🧮 algebra

1. **State the problem:** Find the domains of the functions $$f(x) = \sqrt[4]{3x - 3}$$ and $$g(x) = \sqrt[3]{x + 3}$$ and express them in interval notation. 2. **Recall domain rul

1. **Problem statement:** We have two numbers that add up to 415. One number is a two-digit number (between 10 and 99), and the other is a three-digit number (between 100 and 999).

1. **State the problem:** Solve the equation $w - 3 = \sqrt{5w - 19}$ for $w$. 2. **Understand the equation:** The equation involves a square root. To solve it, we will isolate the

1. **State the problem:** Solve the quadratic equation $$3x^2 + 2x - 21 = 0$$. 2. **Formula used:** The quadratic formula for solving $$ax^2 + bx + c = 0$$ is $$x = \frac{-b \pm \s

1. **State the problem:** Solve for real number $y$ in the equation $$y - 2 = \sqrt{10 - 3y}.$$\n\n2. **Understand the equation:** The right side is a square root, so the expressio

1. **State the problem:** Solve for $v$ in the equation $$\sqrt{-3v + 40} = v - 4.$$\n\n2. **Understand the domain:** The expression inside the square root must be non-negative, so

1. **State the problem:** Solve the equation $$2^{-115x - 15} = (2^9)^{-13x + 14}$$ for $x$. 2. **Use the property of exponents:** Recall that $(a^m)^n = a^{mn}$.

1. **Problem Statement:** We are given the height of a ball during a slam dunk modeled by the quadratic function:

1. **Stating the problem:** We are given the equation $[x] - \{x\} = \frac{x}{3}$, where $[x]$ is the greatest integer function (floor function) and $\{x\}$ is the fractional part

1. **State the problem:** Simplify the expression $$\frac{16x^{40}y^{18}x^{14}}{y^{18}w^{14}}^{19} = 16^4 x^A y^B w^C$$ and identify the integers $A$, $B$, $C$, and $D$. 2. **Rewri

1. **Problem Statement:** Given the graph of $y=\frac{1}{f(x)}$, we need to sketch $y=f(x)$, determine the equation of $f(x)$, and state any asymptotes. 2. **Understanding Reciproc

1. **State the problem:** Solve the system of equations using Cramer's rule: $$\begin{cases} 15x - 4y - 7z = 14 \\ -4x + 6y - 2z = 34 \\ 4x - 3y - 2z + 12z = 1 \end{cases}$$

1. **Problem Statement:** A man buys 20 pens and 30 pencils for a total of 600.

1. The problem is to "make a solution," which is unclear, so I will interpret it as solving a simple algebraic equation for demonstration. 2. Let's solve the equation $2x + 3 = 7$.

1. **State the problem:** Find the domain of the function $$f(x) = \frac{1}{\sqrt{[x]^2 - 3[x] - 10}}$$ where $[x]$ is the greatest integer less than or equal to $x$ (floor functio

1. **State the problem:** Simplify the expression $$\left(\frac{100x^4 y^3}{4x^8 y^{-1}}\right)^{\frac{1}{2}}$$ completely and write the answer using positive exponents. 2. **Write

1. **Problem Statement:** We want to understand why the line $\log_8 y$ is a linear function of $\log_4 y$. 2. **Recall the change of base formula:** For any positive numbers $a,b,

1. **State the problem:** We are given that $\log_8 y$ is a linear function of $\log_4 x$ with vertical intercept 5 and horizontal intercept 3. We need to find which equation among

1. Masalah: Diberikan fungsi profit $P(x) = a(x-b)^2 + Q$ dengan vertex di titik $(b, Q) = (20, 40000)$ dan parabola membuka ke bawah. 2. Diketahui titik lain pada grafik adalah $x

1. **Soal 1: Menentukan nilai $x$ jika $y=200$ pada persamaan $y=5x+7$** Diketahui persamaan garis lurus:

1. **State the problem:** A carton of apples is shared equally among 10 people. Then 4 people give up their shares, and the remaining 6 people each receive 4 more apples than befor