🧮 algebra

1. **State the problem:** Simplify the expression $$3^{n+2} + \left(3^{n+3} - 3^{n+1}\right)$$ and determine which of the given options it equals. 2. **Recall the properties of exp

1. **State the problem:** Simplify the expression $$ (25^{-1}) + (25^{-2}) $$ and understand why the answer might be 26. 2. **Recall the rules for negative exponents:** For any non

1. **State the problem:** Solve the equation $\log_3(x-2) + 2\log_9(x+3) = \log_3 14$ for $x$. 2. **Recall the properties of logarithms:**

1. Diketahui FPB dari $6^{2} + m$ dan 28 adalah 14 dengan $m > 0$. Kita harus mencari nilai terkecil dari $m$. 2. Hitung nilai $6^{2}$:

1. The problem is to simplify the expression $2x$. 2. The expression $2x$ means $2$ times $x$, where $x$ is a variable.

1. Diketahui KPK dari tiga bilangan yaitu $10^2 - 88$, $16a + 20$, dan 45 adalah $m$. 2. Pertama, hitung nilai dari $10^2 - 88$:

1. **State the problem:** Simplify or analyze the expression $2x + 1$. 2. **Understand the expression:** This is a linear expression in terms of $x$, where $2$ is the coefficient o

1. **Problem Statement:** Find the domains and ranges of the functions $f(x) = 2$, $g(x) = x^2 + 1$, $\frac{f}{g}$, and $\frac{g}{f}$.\n\n2. **Recall definitions:**\n- The **domain

1. **Problem Statement:** Find the number of terms and the 12th term for the sequences in problems 4, 5, and 6.

1. **Problem:** Darren buys a car for 35000. The value decreases by 15% in the first year. **Step 1:** Calculate the value at the end of the first year using the formula for deprec

1. The problem is to solve the equation or system given by "solve all" which is ambiguous, so we interpret it as solving all equations or expressions provided. Since no specific eq

1. **Problem:** Simplify and analyze the expressions $(x + 6)^2$ and $x^2 - 36$. 2. **Formula and rules:**

1. Bài toán yêu cầu chứng minh bất đẳng thức với bốn số thực dương $a,b,c,d$ sao cho $abcd=1$: $$a^4 + b^4 + c^4 + d^4 \geq 4 \left[ 1 + (a - b)^2 \right].$$

1. **Problem statement:** We have a quadratic function $f$ with vertex at $(-2,-5)$ and y-intercept at point $P$. We need to find:

1. The problem asks for the solution set of the quadratic function $f(x)$ where $f(x) = 0$. 2. The solutions to $f(x) = 0$ are the x-values where the graph intersects the x-axis.

1. **Problem statement:** We have a quadratic function $f$ with vertex at $(-2,-5)$ and y-intercept at point $P$. We need to find:

1. **بيان المشكلة:** لدينا الاقتران القطعي $$q(x) = \begin{cases} x^2 + 2 & x > 1 \\ \frac{1}{x} & x \leq 1 \end{cases}$$

1. Problem: Find 30% of 60. 2. Formula: To find a percentage of a number, use the formula $$\text{Percentage} \times \text{Number} = \text{Result}$$ where the percentage is convert

1. **State the problem:** We have a patio represented as a rectangle with length $l$ and width $w$. The patio is enclosed on three sides by a fence, and the fourth side is the hous

1. **State the problem:** We want to find the value of $c$ such that the graphs of the two functions $$y = 2x^2 - 36x + c$$

1. نبدأ بكتابة المسألة: \( \frac{s^2 + 9}{s} \). 2. الهدف هو تبسيط التعبير الجبري.