🧮 algebra

1. **State the problem:** Simplify the expression using logarithmic and exponential properties: $$5 \log 10^{-7} - 3 \ln \sqrt{e^6}$$ 2. **Recall the properties:**

1. **State the problem:** Expand the expression $2q(7y - 9q - 8)$. 2. **Formula and rules:** Use the distributive property: $a(b + c + d) = ab + ac + ad$. Multiply each term inside

1. **State the problem:** Expand the expression $$2p(7y - 7p - 5)$$. 2. **Formula and rules:** Use the distributive property, which states that $$a(b + c + d) = ab + ac + ad$$. Her

1. **State the problem:** Solve the equation $$2x^2 - 28x = -58$$. 2. **Rewrite the equation:** Move all terms to one side to set the equation to zero:

1. **State the problem:** We are given the expression $150 - 30h$ which represents the remaining distance after traveling at 30 miles per hour for $h$ hours from an initial distanc

1. **State the problem:** Solve the quadratic equation $4x^2 - 3 = 12x$ for $x$. 2. **Rewrite the equation:** Move all terms to one side to set the equation to zero:

1. **State the problem:** We have an element with an initial mass of 250 grams that decays by 17.3% per minute. We want to find how much of the element remains after 18 minutes, ro

1. **State the problem:** We have an element with an initial mass of 450 grams that decays by 19.4% per minute. We want to find how much of the element remains after 17 minutes, ro

1. **State the problem:** Simplify the expression $$\frac{x}{2} + \frac{7x}{6}$$. 2. **Formula and rules:** To add fractions, they must have a common denominator. Find the least co

1. **Problem:** Solve the system graphically for part (a): $$y = -3x + 9$$

1. **State the problem:** Find the minor and cofactor of entry $a_{11}$ in matrix $$A = \begin{bmatrix} 5 & -3 & 2 \\ -9 & 5 & -4 \\ -3 & 1 & -2 \end{bmatrix}$$ Then find the deter

1. **State the problem:** We want to find which term in the expansion of $$\left(\frac{1}{x} + x\right)^8$$ equals 70. 2. **Recall the binomial expansion formula:**

1. **State the problem:** Simplify the expression $$\left(\frac{1}{x} + x\right)^8$$. 2. **Recall the formula:** The expression is a binomial raised to the 8th power. The binomial

1. The problem is to evaluate the expression $$\left(\frac{1}{x}+x\right)^8$$ when $k=5$.\n\n2. However, the variable $k$ does not appear in the expression, so we assume you want t

1. Problem: Solve the system of equations using the addition (sudėties) method for part (a): $$\begin{cases} x + 2y = 13 \\ -x + y = 5 \end{cases}$$

1. **State the problem:** Solve the cubic equation $$2a^3 - 13a^2 + 27a - 18 = 0.$$\n\n2. **Formula and approach:** To solve a cubic polynomial equation, we try to find rational ro

1. **State the problem:** Add the fractions $\frac{1}{6}$ and $\frac{11}{18}$.\n\n2. **Formula and rules:** To add fractions, they must have a common denominator. The formula is $$

1. **State the problem:** Simplify the expression $150 - 30h$. 2. **Identify the terms:** The expression consists of a constant term $150$ and a variable term $-30h$.

1. Задача: Найти значение выражения $-\frac{6}{2} + -\sqrt{\left(\frac{6}{2}\right)^2} + 4$. 2. Сначала вычислим каждую часть по отдельности.

1. **State the problem:** Convert the given numbers to standard form (scientific notation) correct to three significant figures. 2. **Recall the rules:**

1. The problem asks to write numbers in standard form correct to three significant figures. 2. Standard form means expressing numbers as $a \times 10^n$ where $1 \leq |a| < 10$ and