🧮 algebra

1. **State the problem:** Simplify the expression $$\sqrt[4]{x-6} + \sqrt{x^2+36}$$ and analyze its domain. 2. **Analyze each term:**

1. Given $\log_{10} 2 = m$ and $\log_{10} 3 = n$, evaluate $\log_{10} 24$. We use the property that $\log(ab) = \log a + \log b$.

1. Planteamos el problema: Calcular $$\sqrt[3]{\frac{8}{27}} \times \sqrt[3]{\frac{30}{50}} + \sqrt[3]{\frac{1}{81}} \times \sqrt[4]{\frac{3}{4}} \times \sqrt[5]{\frac{16}{5}}$$.

1. **State the problem:** We want to find how many nurdles are equivalent to 28 ferrules, given the conversion rates: - 1 aglet = 5 ferrules

1. The problem states Ella has R$3390 and wants to convert this amount into Mexican pesos using the conversion rate R$1 = Mex$5.61. 2. To find the amount in Mexican pesos, multiply

1. Stating the problem: Solve the equation $$4x^2y + 9y^2x = 36$$ for variables $x$ and $y$. 2. Factor the left side to find a common factor:

1. Let's start by defining the total profit as $12000$. 2. The businessman said he used $\frac{1}{3}$ of the profit. Calculate this part:

1. Stating the problem: Calculate the determinant of the matrix $$\begin{bmatrix}4 & 4 \\ 4 & -4\end{bmatrix}.$$\n\n2. Recall the formula for the determinant of a 2x2 matrix $$\beg

1. Izračunaj izraze u zadatku 21: 1) $ (ab^{2})^{3} \cdot (a^{2}b)^{3} = a^{3}b^{6} \cdot a^{6}b^{3} = a^{3+6} b^{6+3} = a^{9} b^{9}$

1. Problematika: Farmer ima tri različita prosta broja kao brojeve krava, konja i svinja. Označimo broj krava s $k$, broj konja s $h$, i broj svinja s $s$. 2. Prema zadatku, brojev

1. State the problem: A businessman made a profit of $12000$. He saved $\frac{1}{3}$ of this profit, used $\frac{3}{5}$ of the remainder for food, and used the rest to improve his

1. El problema plantea entender cómo se obtienen las bases en expresiones algebraicas, específicamente si siempre se expresan multiplicando la variable por 1. 2. En álgebra, la bas

1. Soat 7:30 da soat va minut millari orasidagi burchakni topish. Soat mili har bir soatda 30° harakat qiladi, minut mili esa har bir daqiqada 6° harakat qiladi.

1. Muammo shunday: berilgan ifodani tenglama shaklida yozish. 2. Iltimos, aniqlik uchun ifodani yoki masalani to'liq taqdim eting.

1. **State the problem**: We are given two simultaneous equations: $$4x^2 - y^2 = 15$$

1. Dastlab, muammoni aniqlaymiz: "Tenglama qilib ber" bu yerda berilgan ifodani tenglama shaklida yozish yoki yechish talab qilinadi. 2. Iltimos, aniq ifoda yoki misol keltiring, s

1. Kita diberikan pertidaksamaan $3x - 7y < 21$. 2. Tujuan kita adalah mencari daerah penyelesaian dari pertidaksamaan ini.

1. Soat va minut mili orasidagi burchakni topamiz. Soatda har bir soniya uchun soat mili 30° harakat qiladi ($360°/12=30°$).

1. Mari kita tentukan daerah penyelesaian dari sistem pertidaksamaan linear: $$\begin{cases} x + y < 5 \\ 2x + 3y > 12 \\ x = 0 \\ y = 0 \end{cases}$$

1. We are given the equation $12 + \frac{24}{4} - ? = 4$ and need to find the value of $?$. 2. First, simplify the term $\frac{24}{4}$ which equals $6$.

1. Diberikan sistem pertidaksamaan linear. 2. Untuk menentukan daerah penyelesaian, kita harus mencari himpunan titik $(x,y)$ yang memenuhi semua pertidaksamaan secara simultan.