🧮 algebra

1. **State the problem:** Convert the given fractions and decimals to percentages. 2. **Formula:** To convert a fraction or decimal to a percentage, multiply by 100 and add the % s

1. Planteamos el problema: calcular el perímetro de un trapecio cuyas longitudes de lados son polinomios dados. 2. El perímetro $P$ es la suma de las longitudes de todos los lados:

1. نبدأ بكتابة المعادلة المعطاة: د(س) + د\left(\frac{س}{3}\right) = 12 2. نعلم أن د(س) = 3س، إذن نستبدل في المعادلة:

1. نبدأ بكتابة المعادلة المعطاة: د(س) + د\left(\frac{س}{2}\right) = 12 2. المعادلة الثانية المعطاة هي: 12 = \frac{3}{4} \times 3 + 3 \times 3

1. **State the problems:** (a) $3 = \log_5 125$

1. The problem asks us to find a quadratic function $f(x)$ with given x-intercepts at $(2,0)$ and $(5,0)$ and a y-intercept at $(0,5)$.\n\n2. A quadratic function with roots $r_1$

1. **State the problem:** Solve the equation $$\frac{5x+30}{3} = \frac{3y+30}{5}$$ for one variable in terms of the other. 2. **Formula and rules:** To solve equations involving fr

1. **Problem Statement:** You start selling an NFT at 0.5 and make a 10% profit per sale. The price increases by 10% each time until it reaches 150. From each profit, you deduct 1.

1. **State the problem:** Compare the value of the 5th root of (2 times the 3rd root of 2) with the 10th root of 6. 2. **Express the roots using exponents:**

1. **State the problem:** Compare the value of the product of the 5th root of 2 and the 3rd root of 2 with the 10th root of 6. 2. **Express the roots as exponents:**

1. **State the problem:** We need to find two consecutive multiples of 9 whose product is 486. 2. **Define variables:** Let the first multiple be $9n$, where $n$ is an integer.

1. **Problem statement:** Solve the inequality $$|2 + \frac{1}{x}| \leq |3 - \frac{4}{x}|$$ and find how many integer solutions do not satisfy it. 2. **Formula and rules:** To solv

1. **State the problem:** Compare the value of the product of the 8th root of 2 and the 3rd root of 2 with the 10th root of 6. 2. **Express the roots as exponents:**

1. The problem is to express the series $1 - \frac{1}{2} + \frac{1}{4} - \frac{1}{8} + \frac{1}{16} - \frac{1}{32} + \frac{1}{64}$ as a summation. 2. This is a geometric series whe

1. **State the problem:** We need to find a cubic polynomial function $f(x)$ with real coefficients that has zeros at $-2$, $1$, and $0$, and satisfies $f(-1) = -1$. 2. **Use the f

1. **Problem statement:** Find a cubic polynomial function $f(x)$ with real coefficients that has zeros at $-2$, $1$, and $0$, and satisfies $f(-1) = -1$. 2. **General form:** Sinc

1. Simplify $\frac{1}{a} + \frac{2}{a+1} - \frac{3}{a+2}$. Find common denominator: $a(a+1)(a+2)$.

1. The problem involves evaluating the expression $101 - \frac{1}{2} \times 6000$ and $111 - 011 \times 6000$. 2. First, clarify the expressions: $\frac{1}{2} \times 6000$ means ha

1. **State the problem:** Solve the system of linear equations: $$3x - 2y = 4$$

1. The problem is to express the series $3 - 1 + \frac{1}{3} - \frac{1}{9} + \ldots$ in summation notation. 2. This is a geometric series where each term is multiplied by a common

1. The problem asks us to describe the end behavior of the function $$f(x) = x^7 + x - 4$$. 2. End behavior refers to how the function behaves as $$x$$ approaches $$+\infty$$ (posi