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🧮 algebra

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Exponent Multiplication
1. The problem asks us to find the exponent in the expression $W^8 \times W = W^{\square}$. 2. Recall the rule of exponents: When multiplying like bases, add the exponents.
Solution Unique
1. Énoncé du problème : Montrer que l'équation $$\sqrt{x} - 3 = \frac{4}{x^{2}}$$ admet une unique solution. 2. Réécrivons l'équation pour faciliter l'étude : $$\sqrt{x} - 3 = \fra
Fraction Division
1. The problem is to divide two fractions: $\frac{4}{5} \div \frac{8}{7}$. 2. Dividing by a fraction is the same as multiplying by its reciprocal. So, rewrite the division as multi
Fraction Modification
1. Énoncer le problème : Modifier la fraction \( \frac{4}{7} \) en \( \frac{4}{x^2} \) dans le premier énoncé. 2. Remplacer la fraction dans l'expression originale par la nouvelle
Function Examples
1. **Linear functions:** These are of the form $y = mx + b$, where $m$ is the slope and $b$ is the y-intercept.
Curries Salads Ratio
1. The problem asks for the ratio of curries to salads sold by the restaurant on Thursday. 2. From the given data: On Thursday, salads sold = 12 and curries sold = 8.
Fraction Equality
1. Énonçons le problème : nous avons une fraction $\frac{4}{7}$ et une autre expression $\frac{4}{x^2}$. Vous demandez probablement à comparer ou résoudre une équation impliquant c
Ratio Chillies Quiches
1. The problem asks for the ratio of chillies to quiches sold by the restaurant on Wednesday. 2. From the graph description, the number of quiches sold on Wednesday is 20.
Equation Racine
1. Énoncé du problème :\n(a) Montrer que l'équation $\sqrt{x} - 3 = \frac{4}{7}$ possède une unique solution réelle.\n(b) Donner un encadrement à $10^{-2}$ près de cette solution.\
Determination A B
1. Énoncé du problème : On considère la fonction $$f(x) = \frac{3x^2 + ax + b}{x^2 + 1}$$ avec $$a$$ et $$b$$ réels. On veut déterminer les valeurs de $$a$$ et $$b$$ telles que la
Gpa Calculation
1. We are asked to calculate your GPA based on the given credit hours and grades. 2. Here are the data points you provided:
Solve Equation
1. The problem is to solve the equation given by the user, but no specific equation was provided. 2. To solve any algebraic equation, we would first identify the variables and cons
Factorisation Worksheet
1. Problem: Factorize the expression $x^2 + 5x + 6$. 2. To factorize, find two numbers that multiply to $6$ and add to $5$.
Exponential Growth Decay
1. السؤال 3: أ. نعلم أن عدد سكان المدينة سنة 2020 هو 200000 نسمة، ومعدل الزيادة السنوي هو 1.2%.
Prime Number
1. The problem is to identify what the number 11 represents and work with it in a mathematical context. 2. Since 11 is a prime number, it has only two positive divisors: 1 and 11.
Multiple Problems
1. Solve the equation $\frac{2x - 5}{4} \div \frac{3x - 1}{3} = 2$. Rewrite the division as multiplication by the reciprocal:
Composite Function
1. A composite function is a function formed when one function is applied to the result of another function. For example, if we have functions $f(x)$ and $g(x)$, the composite func
Percent Food Increase
1. Stating the problem: John ate 20 pounds of chicken wings and 15 pounds of hot dogs. Kyle ate 20% more chicken wings and 40% more hot dogs. We need to find the approximate percen
Binary Simplification
1. Stating the problem: Simplify the expression $$[(101001)_2 + (1111)_2] - (100110)_2$$ where the numbers are in binary. 2. Convert each binary number to decimal:
Function Prompt
1. The user input is the function notation: $F(x)$. However, no specific function or question is provided. 2. To assist further, please provide the explicit function definition or
Cube Expression
1. We are given that $x + \frac{1}{x} = \sqrt{3}$. Our goal is to find the value of $x^3 + \frac{1}{x^3}$. 2. Recall the identity for cubes: $$x^3 + \frac{1}{x^3} = \left(x + \frac