🧮 algebra

1. **State the problem:** We have cost function $C(x) = 500 + 20x + 0.5x^2$ and revenue function $R(x) = 60x$. We want to find:

1. **State the problem:** Expand and simplify the expression $ (\omega + 7)(\omega + 1) $. 2. **Formula used:** Use the distributive property (also known as FOIL for binomials):

1. **State the problem:** Expand and simplify the expression $ (q + 7)(q - 2) $. 2. **Formula used:** Use the distributive property (also known as FOIL for binomials):

1. **State the problem:** Expand and simplify the expression $ (9 + 7)(-9 - 2) $. 2. **Recall the distributive property:** For any numbers $a$, $b$, and $c$, we have $ (a + b)(c +

1. **State the problem:** Expand and simplify the expression $ (t + 4)(t + 5) $. 2. **Formula used:** Use the distributive property (also known as FOIL for binomials):

1. **State the problem:** Expand and simplify the expression $$(1 + m)(u + 7)(m + u)$$. 2. **Recall the formula:** To expand a product of three binomials, first expand two of them,

1. **State the problem:** We have 5 vans transporting a total of $d$ kg of food. Each van transported the same amount, and this amount is at least 60 kg. 2. **Define variables:** L

1. **Problem 1:** Solve for $x$ in the equation $$\log_5(10x) - 1 = \log_5(3x - 1)$$ 2. **Problem 2:** Solve for $x$ in the equation $$\log_3(8x - 15) - 1 = 4$$

1. **State the problem:** Solve for $x$ in the equation $$\log_5(10x) - 1 = \log_5(3x - 1).$$ 2. **Recall the logarithm properties:**

1. **Stating the problem:** We want to evaluate the sum $$\sum_{i=1}^{n} n^s$$ where $n$ and $s$ are constants and the index $i$ runs from 1 to $n$. 2. **Understanding the sum:** N

1. لنفترض أن المطلوب هو إيجاد الجذر التربيعي لعدد معين يُرمز له بـ زيتا (\zeta). 2. الجذر التربيعي لعدد \zeta يُكتب رياضيًا كالتالي: $$\sqrt{\zeta}$$.

1. **Problem Statement:** Find invoice numbers from Yunus Textile Mills Ltd whose invoice amounts sum to 192104 and 118590 respectively. 2. **Approach:** This is a subset sum probl

1. **State the problem:** We are given the quadratic function $$5x^{2} + 20x + 4$$ and want to analyze its properties, such as vertex, axis of symmetry, and intercepts. 2. **Formul

1. **Problem Statement:** Solve the equation $x^2 - 5x + 6 = 0$ step by step. 2. **Formula Used:** For quadratic equations of the form $ax^2 + bx + c = 0$, the solutions can be fou

1. Problem: Given functions $f(x)$ and $g(x)$, find (a) $f+g$, (b) $f-g$, (c) $fg$, and (d) $\frac{f}{g}$ and state their domains. 2. For problem 29: $f(x) = x^3 + 2x^2$, $g(x) = 3

1. **State the problem:** Prove that $$(ab)^{\log a + \log b} = a^{\log a} b^{2 \log b}$$. 2. **Recall the properties of logarithms and exponents:**

1. **Stating the problem:** We are given the equation $$x^a y^b (x^2 - y^2)^2 = (x^2 + y^2)^3$$ and asked to find the inclined asymptotes. 2. **Understanding the problem:** Incline

1. **Énoncé :** Soit $P(X) = 3X^3 - 2$, $Q(X) = X^2 + X - 1$, $R(X) = aX + b$. Calculer $P + Q$, $P \times Q$, $(P + Q) \times R$ et $P \times Q \times R$. Trouver $a$ et $b$ pour

1. The problem is to simplify the expression $x\{23+y52\}81/67.35\%$.\n\n2. First, interpret the expression carefully. It seems to be $x \times (23 + y \times 52) \times 81$ divide

1. The problem is to expand and simplify the expression $ (x+1)^2 $. 2. We use the formula for the square of a binomial:

1. **State the problem:** We are given two functions: