🧮 algebra

1. **Problem Statement:** Find the pattern (rule) of the sequence: $\frac{4}{6}, \frac{12}{7}, 4, 2, -12, -\frac{28}{5}, -4, \ldots$ 2. **Step 1: Simplify fractions where possible.

1. **Stating the problem:** You provided matching problems for laws of exponents and simplification exercises. We will verify your answers for correctness. 2. **Matching Column A t

1. **State the problem:** We need to find a combination of the given numbers that add up to 6224.35. 2. **List the numbers:** 69.40, 4440.51, 208.27, 359.85, 2591.57, 360.00, 180.0

1. **Problem Statement:** We want to understand why for the function $$y = \frac{x^2 - 3x + 4}{x^2 + 3x + 4}$$ with real $x$, the discriminant condition $D \geq 0$ is used and why

1. The problem is to solve the equation $$\frac{x}{8!} + \frac{x}{9!} = \frac{1}{10!}$$ for $x$. 2. Recall the factorial values and the property that $n! = n \times (n-1)!$. Here,

1. **Énoncé du problème :** Encadrer les expressions $$\frac{x+y}{x-y}$$ et $$x^2 - y^2$$ pour $$-\frac{3}{2} \leq x \leq -\frac{1}{2}$$ et $$\frac{5}{2} \leq y \leq \frac{7}{2}$$.

1. **State the problem:** We have a list of numbers and want to proportion them according to percentages 35%, 15%, and 50%. 2. **Understand the percentages:** The percentages 35%,

1. Polinomial adalah ekspresi matematika yang terdiri dari variabel dan koefisien yang dihubungkan dengan operasi penjumlahan, pengurangan, dan perkalian. 2. Contoh polinomial: $$3

1. The problem is to find the values after 0, 1, 2, 3, 4, and 5 years for a given sequence or function. 2. Since the user did not specify the function or rule governing the sequenc

1. We are given the formula for the tiger population after $t$ years: $$a = 4000 + 50 \sqrt{t}$$ 2. The problem asks to find the population after 4 years, so we substitute $t=4$ in

1. **Problem statement:** Given functions $f(x) = -3x^2 + 1$ and $g(x) = 2^x - 4$, solve the following. 2. **Step 2.1: Determine $f(-3)$**

1. **State the problem:** We know 8 machines can assemble 6 printers in 10 hours. We want to find how many hours 5 machines will take to assemble 12 printers.

1. **Problem:** Calculate 22 (2/9) % of 1080. 2. **Formula:** To find a percentage of a number, use the formula:

1. Problema: Găsiți numărul natural $n$ pentru care $$8^n + 8^{n+1} = 36 \cdot 2^{2011}.$$ 2. Formula și reguli importante:

1. **Stating the problem:** We are given a graph of a function and asked to find its three roots. Roots are the values of $x$ where the function crosses the $x$-axis, i.e., where $

1. **State the problem:** Simplify the expression $$\frac{\frac{10}{(s+1)(s+2)}}{1 + \frac{10}{(s+1)(s+2)} \cdot \frac{1}{2}}$$. 2. **Rewrite the expression:** The numerator is $$\

1. The problem states that there are 3 roots, which typically refers to the solutions of a cubic equation or a polynomial of degree 3. 2. The general form of a cubic equation is $$

1. **Problem Statement:** Find the roots of the function based on the given graph description. 2. **Understanding Roots:** Roots of a function are the values of $x$ where the funct

1. Énoncé du problème : Résoudre dans ℝ l'équation $$\frac{1}{2}x^2 - 5x - 12 = 0$$. 2. Formule utilisée : Pour résoudre une équation quadratique $$ax^2 + bx + c = 0$$, on utilise

1. **State the problem:** Simplify the expression $6 x^5 y^3 \times x^2 y^7$ using the laws of exponents. 2. **Recall the laws of exponents:** When multiplying terms with the same

1. **State the problem:** We need to find the value of $x$ such that $\log x = 0.5109$. 2. **Recall the definition of logarithm:** The logarithm $\log x$ (common logarithm) means $