🧮 algebra

1. The problem asks us to convert $361^7$ to base 10. 2. First, recognize that $361$ is already a base 10 number.

1. **State the problem**: We have two polygons. The sum of the number of their sides is 9, and the sum of their diagonals is 7. We need to find the number of sides of the smaller p

1. The problem is to calculate the value of $3020^5$ in base 10. 2. This means we need to multiply 3020 by itself 5 times: $$3020^5 = 3020 \times 3020 \times 3020 \times 3020 \time

1. Let's denote the number of sides of the two polygons as $x$ and $y$, with $x \le y$. 2. Given that the sum of their sides is 9, we have the equation:

1. The problem is to express the number 0.000508 in standard form. 2. Standard form (scientific notation) means writing a number as $a \times 10^n$ where $1 \leq |a| < 10$ and $n$

1. Stated problem: Simplify and analyze the expression $$\ln\left(\frac{x^{1/2}}{x + 4}\right)$$. 2. Start by writing the logarithm of a fraction as a difference of logarithms:

1. The problem is to find the result of $-1 - (-1)$. 2. Subtracting a negative number is equivalent to adding its positive counterpart. Hence, $-1 - (-1)$ can be rewritten as $-1 +

1. The problem is to write the four numbers $1.2 \times 10^{-7}$, $2.3 \times 10^{5}$, $5.76 \times 10^{-2}$, and $7.81 \times 10^{3}$ in ascending order. 2. First, convert all num

1. The problem is to simplify the expression: $\frac{1000000}{1} \div 9 \times 6 - 500000$. 2. First, rewrite the expression clearly as $1000000 \div 9 \times 6 - 500000$.

1. The problem asks to identify which values are equivalent to $$9.5 \times 10^3$$. 2. First, calculate the value of $$9.5 \times 10^3$$:

1. The problem is to find the value of the division $0 \div 1$.\n\n2. Division means splitting a number into equal parts. Here, we want to split 0 into 1 part.\n\n3. Since 0 divide

1. The problem is to solve the equation $3x - 7 = 11$.\n\n2. Start by isolating the variable $x$. Add $7$ to both sides to cancel out $-7$: \n$$3x - 7 + 7 = 11 + 7$$\nwhich simplif

1. The problem is to find the value of "3 times negative 1/3". 2. Rewrite the phrase as a mathematical expression: $3 \times (-\frac{1}{3})$.

1. The problem asks us to write the number 0.00019 in standard form (scientific notation). 2. Standard form expresses a number as $a \times 10^n$ where $1 \leq a < 10$ and $n$ is a

1. Stated problem: Simplify the expression $$\frac{2a - a^2}{2 - a}$$. 2. Factor the numerator: $$2a - a^2 = a(2-a)$$.

1. Stated problem: Simplify the expression $2a - a^2\frac{a}{b}2 - a$. 2. Rewrite the expression clearly: $2a - a^2 \times \frac{a}{b} \times 2 - a$.

1. **State the problem:** Solve the system of linear equations using Gauss Elimination method: $$\begin{cases} x + 4y - z = -5 \\ x + y - 6z = -12 \\ 3x - y - z = 4 \end{cases}$$

1. **State the problem:** Solve the system of linear equations $$\begin{cases} 3Q_1 - 2Q_2 + Q_3 = -1 \\ Q_1 + Q_2 + 2Q_3 = 8 \\ 2Q_1 + 3Q_2 - 4Q_3 = 12 \end{cases}$$

1. **State the problem**: Solve the system of linear equations using the Gauss Elimination method: $$ \begin{cases} x + 4y - z = -5 \\ x + y - 6z = -12 \\ 3x - y - z = 4 \end{cases

1. The given expression is $\frac{3^{6} \times 3^{5}}{3^{7}}$ and we need to write it in the form $n : 1$, where $n$ is an integer. 2. Using the properties of exponents, $3^{6} \ti

1. **State the problem:** Evaluate the expression $$(1 - w + w^2)(1 + w - w^2).$$ 2. **Expand the expression:** Use the distributive property (FOIL) to multiply each term in the fi