🧮 algebra

1. The problem asks to rewrite the power expression $ (x - 2)^2 $ as repeated multiplication. 2. Recall the rule for powers: $ a^n $ means multiplying $ a $ by itself $ n $ times.

1. **State the problem:** We are given a piecewise function: $$f(x) = \begin{cases} 4x + 17 & \text{for } x < -4 \\ -4 & \text{for } x \geq 0 \end{cases}$$

1. **Stating the problem:** Risolvi l'equazione $$\sqrt{5(x-1)} = 2(x+1)$$. 2. **Formula and rules:** Per risolvere equazioni con radici quadrate, eleviamo al quadrato entrambi i m

1. **State the problem:** Simplify the expression $2\sqrt{-16}$.\n\n2. **Recall the formula and rules:** The square root of a negative number involves imaginary numbers. Specifical

1. The problem is to find the value of $\sqrt{-18}$. 2. The square root of a negative number is not a real number because no real number squared gives a negative result.

1. The problem asks to identify the inequality that matches the graph described. 2. The graph shows a vertical line at $x = -7$ with shading to the left of the line, indicating all

1. **State the problem:** We need to determine which inequality matches the given graph. 2. **Analyze the graph:** The line passes through the point $(2,4)$ with an open circle, me

1. **State the problem:** We are given two functions $f(x) = 3x - 8$ and $g(x) = x^3$. We need to find an expression for the composite function $g(f(x))$. 2. **Recall the definitio

1. Problemet handler om at forstå, hvad bogstaver som a og b betyder i matematik. 2. Bogstaver som a og b kaldes variable, og de repræsenterer tal, som kan ændre sig.

1. Problem statement: We have three functions: $$f(x) = 0.9 \cdot x - 2$$

1. **State the problem:** Simplify the expression $$\frac{s^{723}}{s^{721}}$$. 2. **Recall the rule for dividing powers with the same base:** When dividing powers with the same bas

1. **Stating the problem:** Simplify the expression $$(\sqrt{x} - 1)(\sqrt{x+1} + \sqrt{x-1}) - \sqrt[3]{x\sqrt{x}}$$

1. We are asked to make $y$ the subject of the equations $7x - 2y + 11 = 0$ and $6x + y + 4 = 0$. 2. For the first equation $7x - 2y + 11 = 0$, isolate $y$:

1. **State the problem:** Simplify the expression $$\frac{5^{723}}{5^{721}} \cdot \frac{3^{300}}{3^{249}} \cdot \left(\frac{3 \cdot 4^3}{3^{-2} \cdot 4^{-7}}\right)^0 \cdot \left(\

1. **State the problem:** Solve the equation $2x - 7 = x - 1$ for $x$. 2. **Write down the equation:**

1. **State the problem:** We have the function $$f(x) = 2(x^2 - 3)^2$$ and need to solve parts c and d. 2. **Part c: If $$f(x) = 6$$, find possible values of $$x$$.**

1. **Problem statement:** We are given two numbers expressed as products of prime factors:

1. **State the problem:** We need to write functions modeling the maximal oxygen consumption for two 25-year-old female athletes, where consumption decreases by 0.5% per year after

1. The problem is to find the 46th, 10th, 12th, and 50th terms of a sequence or series, but since no sequence is given, we cannot find specific values. 2. If you provide a sequence

1. The problem is to simplify the fraction $\frac{36}{40}$ to its simplest form. 2. To simplify a fraction, we divide both the numerator and denominator by their greatest common di

1. **State the problem:** We have a sequence of dot patterns where each pattern adds the same number of dots as the previous one. We want to find: a) An expression for the number o