🧮 algebra

1. **State the problem:** Solve the equation $$(2 - 3\ln)^{\frac{4}{3}} = 256$$ for $\ln$. 2. **Rewrite the equation:** Recognize that 256 is a power of 4, since $$256 = 4^4$$.

1. **State the problem:** We are given the function $$y = 1 + 3\sqrt{x + 3}$$ and asked to graph it along with its inverse. 2. **Recall the formula and rules:** The function involv

1. The problem is to graph the inverse of a given function. 2. To find the inverse of a function $y=f(x)$, we swap $x$ and $y$ and solve for $y$.

1. **Problem 3:** Find the inverse of the function $g(x) = -3 + (x - 1)^3$ and graph both the function and its inverse. 2. **Step 1:** Write the function as $y = -3 + (x - 1)^3$.

1. **Problem 2:** Simplify the expression $$\frac{\sqrt[3]{3m^{2}n^{4}}}{\sqrt[3]{4m^{4}n^{4}}}$$. 2. Use the property of cube roots: $$\frac{\sqrt[3]{a}}{\sqrt[3]{b}} = \sqrt[3]{\

1. **State the problem:** Solve the inequality $$x^4 + x^3 - x^2 - x > 0$$ and write the solution in interval form. 2. **Factor the expression:** Group terms to factor by grouping:

1. **State the problem:** Find the inverse of the function $$g(x) = -3 + (x-1)^3$$. 2. **Recall the formula for inverse functions:** To find the inverse function $$g^{-1}(x)$$, we

1. **State the problem:** Solve for $x$ in the equation $$-2(x - 3) = 3x + 41$$. 2. **Apply the distributive property:** Multiply $-2$ by each term inside the parentheses:

1. The problem asks to show that the coordinates of point C are (4, 0). 2. We are given the equation of the line in point-slope form: $$y - y' = m(x - x')$$ where $m$ is the slope

1. **State the problem:** We are given points A(2, 3), B(1, -2), and point C unknown. The angle between lines AB and BC is 45° (acute). We need to find the slope of AB and then use

1. **State the problem:** Solve for $r$ in the equation $r - 14.2 = 1.89$. 2. **Formula and rules:** To isolate $r$, add $14.2$ to both sides of the equation to cancel out the $-14

1. **State the problem:** Solve for $j$ in the equation $$3j = 7.83$$. 2. **Formula and rules:** To isolate $j$, divide both sides of the equation by 3. Remember, dividing both sid

1. Factor the polynomial $wp + 2n + 8p + 16$. 2. Factor the polynomial $3bc - 2b - 10 + 15c$.

1. **Evaluate each expression with negative exponents:** **a)** $(-10)^{-2} = \frac{1}{(-10)^2} = \frac{1}{100}$

1. **State the problem:** Solve the equation $4\log_5 X = \log_5 625$ for $X$. 2. **Recall the logarithm properties:**

1. **State the problem:** Solve for $x$ in the equation $\log x + \log 12 = \log 8$. 2. **Recall the logarithm property:** $\log a + \log b = \log (a \times b)$. This means we can

1. **State the problem:** Write the expression $$\frac{3}{2x-1} - \frac{2}{x+3}$$ as a single fraction, given that $$x \neq \frac{1}{2}$$ and $$x \neq -3$$. 2. **Formula and rules:

1. **State the problem:** We are given that $x-2$ is a factor of the polynomial $3x^2 + kx - 6$. We need to find the value of $k$. 2. **Use the Factor Theorem:** If $x-2$ is a fact

1. **Problemstellung:** Löse die Gleichung $2x + 3 = 7$. 2. **Formel und Regeln:** Um eine lineare Gleichung zu lösen, isolieren wir die Variable $x$ auf einer Seite der Gleichung.

1. **Stel het probleem vast:** We willen de kosten berekenen voor 5 kwartier parkeren in twee garages: Pleingarage en Stationsgarage. 2. **Gegeven informatie:**

1. **Stel het probleem vast:** We willen weten hoeveel er gemiddeld per leerling is opgehaald in klas 2B over de drie maanden april, mei en juni samen. 2. **Gegeven:**