🧮 algebra

1. **State the problem:** We have an initial bacteria population of 50, which increases by 80% every 20 minutes. We want to find the time it takes for the population to reach 1,200

1. **State the problem:** Calculate the value of the expression $$(-2 + 3\sqrt{6})^2$$. 2. **Recall the formula:** The square of a binomial $(a + b)^2$ is given by $$a^2 + 2ab + b^

1. The problem is to expand the expression $$(1+2y)^{-3}$$ up to the term containing $y^4$. 2. We use the Binomial series expansion for negative exponents: $$ (1+x)^n = \sum_{k=0}^

1. Zadatak: Rešiti jednačinu $2x + 3 = 7$. 2. Formula i pravila: Da bismo rešili linearnu jednačinu, cilj je izolovati promenljivu $x$ na jednoj strani jednačine.

1. **State the problem:** Simplify the expression $$- \frac{3}{4}(10m + 8) - \frac{1}{2}(21m - 16)$$. 2. **Apply distributive property:** Multiply each term inside the parentheses

1. **State the problem:** Simplify the expression $(-4a^{-5}) \cdot (2a^{-6}b^{0})$ and identify the correct multiple-choice answer. 2. **Recall the rules:**

1. Problem statement: The exponent on 3 is $x+4$, not $x$. 2. Formula and rule: For any base $a$ and exponents $m,n$ we have $a^{m+n}=a^m a^n$.

1. **State the problem:** Solve the equation $$7^x = 3^x + 4$$ for $x$. 2. **Understand the equation:** We want to find the value of $x$ such that the exponential expression on the

1. Problemstellung: Wir haben einen Planeten mit einer Anfangsbevölkerung von 50.000 im Jahr 2016, die jährlich um 2% abnimmt. 2. Formel: Die Bevölkerungszahl $P(t)$ nach $t$ Jahre

1. Problemstellung: Wir haben einen Planeten mit einer Anfangsbevölkerung von 50.000 im Jahr 2016, die jährlich um 2 % abnimmt. 2. Formel: Die Bevölkerungszahl nach $t$ Jahren ist

1. **Développer** **A = (x^2 - \sqrt{7})^2**

1. مسئله: باقی‌مانده تقسیم چندجمله‌ای $p(x)$ بر $x+1$ برابر ۲ و بر $x-1$ برابر ۳ است. باید باقی‌مانده تقسیم عبارت $$p(3x-2) + 2x^2 p'(x-2) + x p(3x-2)$$ بر $x-1$ را پیدا کنیم. 2. ق

1. **Problem statement:** Given that the remainders of polynomial $p(x)$ when divided by $x+1$ and $x-1$ are 2 and 3 respectively, find the remainder of the polynomial $$x p(x-2) +

1. The problem involves understanding the division expressions given: \n\nFirst division: divisor = 2, quotient = 2, dividend = a - 1 2 (likely meaning a - 12)\n\nSecond division:

1. مسئله: عبارت $$24 - 9x + 7x^2 + 5x^3$$ بر $$x - 2$$ بخش‌پذیر است. باید این عبارت را تجزیه کنیم. 2. قانون بخش‌پذیری: اگر چندجمله‌ای $$P(x)$$ بر $$x - a$$ بخش‌پذیر باشد، آنگاه $$P

1. **State the problem:** Solve the simultaneous equation \( \log_3(2x + y) = 2 \). 2. **Recall the logarithm definition:** \( \log_b(a) = c \) means \( b^c = a \).

1. The problem is to create two equations. 2. An equation is a mathematical statement that asserts the equality of two expressions.

1. **State the problem:** Solve the quadratic equation in two variables: $5x^2 - 5xy + 3y^2 = 0$. 2. **Formula and approach:** This is a homogeneous quadratic equation. To find sol

1. Simplify $a^{-3}$ using the rule $x^{-n} = \frac{1}{x^n}$: $$a^{-3} = \frac{1}{a^3}$$ 2. Simplify $3x^0$ using the rule $x^0 = 1$ for any $x \neq 0$: $$3x^0 = 3 \times 1 = 3$$

1. The problem is to solve the equation given by the user, but since no specific equation was provided, I will demonstrate solving a simple example equation: $2x + 3 = 7$. 2. The f

1. The problem is to solve the equation given by the user, but since no specific equation was provided, I will demonstrate solving a simple example equation: $2x + 3 = 7$. 2. The f