2. ფუნქცია $y=6-5x$ არის სწორი, რომელიც კლებადი ფუნქციაა, რადგან კოეფიციენტი $-5$ უარყ

1. **State the problem:** Solve the equation $x + (x + 9) + (x + 4) = 2x + 4x - 2$ for $x$. 2. **Write down the equation clearly:**

1. **State the problem:** Simplify the expression $8a + (-3b + 5a)$. 2. **Apply the distributive property and combine like terms:** The expression inside the parentheses is $-3b +

1. **State the problem:** Simplify the expression $(6a - 2b) - (5a + 3b)$. 2. **Apply the distributive property:** Remove the parentheses by distributing the minus sign to the seco

1. **Problem:** Solve the equation $3^x 5^{x-1} = 6^{x+2}$. 2. **Rewrite the equation:**

1. المشكلة: حل المعادلة الجبرية لمستوى 1 باك. 2. القاعدة العامة: لحل المعادلات الجبرية، نستخدم قواعد التبسيط، الجمع، الطرح، الضرب، والقسمة، ونهدف إلى إيجاد قيمة المتغير.

1. **Problem:** Given that $(4a + 2b) : a = 19 : 4$ and $b : c = 7 : 3$, find the ratio $a : b : c$. 2. **Step 1: Express the first ratio as an equation.**

1. **Stating the problem:** Solve the system of linear equations: $$\frac{1}{2}x + 3y = 3$$

1. The problem asks to find the value of the constant $B$ in the expression $$6(x - 3)^2 = Ax^2 + Bx + C.$$ 2. First, expand the left side using the binomial expansion formula $ (x

1. Problem: Find the original cost of a computer that costs 14760 after 3 years, depreciating at 5% per annum. 2. Formula: The depreciation formula is $$V = P(1 - r)^t$$ where $V$

1. **Problem:** A first-class job done by an adult alone takes 6 hours. If a child helps, it takes 2 hours. How long will it take for the child to do the job alone? 2. **Formula an

1. **State the problem:** Given the equation $$\frac{12x + 178}{12 + x} = \frac{A}{x} + \frac{B}{x - 1}$$, find the value of $B$. 2. **Understand the problem:** This is a partial f

1. **State the problem:** We are given the equation $MF = 5MG$ and need to understand or solve it. 2. **Identify variables and relationship:** The equation relates $MF$ and $MG$ wi

1. **State the problem:** Solve the equation $3(x - 5) = 2(x + 1) + 4$ for $x$. 2. **Use the distributive property:** Expand both sides:

1. **State the problem:** Find all horizontal asymptotes of the function $$f(x) = \frac{\sqrt{x + 4}}{2x - 3}$$. 2. **Recall the definition of horizontal asymptotes:** Horizontal a

1. **Problem Statement:** Identify which function among the options matches the described graph. 2. **Given Information:** The graph is a logarithmic curve with base 2, moving down

1. The problem asks to find the equation of the function $g(x)$ given the graph and the function $f(x) = -2 \log_2(x + 1) + 3$. 2. From the graph description, $g(x)$ is an increasi

1. **State the problem:** We need to show that the coordinates of the point common to the curve $$y^2=4ax$$ and the line $$ty - x = at^2$$ are $$(at^2, 2at)$$. 2. **Write down the

1. نبدأ بتحديد المشكلة: لدينا متتالية $u_{m+1}$ ونريد حساب الحد العام للمتتالية $u_m$. 2. لفهم المتتالية، نحتاج إلى معرفة قاعدة التكرار أو العلاقة التي تربط بين الحدود المتتالية. ع

1. The problem states that the y value is 4. 2. Since no specific function or equation is given, we understand that y = 4 is a constant function.