🧮 algebra

1. مسئله: ضرب چند جمله‌ای‌ها را محاسبه کنید: $$(x+1)(x-1)(m^2 + x + y)(x^2 - x + y)$$

1. The problem is to understand the meaning or use of the letter "k" in a mathematical context. 2. In algebra and other areas of mathematics, "k" is often used as a constant or a v

1. Énoncé du problème : Réduire au même dénominateur l'expression $$\frac{4x - 1}{9} - \frac{6x - 8}{2}$$ puis simplifier le numérateur. 2. Trouvons le dénominateur commun : Le dén

1. The problem is to subtract two binary numbers in base 2. 2. The subtraction rule in base 2 is similar to decimal subtraction but uses binary digits (0 and 1).

1. **State the problem:** We are given the hyperbola equation $$\frac{(y+2)^2}{36} - \frac{(x+5)^2}{64} = 1$$ and need to analyze its properties including center, vertices, and asy

1. **Problem Statement:** We have 400 kg of rice. The owner sells 80% of it at 20 per kg.

1. **Stating the problem:** Given the expressions: $$x=5a+7b+9c,\quad y=b-3a-4c,\quad z=c-2b+a,$$

1. **Problem statement:** Mr. Jamil has $10^{2/7}$ acres of cultivable land. He cultivates rice on $\frac{3}{6}$ of his land and wheat and jute on $\frac{5}{14} \times \frac{3}{10}

1. **Problem statement:** Mr. Jamil has $10^{2/7}$ acres of cultivable land.

1. **State the problem:** We are given two functions: $f(x) = \log x$ and $g(x) = \log(x - 1) + 1$. We need to graph both on the same viewing rectangle and describe the relationshi

1. **State the problem:** Rewrite the equation $y = 4.6(0.6)^x$ in terms of base $e$ and express the answer using a natural logarithm. 2. **Recall the formula:** Any exponential ex

1. The problem asks to rewrite the exponential function $$y = 4.6 \times (0.6)^x$$ in terms of the base $$e$$, the natural exponential base. 2. Recall the property of exponents: fo

1. **Stating the problem:** Find the vertex of the quadratic function $$f(x) = 4(x-3)^2 - 6$$. 2. **Formula and explanation:** The vertex form of a quadratic function is $$f(x) = a

1. **Problem Statement:** We are given the x-intercepts of a quadratic function's graph as points (0, -2) and (0, 6). We need to determine if the axis of symmetry is $x = -2$. 2. *

1. **Problem Statement:** We are given the x-intercepts of a quadratic function's graph as points (0, -2) and (0, 6). We need to determine if the axis of symmetry is $x = -2$. 2. *

1. **Problem Statement:** The vertex of a quadratic function's graph is at the point $(-7,-6)$. We need to determine if the axis of symmetry is $x = -6$. 2. **Recall the axis of sy

1. **Problem Statement:** The graph of a business' profit function is given. We need to find the highest possible profit the business can earn.

1. **Problem Statement:** The graph of a business' profit function is given. We need to find the number of sales that should be targeted to earn the highest profit.

1. **Problem Statement:** We are given the quadratic function $$f(x) = x^2 - 14x + 48$$ and need to describe its graph by identifying key features such as intercepts, direction of

1. **Problem Statement:** We are given the quadratic function $$f(x) = x^2 - 14x + 48$$ and need to describe its graph by identifying key features such as intercepts, direction of

1. **Stating the problem:** We are given the quadratic function $$f(x) = x^2 - 14x + 48$$ and need to describe its graph by identifying key features such as intercepts, direction o