🧮 algebra

1. **Problem a:** Xavier thinks of a number. He multiplies it by 2 then adds 8. The answer is 20. 2. **Write the equation:** Let the number be $x$. The equation is:

1. **State the problem:** Find the function $f(x)$ given by $$f(x) = -(x+1)^3 + 2.$$ 2. **Understand the function:** This is a cubic function shifted and reflected.

1. **Problem statement:** Xavier thinks of a number. He multiplies it by 2 then adds 8. The answer is 20. What number did Xavier think of?

1. **Problem:** In an arithmetic progression (AP), given $a_1 = 7$ and common difference $d = 3$, find the 10th term $a_{10}$. 2. **Formula:** The $n$th term of an AP is given by:

1. The problem asks to find the value of $\frac{\binom{9}{6}}{\binom{6}{2}}$. 2. Recall the combination formula: $\binom{n}{r} = \frac{n!}{r!(n-r)!}$, where $n!$ is the factorial o

1. The problem is to simplify the fraction $\frac{19}{15}$. 2. To simplify a fraction, find the greatest common divisor (GCD) of the numerator and denominator.

1. **المسألة:** أوجد ناتج القسمة $\frac{3}{8} \div \frac{3}{4}$ في أبسط صورة. 2. **القاعدة:** عند قسمة كسر على كسر آخر، نضرب الكسر الأول في مقلوب الكسر الثاني:

1. **State the problem:** Simplify the expression $$\frac{x^2 - 49}{2x^2 - 3x - 5} \div \frac{x^2 - x - 42}{x^2 + 7x + 6}$$. 2. **Rewrite division as multiplication:** Dividing by

1. **Problem Statement:** Calculate the average amount Dr. Gita earned per shift over 100 shifts, given the number of patients per shift $X$ and the earning formula $1000 (X - 0.2)

1. **State the problem:** Simplify the expression $5x - 2(2 - x)$. 2. **Apply the distributive property:** Multiply $-2$ by each term inside the parentheses:

1. **State the problem:** Find 2/3 of 78. 2. **Formula:** To find a fraction of a number, multiply the fraction by the number.

1. The problem is to add the fractions $\frac{2}{9}$ and $\frac{8}{9}$. 2. When adding fractions with the same denominator, you add the numerators and keep the denominator the same

1. **Problem statement:** The price of an article is increased first by 15% and then by 10%. We need to find the total percentage increase. 2. **Formula used:** When successive per

1. **Problem:** Determine the domain, intercepts, asymptotes, and sketch the graph of $$f(x) = \frac{x^2 + 3x + 2}{x^2 - 1}$$. 2. **Formula and rules:**

1. **State the problem:** Given the cubic equation $$x^3 - 9x^2 + 23x - 15 = 0$$ with roots $$\alpha, \beta, \gamma$$, find the value of $$\frac{1}{\alpha+2} + \frac{1}{\beta+2} +

1. **State the problem:** Simplify the expression $20x - 6y + 2 - 12x + 8y - 10 + 15$. 2. **Group like terms:** Combine the terms with $x$, the terms with $y$, and the constant ter

1. **הבעיה:** מצא את משוואת הישר AB, הישר המקביל לו שעובר דרך נקודה C, והישר המאונך לו שעובר דרך נקודה C. 2. **נתונים:**

1. **Problem statement:** We want to find the number of functions $f:\{1,2,\ldots,10\} \to \{1,2,\ldots,10\}$ such that $f(f(i))=i$ for all $i \in \{1,2,\ldots,10\}$. 2. **Understa

1. The problem is to prove a given relation without finding the value of any variable. 2. To prove a relation, we start by stating the relation clearly and then use algebraic ident

1. The problem is to find the value of the expression or equation that your textbook shows as -6. 2. Since you did not provide the exact expression, I will explain a common scenari

1. **State the problem:** Solve the equation $8 - \frac{1}{4} = \frac{24}{4} - \frac{1}{4}$. 2. **Rewrite the whole numbers as fractions:**