🧮 algebra

1. **State the problem:** Simplify the expression $$\left(\frac{x^3}{y^3}\right) \times \left(\frac{y^8 + x^4}{z^4}\right).$$ 2. **Recall the multiplication rule for fractions:** W

1. The problem is to graph the quadratic function $y = x^2 + 5x + 6$. 2. The general form of a quadratic function is $y = ax^2 + bx + c$ where $a$, $b$, and $c$ are constants.

1. The problem is to graph the quadratic function $y = x^2 + 5x + 6$. 2. The general form of a quadratic function is $y = ax^2 + bx + c$. Here, $a=1$, $b=5$, and $c=6$.

1. **State the problem:** We are given the quadratic function $y = x^2 + 5x + 6$ and want to analyze it. 2. **Formula and rules:** A quadratic function is generally written as $y =

1. مسئله: تابعی که نمودار داده شده را توصیف می‌کند، باید به صورت قطعه‌ای نوشته شود. 2. تعریف تابع قطعه‌ای: تابعی است که در بازه‌های مختلف، قوانین متفاوتی دارد.

1. مسئله: حل نامعادله $m(16-m) > 0$. 2. ابتدا نامعادله را بازنویسی می‌کنیم: $$m(16-m) > 0$$.

1. مسئله را بیان می‌کنیم: معادله درجه دوم $$(m - 2)x^2 + r m x + r^2 = 0$$ را داریم و می‌خواهیم مقادیر $m$ را پیدا کنیم که این معادله دو ریشه مثبت داشته باشد. 2. فرمول کلی معادله د

1. **Problem statement:** Nakesa deposited an amount $P$ in a bank for 2 years. The bank offers two types of interest rates: simple interest (SI) at 5% per annum and compound inter

1. The problem asks to find the domain of the function $$f(x) = \sqrt{5 - 2x + bx}$$ with $$b = \frac{1}{2}$$. 2. Substitute $$b = \frac{1}{2}$$ into the function:

1. **State the problem:** Calculate the value of the expression $$\frac{93399495}{36738281} \times 484848$$. 2. **Formula and rules:** Multiplication and division of numbers follow

1. The problem is to solve the equation $$\frac{2x-3}{x+1} = 3$$ for $x$. 2. We use the property that if $$\frac{A}{B} = C$$, then $$A = B \times C$$, provided $B \neq 0$.

1. **State the problem:** Solve the equation $x^x = 36$ for $x$. 2. **Understand the equation:** The equation $x^x = 36$ is transcendental and cannot be solved using elementary alg

1. **Problem:** Find which term 2048 is in the geometric sequence 2, 8, 32, 128, ... 2. **Formula:** The $n$th term of a geometric sequence is given by $$a_n = a_1 \times r^{n-1}$$

1. The problem asks why asking the first 10 students on the register may not produce a good sample for Jamil's survey. 2. Reason 1: The sample is not random because it only include

1. The problem is to solve for $x$ given the values $x=2$ and $x=\frac{-107}{23}$. 2. These are two distinct solutions for $x$.

1. **State the problem:** Solve for $x$ in the equation: $$\frac{2x - 10}{x + 4} + 10 = \frac{-2}{x - 3} - 11$$

1. Stating the problem: Simplify the expression $$\frac{-x^3 + 2x^2 - 3x - 6}{2x + 1}$$. 2. Formula and rules: To simplify a rational expression, we try to factor the numerator and

1. **Stating the problem:** We are given tables with student scores in various assessment components: TEST 1 (15), GROUP WORK (10), TEST 2 (15), PROJECT (20), SUB TOTAL (60), (A) 5

1. **Stating the problem:** We have two functions $f(x) = x^2$ and $g(x) = 2x + 1$. We need to find the following combined functions: - $(f+g)(x)$

1. **Stating the problem:** Three friends want to join health clubs for different durations: D’juan for 6 months, Cho for 10 months, and Lina for 12 months. We need to determine wh

1. The problem is to subtract fractions with unlike denominators and simplify the result. 2. The formula for subtracting fractions with unlike denominators is: