🧮 algebra

1. Let's analyze the relationship between $v$ and $I$ as shown on the graph. 2. Identify the point on the graph where $I=2$.

1. **State the problem:** Simplify the expression $$\frac{x^{-2}y^{\frac{1}{2}}}{x^{\frac{1}{3}}y^{-1}}$$ and find which option it matches. 2. **Recall the rules for exponents:**

1. **State the problem:** We have an exponential decay function $$f(x) = 5470(0.64)^{\frac{x}{12}}$$ where $$x$$ is in months. We want to find the yearly percentage decrease $$p$$

1. **State the problem:** Solve the system of linear equations: $$-10y + 9x = -9$$

1. **State the problem:** Solve the system of linear equations: $$-5x + 13y = -7$$

1. The problem is to understand how to multiply or scale a graph horizontally. 2. The general formula for horizontal scaling of a function $f(x)$ is given by $g(x) = f(bx)$, where

1. **State the problem:** We have a circle with equation $$(x-6)^2 + (y+a)^2 = 18$$ and a line $$y = 2a - x$$ that is tangent to the circle. We need to find the values of $$a$$ for

1. **State the problem:** We need to find which inequality corresponds to the solution set $[6, +\infty)$, meaning all $x$ values starting at 6 and going to infinity. 2. **Analyze

1. **State the problem:** Solve the compound inequality $$-3 \cdot (x + 2) > 15$$ or $$(x - 3) \leq -1$$ and express the solution in interval notation. 2. **Solve the first inequal

1. **State the problem:** Solve the equation $20x = 50$ for $x$. 2. **Formula and rules:** To solve for $x$, divide both sides of the equation by the coefficient of $x$, which is 2

1. **State the problem:** We need to find the $x$- and $y$-intercepts of the lines $y = 50x + 50$ (Studio A) and $y = 25x + 100$ (Studio B). 2. **Recall intercept definitions:**

1. Let's clarify how the value $-6$ was obtained. 2. When solving equations, multiplying or dividing both sides by a negative number changes the sign of the terms.

1. Let's start by understanding the problem: How does the number $6$ become $-6$? 2. The key concept here is the idea of the negative sign, which means the opposite or additive inv

1. **Problem statement:** Vi har et andengradspolynomium $f(x) = x^2 + bx + 8$ og ved, at grafen er symmetrisk omkring linjen $x = 3$. Vi skal bestemme konstanten $b$. 2. **Vigtig

1. **Problem:** Vi skal finde for hvilke værdier af $c$ polynomiet $f(x) = -x^2 - 2x + c$ har henholdsvis ingen, én eller to rødder. 2. **Formel:** Antallet af rødder bestemmes af

1. The problem is to understand the notation $c \in (-\infty, -1)$. 2. This notation means that the variable $c$ belongs to the interval from negative infinity to $-1$, not includi

1. **Problem:** Vi skal finde for hvilke værdier af $c$ polynomiet $f(x) = -x^2 - 2x + c$ har ingen rødder, én rod eller to rødder. 2. **Formel:** For et andengradspolynomium $ax^2

1. **State the problem:** We start with 24 Redcliff Knights and 32 Korblox warriors. One fourth of each army is defeated at the start. 2. **Calculate the number of warriors defeate

1. **State the problem:** We are given two functions $f(x) = 3x + 2$ and $g(x) = 5x - 4$, and we need to find the composition $f \circ g$, which means $f(g(x))$. 2. **Recall the fo

1. **State the problem:** Calculate the value of the expression $6+6-6\times6\div6$. 2. **Recall the order of operations:** Use PEMDAS/BODMAS rules: Parentheses, Exponents, Multipl

1. **State the problem:** We need to find the interval where the graph is decreasing. 2. **Analyze the graph description:**