🧮 algebra

1. **Simplify the expression** $\frac{n}{5-n} + \frac{2n-5}{n-5}$. Note that $n-5 = -(5-n)$, so rewrite the second fraction:

1. **State the problem:** We need to find how many kids (k), parent (p), and sponsor (s) tickets were sold given the total tickets sold is 400 and total revenue is 6800. 2. **Defin

1. Problem 1: Two numbers have a sum of 432 and their GCF is 12. We need to find the greater number from the options 18, 36, 72, 16. 2. Since the GCF is 12, both numbers can be wri

1. The problem is to complete the square for the number 4. 2. Completing the square usually applies to quadratic expressions, but here we interpret it as expressing 4 as a perfect

1. **State the problem:** Find the greatest number divisible by both 3.5 and 4.5. 2. **Understand the problem:** To find a number divisible by both 3.5 and 4.5, we need to find the

1. The problem asks for the values of $k$ such that the quadratic equation $2x^2 + kx + 2 = 0$ has no real roots. 2. Recall that a quadratic equation $ax^2 + bx + c = 0$ has no rea

1. **State the problem:** We are given a quadratic function $f(x) = x^2 + bx + 1$ and asked to find its minimum value. 2. **Recall the formula for the vertex of a quadratic:** For

1. **State the problem:** Simplify the expression $\sqrt{72} + \sqrt{50} - \sqrt{25}$.\n\n2. **Recall the formula and rules:** The square root of a product can be expressed as the

1. **State the problem:** Evaluate the function $f(x) = x^2 + 2x - 3$ at $x = -2$. 2. **Write the formula:** The function is given by

1. The problem is to evaluate or understand the value of the variable $x$ given as $x = -2$. 2. Here, $x$ is simply assigned the value $-2$. There is no equation to solve or expres

1. The problem is to evaluate or understand the value of $x$ given as $x = -3$. 2. Here, $x$ is simply assigned the value $-3$. This means $x$ is a constant with a negative value.

1. **State the problem:** We are given the quadratic function $f(x) = x^2 + 2x - 3$ and want to analyze it. 2. **Formula and rules:** A quadratic function is generally written as $

1. **State the problem:** We are given the quadratic function $f(x) = x^2 + 2x - 3$ and want to analyze it. 2. **Formula and rules:** A quadratic function is generally written as $

1. Masalah yang diminta adalah menyelesaikan suatu soal matematika tanpa langsung melakukan substitusi. 2. Dalam menyelesaikan soal matematika, terutama aljabar, penting untuk mema

1. The problem is to calculate $4^2$. 2. The expression $4^2$ means 4 raised to the power of 2, which is the same as multiplying 4 by itself.

1. **Problem:** Solve for $n$ in the equation $$3 \left(n + \frac{1}{3}\right) = 7 \left(\frac{n}{2}\right)$$ 2. **Formula and rules:**

1. **Stating the problem:** We need to find the solution to the system of linear equations (SPL): $$\begin{cases} 2p - 2q - r + 3s = 4 \\ p - q + 2s = 1 \\ -2p + 2q - 4s = -2 \end{

1. **Stating the problem:** We need to find the solution to the system of linear equations (SPL): $$\begin{cases} 2p - 2q - r + 3s = 4 \\ p - q + 2s = 1 \\ -2p + 2q - 4s = -2 \end{

1. **Problem statement:** We have a polynomial $f(x)$ divisible by $x+2$, and when divided by $x^2$, the remainder is $-20x + 8$. We want to find $R(-1)$ where $R(x)$ is the remain

1. The problem is to simplify the expression $$\sqrt[3]{-8 \cdot 3}$$. 2. We use the property of cube roots that $$\sqrt[3]{a \cdot b} = \sqrt[3]{a} \cdot \sqrt[3]{b}$$.

1. The problem is to convert the fraction $\frac{3}{4}$ to a decimal. 2. The formula to convert a fraction to a decimal is to divide the numerator by the denominator: $$\text{Decim