🧮 algebra

1. **State the problem:** We need to find the rate of simple interest that will make ₱7500 earn ₱2050 in 3 years and 4 months.

1. **State the problem:** We are given the function $$f(x) = e^{x+4} - 1$$ and need to find its inverse function $$f^{-1}(x)$$. 2. **Recall the definition of inverse function:** Th

1. **โจทย์:** กำหนดให้ $$f(x) = x^2 + 3x - 4$$, $$g(x) = 5 - 6x$$ และ $$h(x) = 7x + 8$$ จงหา

1. Bài toán yêu cầu tìm $x$ thỏa mãn các phương trình chứa căn bậc hai với điều kiện miền xác định của $x$. 2. Công thức cơ bản: $\sqrt{x} = a \Rightarrow x = a^2$ với $a \geq 0$.

1. Planteamos el problema: Hay un grupo de empleados con menos de 20 años de trabajo, entre ellos 4 futuras madres. 2. Se debe comprar regalos que cuestan $$3800$$ en total.

1. **Problem 10A:** Show that the relationship between peanut butter $x$ and cracker packages $y$ is proportional. 2. To check proportionality, verify if the ratio $\frac{y}{x}$ is

1. **Problem Statement:** We are given two tables showing proportional relationships and asked to verify proportionality, write equations, and find specific values.

1. **Problem Statement:** We are given a piecewise linear function with points at $(-5,0)$, $(-1,2)$, and $(5,-1)$. We need to find the domain, range, intercepts, intervals where t

1. **Problem Statement:** Identify the domain, range, x- and y-intercepts, intervals where the function is positive/negative, and intervals where it is increasing/decreasing from t

1. The user has provided several sequences of numbers separated by dashes. 2. Since no explicit question or problem is stated, we interpret the first sequence as the problem to ana

1. Resolver los siguientes productos notables: a) $(x + 5)^2$

1. Resolver los siguientes productos notables: a) Calcular $(x + 5)^2$.

1. **State the problem:** We analyze the given piecewise linear function with points $(-5,0)$, $(-1,2)$, $(5,-1)$, crossing the y-axis at $(0,1)$ and x-axis at $x=-5$ and $x=3$. 2.

1. **Problem Statement:** Solve the system of simultaneous equations. 2. **General Formula:** For two linear equations in two variables:

1. **Problem Statement:** Solve the simultaneous equations involving surds. 2. **General Approach:** To solve simultaneous equations, we use substitution or elimination methods. Wh

1. **State the problem:** We are given a set of ordered pairs $\{(-3,3), (0,7), (1,-5), (2,4)\}$ and need to find the domain and range of this relationship. 2. **Recall definitions

1. **State the problem:** We need to write an algebraic expression for the phrase "the quotient of five and $w$ decreased by eight." 2. **Understand the phrase:** "Quotient of five

1. El problema es graficar la función $$f(x)=x^2+4$$. 2. Esta es una función cuadrática de la forma $$f(x)=ax^2+bx+c$$, donde $$a=1$$, $$b=0$$ y $$c=4$$.

1. **Nêu bài toán:** Chúng ta có một đồ thị đường cong và cần xác định hàm số tương ứng trong bốn phương án đã cho.

1. **Bài toán:** Xác định hàm số tương ứng với đồ thị đã cho trong Câu 3 và Câu 4 dựa trên các tiệm cận và điểm đặc trưng của đồ thị.\n\n2. **Câu 3:**\n- Đồ thị có tiệm cận đứng $x

1. **Problem statement:** We have two graphs of rational functions and four options for each. We need to identify which function corresponds to each graph based on vertical and hor