🧮 algebra

1. **Solve the system:** $$\begin{cases} 2x - 3y = 2 \\ 3x + 2y = 16 \end{cases}$$

1. **State the problem:** We are given a quadratic function modeling the height of a slide: $$f(x) = a(x - 5)^2$$ with initial height 2.5 m at $x=0$. We need to find the height of

1. **State the problem:** Solve the equation $ (x - 3)(x - 5) = 35 $ for $ x $.\n\n2. **Use the distributive property (FOIL) to expand the left side:**\n$$ (x - 3)(x - 5) = x^2 - 5

1. **State the problem:** We need to find which value of $x$ satisfies the equation $$(x - 3)(x - 5) = 35.$$\n\n2. **Use the formula:** The equation is a product of two binomials e

1. **State the problem:** Simplify the expression $$\left(\frac{2n^4}{3m^3n^7}\right)^2$$ and write the answer using only positive exponents. 2. **Recall the formula:** When raisin

1. **State the problem:** Simplify the expression $$\left(\frac{a^7 b^6}{a^2 b}\right)^4$$ and write the answer using only positive exponents. 2. **Apply the quotient rule for expo

1. **Planteamiento del problema:** Queremos encontrar las raíces de la función cuadrática $$y = -1(x+4)(x+3)$$ y verificar su forma expandida $$y = -x^2 - 7x - 12$$.

1. **State the problem:** Simplify the expression $\log(n^3)$. 2. **Recall the logarithm power rule:** For any positive number $a$ and real number $b$, $\log(a^b) = b \log(a)$.

1. **State the problem:** Find all x-intercepts of the function $$f(x) = \frac{x^2 - 16x + 64}{3x^2 - 24x}$$ and write them as coordinate points. 2. **Recall the formula and rules:

1. **State the problem:** Find all x-intercepts of the function $$f(x) = \frac{9x^2 - 64}{6x^2 + 16x}$$.\n\n2. **Recall the rule for x-intercepts:** The x-intercepts occur where th

1. **State the problem:** Find all x-intercepts of the function $$f(x) = \frac{5x^2 + 3x}{x^2 - 2x - 63}$$. The x-intercepts occur where the function equals zero, i.e., where the n

1. **State the problem:** Find all x-intercepts of the function $$f(x) = \frac{2x + 7}{2x^2 + 25x + 63}$$. The x-intercepts occur where the function equals zero, i.e., where the nu

1. **State the problem:** Find all x-intercepts of the function $$f(x) = \frac{5x^2 - 47x + 56}{2x + 8}$$. The x-intercepts occur where the function equals zero, i.e., where the nu

1. **Énoncé du problème** : Déterminer la fonction linéaire $g$ telle que $g(-3) = 4$.

1. **State the problem:** Find all x-intercepts of the function $$f(x) = \frac{x + 8}{5x + 8}$$ and write them as coordinate points. 2. **Recall the formula for x-intercepts:** The

1. **State the problem:** Find all x-intercepts of the function $$f(x) = \frac{x^2 + 8x}{x^2 + 4x - 21}$$. 2. **Recall the rule for x-intercepts:** The x-intercepts occur where the

1. **Énoncé du problème** : On considère la fonction $f$ définie par $f(x) = 4x - 7$.

1. **State the problem:** Simplify the expression $\log_2 \sqrt[4]{p^2 y^{12}}$. 2. **Recall the formula:** The logarithm of a root can be rewritten using the power rule: $\log_b (

1. The problem involves understanding the relationship between two variables: years since colonization (independent variable) and population (dependent variable). 2. In graphing re

1. **State the problem:** We need to find the correct graph representing the value of a car that starts at 8000 and depreciates by 25% each year.

1. The problem gives a table showing jump heights (meters) depending on ankle weights (kilograms). 2. The independent variable is the one that you control or choose values for. Her