🧮 algebra

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

1. The problem asks to write $9^{-2}$ as a fraction without indices. 2. Recall the rule for negative exponents: $a^{-n} = \frac{1}{a^n}$.

1. **State the problem:** We have data points $(20, 57.5)$, $(33, 34.8)$, and $(42, 27.4)$ and want to extrapolate $y$ at $x=49$ assuming the model $y = Ax^p$. 2. **Formula and app

1. **Problem statement:** We are given two functions: $$f_9(w) = w^2 + 2$$

1. **State the problem:** Describe the end behavior of the cubic function whose graph passes through the origin and exhibits typical cubic end behavior. 2. **Recall the general beh

1. **State the problem:** We are given the first 4 terms of an arithmetic sequence: 12, 7, 2, -3. We need to find an expression for the nth term of the sequence.

1. **State the problem:** Solve for $x$ in the equation $$\sqrt{\frac{(x+2)!}{x!}} = \sqrt{3!} \times 7.$$\n\n2. **Recall factorial and square root properties:** The factorial $n!$

1. **State the problem:** We are given two functions:

1. **State the problem:** Solve for $x$ in the equation $$\sqrt{\frac{(x+2)!}{x!}} = \sqrt{3!} \times 7.$$\n\n2. **Recall factorial and square root properties:**\n- Factorial: $n!

1. **State the problem:** We have two functions:

1. **State the problem:** You start with the number 5036. Then you add 60, subtract 462, and divide the result by 1.5. You want to find the 10th number in this sequence. 2. **Under