🧮 algebra

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

1. **State the problem:** Solve for $x$ in the equation $5(9-4) + x(2-5) = 0$. 2. **Apply the distributive property:** Calculate the values inside the parentheses.

1. **State the problem:** Solve the equation $-8(x-3)+4=4(-x+8)-4x$ for $x$. 2. **Apply the distributive property:**

1. **State the problem:** Solve the equation $3(a+2)-2a=\frac{1}{7}(-7a+42)$. 2. **Write down the equation:**

1. **State the problem:** Solve the equation $$\frac{7x - 2}{4} = 3x + 1$$ for $x$. 2. **Formula and rules:** To solve for $x$, we want to isolate $x$ on one side. Since $x$ is ins

1. **State the problem:** Solve the equation $5(K+4) = 2(2.5K - 3) + 12$ for $K$. 2. **Write the formula and rules:** Use the distributive property to expand both sides and then is

1. **State the problem:** Simplify the expression $28y^2 - 21y$. 2. **Identify the common factors:** Both terms have a common factor of 7 and a factor of $y$.