🧮 algebra

1. The problem is to find a sum of numbers in Excel that results in zero. 2. The formula for summing numbers in Excel is =SUM(range), where range is the cells you want to add.

1. **State the problem:** Decompose the rational function

1. The problem is to perform partial fraction decomposition on a given rational expression. 2. Partial fraction decomposition is used to express a rational function as a sum of sim

1. The problem is to evaluate the expression $\log_2 7 - \log_{14} 2$. 2. Recall the logarithm subtraction rule: $\log_a b - \log_a c = \log_a \frac{b}{c}$, but here the bases diff

1. The problem is to evaluate the expression $$\left(1024x^{10} - 23040x^{8} + 161280x^{6} - 403200x^{4} + 302400x^{2} - 30240\right)e^{-x^{2}}$$ at $x=2$. 2. We substitute $x=2$ i

1. The problem is to find the value of the expression when $x=2$. 2. Since the expression is simply $x$, substituting $x=2$ gives:

1. **State the problem:** Simplify the expression $-(4^{-1} + 3)$. 2. **Recall the rule for negative exponents:** $a^{-n} = \frac{1}{a^n}$. So, $4^{-1} = \frac{1}{4}$.

1. **State the problem:** Sharon has 71 marbles and fills tins with 6 marbles each, with 5 marbles left over. We need to find how many tins she filled. 2. **Set up the equation:**

1. **Énoncé du problème :** Déterminer l'intersection et la réunion des deux intervalles :

1. The problem is to solve the matrix equation: $$\begin{pmatrix}1 & -2 \\ 3 & -1\end{pmatrix} \begin{pmatrix}2 & 3 \\ 6 & 5\end{pmatrix} = \begin{pmatrix}3 & 2 \\ 1 & -2\end{pmatr

1. **بيان المسألة:** لدينا الدالة $f$ معرفة ب $f(x) = \frac{x^2 + 3}{x - 1}$. 2. **التحقق من مجال الدالة:** الدالة معرفة لكل $x$ حيث المقام لا يساوي صفرًا، أي $x \neq 1$.

1. The problem is to find the sum of the numbers 1 through 100. 2. We use the formula for the sum of the first $n$ natural numbers: $$S = \frac{n(n+1)}{2}$$ where $n=100$.

1. Given the problem, we start with the equation or expression to solve. 2. Apply the necessary algebraic manipulations or formulas directly.

1. **Problem Statement:** We are given two equations based on the cost of coffee and toast:

1. **Problem statement:** Find $(f+g)(x)$ where $$f(x) = 6x^4 - x^3 + 3x^2 - 4x + 7$$

1. Muammo: Kvadratik formaning ishorasini aniqlash uchun uchta asosiy determinantlarni hisoblash kerakmi va ularning qiymatlari qanday ishoralarni beradi? 2. Kvadratik forma uchun

1. Problem (a): Express $2x^2 - 12x + 3$ in the form $a(x+b)^2 + c$ where $a,b,c$ are integers. 2. Use the method of completing the square.

1. **State the problem:** We are given the hyperbola equation $$\frac{(x-3)^2}{36} - \frac{(y+2)^2}{9} = 1$$ and need to verify its properties and help graph it.

1. The problem asks us to express the quadratic expression $$q + 12x - qx^2$$ in the form $$a - b(x - c)^2$$ where $$a$$, $$b$$, and $$c$$ are in terms of $$q$$. 2. Start with the

1. **State the problem:** Solve the inequality $$x - 15 \leq -6$$ for $$x$$. 2. **Formula and rules:** To solve inequalities, we isolate $$x$$ by performing inverse operations. Whe

1. **State the problem:** Solve the inequality $$\frac{x}{-9} \geq 3$$ for $x$ and simplify the answer. 2. **Recall the rule for inequalities:** When multiplying or dividing both s