🧮 algebra

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:

1. **State the problem:** Calculate the product $9^7 \times 9^8$. 2. **Formula used:** When multiplying powers with the same base, use the rule:

1. **State the problem:** Solve the equation $$\ln\left(\frac{e^3}{\sqrt{x+0}}\right) \cdot x = \ln\left(\frac{e^3}{\sqrt{n+1}}\right)$$ for $x$.

1. **State the problem:** We need to find the dimensions of a rectangular container with volume 50 ft³. The container has dimensions: length = $4x + 10$ ft, width = $x$ ft, and hei

1. **State the problem:** Solve the equation $16-2t=5t+9$. 2. **Use the goal of isolating $t$:** Put all $t$ terms on one side and constants on the other.

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

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

1. **Problem:** Bestimmen Sie die Nullstellen der Gleichungen a) bis i) im Kopf. 2. **Formel:** Nullstellen einer Funktion sind die Werte von $x$, für die $f(x) = 0$ gilt.

1. **State the problem:** Solve the system of linear equations: $$2x + y = 8$$