🧮 algebra

1. **State the problem:** Calculate $11^4 \div 11$. 2. **Recall the exponent division rule:** When dividing powers with the same base, subtract the exponents: $$a^m \div a^n = a^{m

1. The problem states that the line $T$ passes through the points $(0, -5)$ and $(1, 3)$ and can be written in the form $y = mx + c$. 2. To find $m$ (the slope), use the formula:

1. **Stating the problem:** Calculate 25% of 58,458. 2. **Formula used:** To find a percentage of a number, use the formula:

1. **State the problem:** Dorothy bought a clutch at a 35% discount and saved 42. We need to find the original price of the clutch. 2. **Formula and explanation:** The discount amo

1. **State the problem:** Winifred bought a bib necklace at a 45% discount, saving $63. We need to find the original price of the necklace. 2. **Formula and explanation:** The disc

1. **Problem statement:** Kürzen Sie so weit wie möglich den Bruch $\frac{9rs}{63st}$. 2. **Formel und Regeln:** Beim Kürzen von Brüchen kürzen wir gemeinsame Faktoren im Zähler un

1. **Problem Statement:** We need to find the total cost for each company (Thunder Cable and Flash Cable) for the first 12 gigabytes of data usage. 2. **Formula:** Total cost for e

1. **Problem Statement:** We are given a function $f(x)$ with inputs and outputs in a table and asked to complete the table for its inverse function $f^{-1}(x)$.

1. **State the problem:** Simplify the expression $$\frac{3f^3}{12f^{18}}$$. 2. **Recall the rules:** When dividing powers with the same base, subtract the exponents: $$\frac{a^m}{

1. **Problem statement:** We are asked to explain what a function is and why the composition of two functions is still a function. Then, we will solve the first example: given $f_{

1. **State the problem:** Simplify the expression $$\frac{10a^2}{15a^6}$$. 2. **Write down the formula and rules:** When simplifying fractions with variables, divide the coefficien

1. Solve equation (13): $2^x - 5 = 10$ Add 5 to both sides:

1. Problem: Expand the logarithmic expressions. 2. Recall the logarithm rules:

1. **Problem:** Condense the expression $6 \log 2 + 2 \log 12 - 3 \log 4$ into a single logarithm and find its value. 2. **Formula and rules:**

1. Problemet er at finde værdierne af $y$ og $z$ for $x = -1, 0, 2$. 2. For at løse dette, skal vi kende funktionerne for $y$ og $z$ i forhold til $x$. Da funktionerne ikke er give

1. The problem asks to identify the values of $a$ and $b$ in the quadratic function. 2. A quadratic function is generally written as $y = ax^2 + bx + c$.

1. **Evaluate the logarithms:** (1) Find $\log_{81} \frac{1}{3}$.

1. The problem asks for the equation of the axis of symmetry of a parabola. 2. The axis of symmetry of a parabola is a vertical line that passes through the vertex.

1. **Stating the problem:** We have a pattern of square-based shapes made of smaller squares. Step 1 is a 2x2 grid (4 squares), Step 2 is a 3x3 grid (9 squares) with the middle squ

1. **State the problem:** Solve the equation $$x - \frac{2 - x}{3} = \frac{3}{2} - \frac{x + 1}{3}$$. 2. **Identify the goal:** We want to find the value of $x$ that makes the equa

1. The problem is to write $5^{-3}$ as a fraction in simplest form without indices. 2. Recall the rule for negative exponents: $a^{-n} = \frac{1}{a^n}$ where $a \neq 0$ and $n$ is