🧮 algebra

1. The problem asks to explain why the expression $$\frac{4}{3} \pi r^3$$ is a monomial and to identify its degree. 2. A monomial is an algebraic expression consisting of only one

1. **State the problem:** Simplify the expression $$\left(\frac{100a}{25a^2 b^{\frac{1}{2}}}\right)^{\frac{1}{2}}$$. 2. **Write the formula and rules:** When simplifying expression

1. The problem is to solve for $h$ in an equation (not specified by the user). 2. Since the exact equation is not given, let's assume a general linear equation involving $h$, for e

1. **Problem statement:** Simplify the expression $(\sqrt{x} - 2\sqrt{y})(\sqrt{x} + 2\sqrt{y}) + (3\sqrt{x} + \sqrt{y})^2$ using distribution. 2. **Recall formulas:**

1. **Problem Statement:** Identify intervals of increase/decrease, symmetry, domain, and range for the function $f(x) = 3x^2$. 2. **Function Type:** This is a quadratic function of

1. **Problem Statement:** Identify the intervals of increase/decrease, symmetry, domain, and range for the function $f(x) = 3x - 5$. 2. **Formula and Rules:** For a linear function

1. **State the problem:** Simplify the expression $$\left(\frac{100a}{25a^{2}b^{\frac{1}{2}}}\right)^{-\frac{1}{2}}$$. 2. **Recall the rules:**

1. **State the problem:** Simplify the expression $$\frac{100a^{-2}b^{2/3}}{25a^{2}b^{-1/3}}$$. 2. **Recall the rules:**

1. **State the problem:** Solve the logarithmic equation $$\log_2 4 + \log_2 (c - 9) = 5$$ for $c$. 2. **Recall the logarithm property:** The sum of logarithms with the same base c

1. **State the problem:** Solve the logarithmic equation $$\log_3(3x - 11) = \log_3(25 - x)$$ and check for extraneous solutions. 2. **Recall the logarithm property:** If $$\log_b

1. El problema es resolver la ecuación $$7x + \frac{4(5 - 2x)}{5} = 4$$. 2. Para eliminar el denominador, multiplicamos ambos lados de la ecuación por 5:

1. Statement of the problem. Solve the system of linear equations:

1. **Simplify the expression** $\frac{r^6 n^{-7}}{r^4 n^2}$. 2. Use the rule for dividing powers with the same base: $\frac{a^m}{a^n} = a^{m-n}$.

1. **State the problem:** We want to find the time $t$ when Spider-Man reaches his maximum swinging distance and the value of that maximum distance. 2. **Given function:** The dist

1. **Stating the problem:** Solve the system of equations for part d): $$3 - 2(x - 4) = 5y + 6$$

1. **State the problem:** We want to find which expressions are equivalent to $$4m + 4n + 10$$. 2. **Recall the distributive property:** $$a(b + c) = ab + ac$$. This helps us expan

1. El problema pide representar funciones exponenciales basadas en la función base $y=2^x$. 2. La función base es $y=2^x$. Las transformaciones incluyen desplazamientos horizontale

1. **State the problem:** Simplify the expression $$\frac{1}{3}(18a + 6b) - 2(2a + 4b)$$ and find which given expressions are equivalent to it. 2. **Apply the distributive property

1. **State the problem:** We have a piecewise function defined as: $$f(x) = \begin{cases} -3x + 4 & \text{for } x < 1 \\ -2x + 3 & \text{for } 1 \leq x \leq 5 \\ 3x - 24 & \text{fo

1. **State the problem:** We are given the value of a car over time and need to find an exponential regression equation of the form $$y = ab^x$$ where $y$ is the value of the car a

1. **Problemstellung:** Wir sollen die Wertetabellen für die linearen Funktionen aus Aufgabe 2 vervollständigen.