🧮 algebra

1. Le problème consiste à résoudre le système linéaire : $$\begin{cases} 0.12x + 0.09y + 0.05z = 8 \\ x + 0.5y = 40 \\ x + y + z = 100 \end{cases}$$

1. **State the problem:** Solve the system of equations: $$\frac{9}{2}x + 4y = 27$$

1. The problem asks to calculate \( cd \), which means multiplying the variables \( c \) and \( d \).\n\n2. To multiply two variables, you simply write them together: \( cd \).\n\n

1. **State the problem:** Solve the system of equations: $$y = 3x + 5$$

1. The problem is to simplify the algebraic fraction expression: \( \frac{a}{14} + \frac{b}{14} = \frac{a}{2x} + \frac{b}{2x} = \frac{c}{x} + \frac{y}{5x} \). 2. We use the rule th

1. **Problem:** Solve the system of equations: $$y = 3x + 5$$

1. **Problem:** Solve the system of equations: $$y = 3x + 5$$

1. Problem: You want to practice math problems involving natural and rational numbers, including addition, subtraction, multiplication, division, equations, inequalities, and conve

1. **State the problem:** We are given the quadratic function $f(x) = 3(x + 2)(x + 4)$ and want to understand its shape and key features. 2. **Formula and explanation:** The functi

1. The problem is to analyze the function $f(x) = -(x+1)^2 + 16$ and understand its graph. 2. This is a quadratic function in vertex form: $f(x) = a(x-h)^2 + k$, where $(h,k)$ is t

1. **Stating the problem:** Create a similar problem to the given one: For $$y = \frac{2x - 1}{x^2 - x - 6}$$ find all asymptotes, state the domain and range, find the intercepts,

1. **Stating the problem:** Abhasra sold half of her comic books, then bought 17 more, and now has 32. We need to find how many comic books she started with. 2. **Define the variab

1. **Problem:** Evaluate each power without using a calculator. 2. **Key formula:** For any positive number $a$ and rational exponent $\frac{m}{n}$, we use the rule:

1. **Menyatakan masalah:** Diketahui setiap pekerja menyelesaikan $\frac{2}{5}$ bagian tugas pada pagi hari dan $\frac{3}{8}$ bagian pada sore hari. Ada 10 pekerja. Kita diminta me

1. Problem: Given $a = 19 + 8 \sqrt{3}$, find the value of $\sqrt{a} + \frac{1}{\sqrt{a}}$. 2. Formula and rules: To find $\sqrt{a} + \frac{1}{\sqrt{a}}$, we can use the identity:

1. **State the problem:** We are given a piecewise function: $$f(x) = \begin{cases} x^2 - 4x + 3, & x \neq 0 \\ 3, & x = 0 \end{cases}$$

1. **State the problem:** We need to determine if the cubic equation $x^3 - 3x^2 - x + 4 = 0$ has a root in a given interval (though the interval is not specified, we will analyze

1. المشكلة: نريد إيجاد المقلوب (résiproque) لعدد معين. 2. تعريف المقلوب: المقلوب لعدد $a$ هو العدد الذي إذا ضربناه في $a$ يعطي 1.

1. The problem is unclear as "gof" is not a standard mathematical expression or function notation. 2. If you meant the composition of functions, such as $g \circ f$, it means apply

1. Muammo: 1-tokcada 80 ta non, 2-tokcada 95 ta non bor. Nonlar qo'shildi va umumiy son 15% ga oshdi. So'ngra sotildi va 20% ga kamaydi. Nonlarning umumiy soni necha foizga o'zgarg

1. We are asked to find the inverse of the function $$f(x) = -1 - \frac{1}{5}x$$ and then graph both the function and its inverse. 2. To find the inverse, start by replacing $$f(x)