🧮 algebra

1. **State the problem:** Multiply the expressions $$\sqrt{10c^5} \cdot \sqrt{8c}$$ assuming all variables represent positive real numbers. 2. **Recall the property of radicals:**

1. **State the problem:** Multiply the expressions $$\sqrt{4n^3} \cdot \sqrt{50n}$$ assuming all variables represent positive real numbers. 2. **Use the property of radicals:** $$\

1. **State the problem:** Solve the system of equations using the elimination method. 2. **First system:**

1. **State the problem:** Graph the function $f(x) = -2 \left(\frac{1}{5}\right)^x$ and identify the asymptote.

1. The problem is to add the fractions $\frac{12}{7}$ and $-\frac{5}{7}$.\n\n2. Since the denominators are the same, we can add the numerators directly: $$\frac{12}{7} + \left(-\fr

1. **State the problem:** Simplify the expression $$\frac{m}{3} + \frac{2m}{3}$$. 2. **Formula and rules:** When adding or subtracting rational expressions with the same denominato

1. **State the problem:** Rachel loaned Adam 8510 at an interest rate of 13% for 2 years. We need to find how much Adam will pay at the end of 2 years. 2. **Formula for simple inte

1. Problemet är att beräkna arean av det markerade området som begränsas av x-axeln, grafen till funktionen $f(x) = 9x^2$, och linjen $x=2$.\n\n2. Formeln för arean under en kurva

1. **State the problem:** We need to find the sum of the two polynomials $-2x^2 + 5x + 10$ and $-7x - 3$. 2. **Formula and rules:** To add polynomials, add the coefficients of like

1. **State the problem:** Simplify the expression $$(-x^2 - 4x + 1) - (2x^2 + 9)$$. 2. **Apply the subtraction:** Distribute the minus sign to the second polynomial:

1. **State the problem:** Simplify the expression $$\sqrt{3}(\sqrt{24} - \sqrt{6})$$. 2. **Recall the property of square roots:** $$\sqrt{a} \times \sqrt{b} = \sqrt{a \times b}$$.

1. **State the problem:** Solve the equation $$\frac{x}{x+3} + \frac{12}{x^2 - 9} = \frac{2}{x-3}$$ for $x$. 2. **Identify the denominators and restrictions:**

1. The problem is to solve the equation $$\frac{2x+3}{x-1} = 4$$ for $x$. 2. We use the formula for solving rational equations: multiply both sides by the denominator to eliminate

1. The problem is to find the formula for percentage loss. 2. Percentage loss is calculated when the selling price is less than the cost price.

1. **Problem:** Find the percentage profit on the following items. 2. **Formula for percentage profit:**

1. **State the problem:** Simplify the expression $$\frac{x^2-25}{x^2+5x} \div \frac{xy+6x-5y-30}{5x-15}$$. 2. **Rewrite division as multiplication by reciprocal:**

1. **State the problem:** Solve the inequality $x \ln(x-1) - 2 > 0$. 2. **Rewrite the inequality:**

1. **State the problem:** We are given two linear equations: $$2x + 3y = 7$$

1. Find four consecutive integers such that if the sum of the first and third is increased by 10, the result is 6 greater than 4 times the fourth. Let the four consecutive integers

1. **Problem:** Find the vertical and horizontal asymptotes of the function $$f(x) = \frac{x^2 - 9}{2x^2 - 5x - 3}$$. 2. **Vertical asymptote:** occurs where the denominator is zer

1. **State the problem:** Simplify the expression $ (4^3)^5 $. 2. **Use the power of a power rule:** When raising a power to another power, multiply the exponents: