🧮 algebra

1. **Problem Statement:** Jenny works from 8:00 A.M. to 5:00 P.M. daily and earns 537 per day. We need to compute her overtime pay based on her working hours.

1. **State the problem:** We are given the quadratic function $$f(x) = x^2 + 2px + p - 6$$ where $$p$$ is a constant. We need to find the values of $$m$$ and $$n$$ such that $$f(x)

1. **State the problem:** Solve the equation $\left(2e\right)^{x^2} - 3 = e^9$ for $x$. 2. **Rewrite the equation:** Add 3 to both sides to isolate the exponential term:

1. **State the problem:** Solve the equation $$\frac{2e^x}{2} - 3 = e^9$$ for $x$. 2. **Rewrite the equation:** Simplify the left side by canceling the 2 in numerator and denominat

1. El problema es simplificar y entender la expresión algebraica: $-2x^3 + 3$. 2. La expresión consta de dos términos: $-2x^3$ y $+3$.

1. El problema es encontrar la función dada: $f(x) = 2x^3 + 1$. 2. Esta es una función polinómica de grado 3, donde el término principal es $2x^3$ y el término constante es $1$.

1. Misalkan kita memiliki persamaan bertingkat: $$\sqrt{x\sqrt{x\sqrt{x\cdots}}} = \sqrt{2013x + \sqrt{2013x + \sqrt{2013x + \cdots}}}$$ dan $$\sqrt{x + a} = 45.$$\n\n2. Pertama, k

1. **Show that the set of rational numbers $\mathbb{Q}$ is a Field.** A field is a set equipped with two operations (addition and multiplication) satisfying certain axioms: closure

1. The problem appears to involve understanding the expression $x_i\sqrt[\lfloor x\rfloor \sin(x) \omega]{}$, which is not fully defined as it lacks a radicand (the expression unde

1. The problem states that $|a + b| = a + b$ and $|b| = b$. We need to understand what these conditions imply about $a$ and $b$. 2. Recall the definition of absolute value: for any

1. ปัญหาคือ ถ้าใส่น้ำมันทอดปลาไป $\frac{2}{5}$ ลิตร แล้วจับเหลือตักน้ำมันจากบรรจุภัณฑ์เดิมนั้น น้ำมันอยู่ในขวดเท่าไร 2. สมมติว่าปริมาณน้ำมันเดิมในขวดคือ $x$ ลิตร

1. **مشكلة السؤال الأول (أ-1):** معطى المصفوفة أ = \begin{bmatrix} 3 & -4 \\ 2 & 0 \end{bmatrix}، المطلوب حساب 3 أ_{12} - 2 أ_{21} حيث أ_{12} هو العنصر في الصف الأول والعمود الثاني

1. **Problem (i): Solve the equation** $$2^{2x-1} - 9 \cdot 2^{x-2} + 1 = 0$$ 2. **Rewrite terms using properties of exponents:**

1. **Problem:** Löse das Gleichungssystem mittels Additionsverfahren: $$\begin{cases} 2e - f = 9 \\ e + 3f = -6 \end{cases}$$

1. The problem is to understand and classify different types of real numbers. 2. Real numbers include rational numbers (which can be expressed as a fraction $\frac{p}{q}$ where $p$

1. **State the problem:** Compare the fractions $1 \frac{1}{2}$, $\frac{3}{2}$, and $\frac{17}{6}$ using $<$, $>$, or $=$. 2. **Convert mixed fractions to improper fractions:**

1. **State the problem:** We are given two equations: $$2x + 3y = 7$$

1. **State the problem:** Simplify the expression $$\frac{x^2-25}{x^2+5x} \div \frac{xy+6x-5y-30}{5x-15}$$. 2. **Rewrite the division as multiplication by the reciprocal:**

1. **State the problem:** Factor the quadratic expression $x^2 + 5x + 6$. 2. **Recall the factoring formula:** For a quadratic $ax^2 + bx + c$, we look for two numbers that multipl

1. **State the problem:** Solve the system of linear equations for $x$ and $y$: $$2x + y = 8$$

1. **State the problem:** We need to find values of $x$ and $y$ such that $$3^x - 3^y = 234.$$ 2. **Rewrite the equation:** We can factor the left side using the property of expone