🧮 algebra

1. The problem is to simplify the expression $-9-9$. 2. This is a subtraction problem involving two integers.

1. The problem is to evaluate the expression $-1 + [-4]$. 2. The brackets around $-4$ indicate it is a single number, so the expression simplifies to $-1 + (-4)$.

1. The problem is to determine if a certain expression is equivalent to $\frac{\log 5}{\log 4}$. 2. Recall the change of base formula for logarithms:

1. **State the problem:** Simplify the expression $$\frac{20}{\log 4^2 - \log 4}$$. 2. **Recall logarithm properties:**

1. **State the problem:** Simplify the expression $$\frac{3^{8} \cdot 2^{7} \cdot 4^{2} \cdot 25^{2}}{3^{6} \cdot 2^{5} \cdot 2^{4} \cdot 5^{4}} - \frac{243^{\frac{1}{2}}}{9^{\frac

1. **Problem statement:** We are given two linear equations: $$x_1 + kx_2 = c$$

1. **State the problem:** Solve the equation $3(5x-29)-9=-6$ for $x$. 2. **Apply the distributive property:** Multiply 3 by each term inside the parentheses:

1. **State the problem:** Solve the equation $$\frac{1}{2}r - \frac{3}{4} = \frac{1}{2}$$ for $r$. 2. **Isolate the variable term:** Add $\frac{3}{4}$ to both sides to get rid of t

1. **Problem statement:** We have a battery level function $$B(t) = 100\left(1 - \frac{t}{10} e^{-0.2t}\right)$$ for $$t \in [0,10]$$ hours. We need to find: a. The maximum and min

1. **State the problem:** We have a piecewise function: $$f(x) = \begin{cases} 2x + 1 & \text{if } x \leq 2 \\ -4 & \text{if } x > 2 \end{cases}$$

1. The problem is to understand the structure of the ring $Q[x,y]$, which is the ring of polynomials in two variables $x$ and $y$ with coefficients in the rational numbers $Q$. 2.

1. **State the problem:** We are given the function $f(x) = (x - 1)^2 + 2$ and need to find its domain and range. 2. **Domain:** The domain of a function is the set of all possible

1. Problemi: Të kuptojmë nëse (y^2, x) është një ideal i thjeshtë në një unazë polinomiale. 2. Përkufizimi: Një ideal I në një unazë R quhet i thjeshtë nëse nuk ka ideale të tjera

1. **State the problem:** We need to find the concentration $C$ of medication in the bloodstream 4 hours after administration, given by the formula: $$C = 66 \left(e^{-0.5t} - e^{-

1. **Problem Statement:** Sketch the function $f(x) = (x - 1)^2 + 2$ using transformations and find its domain and range.

1. **Problem Statement:** Graphically compare the function $f(x) = 3x - 5$ and its inverse. 2. **Step a: Graph the function $f(x) = 3x - 5$.**

1. **State the problem:** We want to find the time $t$ when the amount of nitrogen pentoxide remaining, $N(t)$, is 2 grams. 2. **Recall the model:** The amount remaining at time $t

1. **السؤال:** جد ناتج (3k + 5)² 2. **القاعدة:** مربع مجموع حدين يُحسب باستخدام الصيغة:

1. The problem is to simplify or understand the expression $\left(\;\right)\frac{4}{3}$. 2. Notice that $\left(\;\right)$ represents an empty set of parentheses, which means it doe

1. The problem is to simplify the fraction $\frac{3}{4}$. 2. A fraction represents a part of a whole and is written as $\frac{a}{b}$ where $a$ is the numerator and $b$ is the denom

1) جد ناتج (3k+5)^2 - نبدأ بتطبيق صيغة مربع الحدين: $ (a+b)^2 = a^2 + 2ab + b^2 $