🧮 algebra

1. The problem states the function relationship: $y(t) = x(2t)$. We want to understand how $y$ depends on $t$ given $x$ as a function of its argument. 2. This means that the value

1) Simplify each expression involving complex numbers: (a) $ (3 - 4i) + (6 + i) = (3 + 6) + (-4i + i) = 9 - 3i $

1. The problem is to understand and graph the function $y(t) = x^{2t}$. 2. Here, $x$ is the base and $2t$ is the exponent, where $t$ is the variable.

1. The problem is to understand the variable $y$ as given. 2. Since the user only provided the variable $y$ without any equation or context, there is no further calculation or simp

1. Problem: Factor the expression $x^2$. 2. Observation: The symbol $x^2$ denotes $x$ multiplied by itself, so $x^2 = x \cdot x$.

1. State the problem: Factor $x^2$. 2. Recognize that $x^2$ is a perfect square and can be written as $x \cdot x$.

1. Állítsuk fel a problémát: Elemezzük a függvényt $$f(x) = x^2 + 4x + 6$$ és jellemezzük a tulajdonságait. 2. Határozzuk meg a függvény típusát: Ez egy másodfokú függvény, parabol

1. **State the problem:** We need to find the equation of line $L_2$ which is perpendicular to line $L_1$ and passes through point $P(4,5)$. The equation of $L_1$ is given as $$y =

1. Állítsuk fel az összetett függvényt: $$F(x) = \ln\big((x+3)^2 - 1\big)$$. 2. Az összetett függvény bontása külső és belső függvényre:

1. The problem asks to find the values of compositions of functions \(f\) and \(g\) at given points: \((f \circ g)(4)\), \((f \circ g)(2)\), \((g \circ f)(-5)\), \((g \circ g)(-5)\

1. **State the problem:** We are given two functions $f(x)$ and $g(x)$ with their graphs and need to evaluate expressions involving these functions at specific points. 2. **Given v

1. The problem asks to evaluate $f(-5) + g(-5) \times 7$. 2. Next, calculate $(g)(-2) - f(-3) \times (-5)$.

1. **State the problem:** Calculate $f(-5) + g(-5)$ given the values from the graphs. From the description, approximate values:

1. Let's clarify what "finding the difference" means in math. It usually refers to subtracting one number or expression from another. 2. To find the difference between two numbers

1. The problem states Carly and James share money in the ratio 5 : 3, and Carly gets 70 more than James. 2. Let the common multiplier be $x$. Then Carly's amount is $5x$ and James'

1. The problem is to convert each given equation into function notation $f(x) = \ldots$ where $y$ is expressed as a function of $x$. 2. For $y = x$, the function notation is straig

1. **State the problem:** Solve the equation $x + \log_2(2^x - 6) = 4$ for $x$. 2. **Rewrite the logarithmic expression:** Recall that $\log_2(2^x) = x$. Here, the argument inside

1. **State the problem:** Solve the system of linear equations: $$-10x = -10$$

1. **State the problem:** Solve the system of linear equations: $$2x - 8y = -10$$

1. **State the problem:** Solve the system of linear equations: $$2x - 8y = -10$$

1. **Expand and simplify** the expression $(x + 5)(x + 4)(x - 3)$ to find constants $A$, $B$, $C$, and $D$. Start by expanding two brackets first: