🧮 algebra

1. **State the problem:** Simplify the expression $$\sqrt{x}20x^2 + \sqrt{x}40x^2$$. 2. **Recall the properties:** The square root of $x$ is written as $\sqrt{x} = x^{\frac{1}{2}}$

1. **State the problem:** Solve the system of linear equations: $$x + 4y = 5$$

1. **State the problem:** Solve the system of six equations with variables $T_{11}$, $T_{12}$, $T_{22}$, and $T_{32}$: $$

1. The problem is to understand the mapping defined by the expression $X - 2 - 3X$. 2. First, combine like terms: $X - 3X = -2X$.

1. The problem is to evaluate the expression $5 + 4 \times (6 \div 2)$.\n\n2. According to the order of operations (PEMDAS/BODMAS), we first solve the expression inside the parenth

1. The problem is unclear as "this mapping" is not specified. 2. Please provide the explicit function or mapping you want to analyze or solve.

1. **Problem Statement:** Consider the piecewise function $f$ described by the graph with the following properties:

1. **State the problem:** Simplify the expression $X - 2 - 3X$. 2. **Recall the rules:** When simplifying algebraic expressions, combine like terms. Like terms have the same variab

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