🧮 algebra

1. The problem is to solve the system of 8 simultaneous linear equations with 8 variables. 2. The general form of a system of linear equations is:

1. **State the problem:** Given $a = 1 + \frac{1/2024}{2025}$ and $b = 1 + \frac{1/2025}{2026}$, find the value of $$\frac{a+b}{\frac{1}{a} + \frac{1}{b}}.$$\n\n2. **Rewrite $a$ an

1. **State the problem:** We are given a function defined as $f(5x) = \frac{5}{2 + x}$ and asked to find the value of $f(-5)$. 2. **Understand the function:** The function is given

1. The problem is to solve the equation $2x + 3 = 11$ for $x$. 2. We use the basic algebraic principle: to isolate $x$, perform inverse operations to both sides of the equation.

1. The problem is to solve the equation $2x + 3 = 11$ for $x$. 2. The formula used here is to isolate $x$ by performing inverse operations. We subtract 3 from both sides to get rid

1. The problem is to solve the equation $2x + 3 = 11$ for $x$. 2. We use the basic algebraic principle: to isolate $x$, perform inverse operations to both sides of the equation.

1. The problem is to solve the equation $2x + 3 = 11$ for $x$. 2. We use the basic algebraic principle: to isolate $x$, perform inverse operations.

1. **State the problem:** Given $x = -1234567$, find the value of the expression

1. **State the problem:** Find how many trailing zeroes are in the product $$650 \times 4^6 \times 5^9$$. 2. **Recall the rule for trailing zeroes:** Trailing zeroes in a number co

1. **Problem Statement:** We have four inverse function machines:

1. **Énoncé du problème :** Calculer $AB$ et $A^2 + B^2$ avec

1. **State the problem:** Find the sum of all even numbers from 5 to 15. 2. **Identify the even numbers in the range:** The even numbers between 5 and 15 are 6, 8, 10, 12, and 14.

1. **Problem Statement:** Find the domain and range of the composition $f \circ g$, where $f$ and $g$ are functions with given domains and ranges. 2. **Recall:** The composition $f

1. **State the problem:** Simplify the expression $3 \cdot 1 \cdot b + b ( 2 t^2 + 3 b^2 )$. 2. **Write the expression clearly:**

1. **Problem statement:** A local train travels 50% faster than Rohan's car. Both start from Dadar and reach Borivali, 30 km away, at the same time. The train loses 5 minutes due t

1. Problem statement: Given the exponential function $f(x) = a^x$ and a point $A = (1, 2)$ on its graph, find the base $a$ of the exponential function. 2. Formula used: Since the p

1. Stwierdźmy problem: Znajdź punkt wspólny wykresów funkcji $f(x) = \left(\frac{1}{2}\right)^x$ oraz $g(x) = -f(-x)$.\n\n2. Zapiszmy funkcję $g(x)$ w prostszej formie. Ponieważ $f

Let's draw the points for the function $cf(x)$ step by step! 🎯 **Box 1:**

1. **Problem statement:** Find the equation of the ellipse passing through the points $(3,0)$, $(-3,0)$, and $(2,2\sqrt{5})$. 2. **General form of ellipse centered at origin:**

1. The problem involves understanding and solving inequalities and expressions involving variables $x$, $v$, constants, and exponential functions like $e^x$. 2. Let's analyze the f

1. The problem involves solving and understanding a system of inequalities with variables $v, w, p, n, \lambda, q, x, m$ arranged vertically. 2. The inequalities given are: