🧮 algebra

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.

1. **Problem statement:** Simplify and solve the system of equations for part (a): $$\frac{x}{y} = \frac{7}{5}$$

1. **State the problem:** Simplify the expression $\left(2^2 \cdot 5^2\right)^{\frac{1}{2}} \cdot 8^{\frac{1}{3}} \div \frac{1}{2} - 11$. 2. **Use the properties of exponents:**

1. The problem asks for the smallest possible answer to the multiplication $20 \times 300$ given that Isaac estimated it by rounding each number to 1 significant figure. 2. Isaac's

1. **State the problem:** We are given the cubic function $$f(x) = -0.3x^3 - 0.3x^2 + 1.8x$$ and want to analyze its behavior including intercepts and extrema. 2. **Formula and rul

1. Il problema chiede di trovare quanto ha speso Marta in pizzeria sapendo che insieme hanno speso 31 e che Luca ha speso 5 in più di Marta. 2. Definiamo le variabili:

1. **State the problem:** We are given three points on a number line: R, M, and S, with M = $\sqrt{270}$. We need to find the values of R and S to one decimal place, knowing that R

1. The problem is to simplify the expression $$\frac{3^{-2}}{5^{-2}}$$ and verify the equivalence to $$\frac{5^2}{3^2}$$. 2. Recall the rule for negative exponents: $$a^{-n} = \fra

1. **State the problem:** Find the equation of the line passing through the points (0,4) and (1,6) in slope-intercept form $y=mx+b$. 2. **Formula and rules:** The slope $m$ is calc