🧮 algebra

1. **State the problem:** Find the inverse relation of the function $$f(x) = 3x^2 - 4$$. 2. **Recall the definition:** The inverse relation swaps the roles of $$x$$ and $$y$$. If $

1. The problem asks for the domain of the inverse function of $f(x) = \frac{2\sqrt{x+4}}{3}$.\n\n2. To find the domain of the inverse function, we first need to find the range of t

1. **State the problem:** We need to find a formula for the total cost $L$ of a box containing 50 lemons, where each lemon costs $n$ cents. 2. **Formula used:** The total cost is t

1. The problem is to determine which integer values to use in a given mathematical context. 2. Generally, the choice of integer values depends on the problem's domain or constraint

1. **State the problem:** Find the equation of the line passing through the points $(-6,5)$ and $(-3,-3)$.\n\n2. **Formula used:** The slope $m$ of a line through points $(x_1,y_1)

1. The problem asks: "17/25 of what number equals 9?" We need to find the unknown number. 2. Let the unknown number be $x$. The equation is:

1. The problem states that lemons cost $n$ cents each and the total cost of a box of lemons is $L$ cents. 2. We want to find a formula for the cost of a box of lemons when each lem

1. **State the problem:** Simplify the expression $$\left(\frac{25}{4}\right)^{-\frac{3}{2}}$$ and express the answer with positive exponents. 2. **Recall the rule for negative exp

1. **State the problem:** Simplify the expression $$(2x^3 y^4)^5$$ and express the answer with positive exponents. 2. **Recall the power of a product rule:** When raising a product

1. The problem is to simplify the expression $100^{-\frac{3}{2}}$ and express the answer with positive exponents. 2. Recall the rule for negative exponents: $a^{-n} = \frac{1}{a^n}

1. Problem: Razumeti i primeniti Vietove formule za rastavljanje kvadratnog trinoma na linearne činioce. 2. Vietove formule se koriste za kvadratne jednačine oblika $$ax^2 + bx + c

1. The problem is to simplify the expression $\left(\frac{3}{4}\right)^{-2}$ and express the answer with positive exponents. 2. Recall the rule for negative exponents: $a^{-n} = \f

1. The problem asks to determine the domain of the given graph. 2. The domain of a graph is the set of all possible $x$-values for which the function is defined.

1. The problem is to simplify the expression $(-7)^0$ and express the answer with positive exponents. 2. The rule for any nonzero number raised to the power of zero is:

1. **State the problem:** Simplify the expression $$(-8)^{-\frac{1}{3}}$$ and express the answer with positive exponents. 2. **Recall the rule for negative exponents:** For any non

1. **Stating the problem:** We are given points $(-2,-1)$, $(-1,0)$, $(0,-1)$, $(1,-1)$, and $(2,3)$ and need to analyze or find a function that fits these points. 2. **Approach:**

1. **State the problem:** Simplify the expression $$(-8)^{-\frac{1}{3}}$$. 2. **Recall the rule for negative exponents:** For any nonzero number $a$ and rational exponent $m$, $$a^

1. **State the problem:** We need to graph the function $h(x) = (f+g)(x)$, which means for each $x$, $h(x) = f(x) + g(x)$. We are given piecewise linear graphs for $f$ and $g$ with

1. **State the problem:** Solve the equation $$2\left(\frac{1}{2}q + 1\right) = -3(2q - 1) + 8q + 4$$ for $q$. 2. **Distribute the constants inside the parentheses:**

1. **Énoncé du problème** : Écrire le système d'inéquations associé aux polygones de contraintes A, B, et C. 2. **Polygone A** :

1. **State the problem:** Find the slope of the line passing through the points $(-3, -2)$ and $(1, 3)$.\n\n2. **Formula for slope:** The slope $m$ of a line passing through points