🧮 algebra

1. **State the problem:** We have a function $P(n) = 0.4n + 6.6$ that gives the price in dollars for $n$ grams of vitamins. We want to find the inverse function $P^{-1}(x)$ and ans

1. **State the problem:** Determine the domain and range of the function $$f(x) = \frac{1}{x^2 - 4}$$. 2. **Recall the domain rules:** The domain of a function includes all real nu

1. **State the problem:** Determine the domain and range of the function $$f(x) = \frac{1}{x^2 - 4}$$. 2. **Domain:** The domain consists of all real numbers $x$ for which the func

1. We are given the quadratic equation $x^2 - 12x + 29 = 0$ and asked to solve it by completing the square. 2. The general form for completing the square is to write the quadratic

1. Zadatak: Rešimo jednačinu $2x + 3 = 11$. 2. Pravilo: Da bismo rešili jednačinu, cilj nam je da izolujemo promenljivu $x$ na jednoj strani jednačine.

1. **State the problem:** Solve the equation $$3 \cdot (x+1) - 4 \cdot (x+2) = 7 \div 7 + 21 \div (-3)$$. 2. **Recall the order of operations:** Perform multiplication and division

1. **State the problem:** Simplify the expression $$\frac{5xy - 10x + y - 2}{8 - 2y^2}$$. 2. **Identify the numerator and denominator:**

1. **State the problem:** Solve the equation $$|2y + 7| - 28 = -11$$ for $y$. 2. **Isolate the absolute value expression:** Add 28 to both sides:

1. **State the problem:** Solve the equation $$y^4 - 17y^2 + 16 = 0$$ for $y$. 2. **Use substitution:** Let $z = y^2$. Then the equation becomes a quadratic in $z$:

1. **State the problem:** Find the equation of the hyperbola with foci at $(-2 - \sqrt{25}, 0)$ and $(-2 + \sqrt{25}, 0)$ and asymptotes $y = \frac{4}{3}x + \frac{8}{3}$ and $y = -

1. **State the problem:** Find the equation of the hyperbola with foci at $$\left(-2 - \sqrt{45}, 3\right)$$ and $$\left(-2 + \sqrt{45}, 3\right)$$ and asymptotes $$y = 2x + 7$$ an

1. **State the problem:** Solve the literal equation $$5kx + 6 = 7kx$$ for $$x$$. 2. **Write down the equation:** $$5kx + 6 = 7kx$$.

1. **State the problem:** Simplify the expression $$\frac{x^2 - 9}{x^2 + x - 6}$$. 2. **Recall the formula and rules:** To simplify a rational expression, factor both numerator and

1. **State the problem:** We are given the quadratic function $$y = x^2 - 4x + 3$$ and need to find the y-coordinate of its vertex. 2. **Formula for vertex:** The vertex of a parab

1. The problem is to solve the equation or expression given by the user. However, no specific equation or expression was provided. 2. To solve an equation, we typically isolate the

1. **Stating the problem:** We need to solve the algebraic expression or equation provided by the user. Since no specific problem was given, please provide the exact math problem y

1. The problem is to solve the equation or expression given by the user. However, no specific equation or expression was provided. 2. To solve an equation, we typically isolate the

1. **State the problem:** Simplify the expression $4(7x-3)-3(5x-4)$ by removing the brackets and combining like terms. 2. **Use the distributive property:** Multiply each term insi

1. **State the problem:** Simplify the expression $$\frac{x^2 - y^2 + 3x + 3y}{x - y + 3}$$. 2. **Recall the formula and rules:**

1. **State the problem:** Simplify the expression $$\frac{x^2 - y^2 + 3(x + y)}{\text{denominator}}$$. Since the denominator is not provided, we will focus on simplifying the numer

1. **State the problem:** Calculate the total monthly pay for a salesperson at Xara showroom who has a base salary of 3800 plus a commission of 3.6% on sales up to 80000 and 7.2% o