🧮 algebra

1. **State the problem:** Solve the cubic equation $$n^3 - 3n - 2 = 0$$ to find the exact roots. 2. **Recall the formula and approach:** For cubic equations of the form $$n^3 + an^

1. **State the problem:** Calculate the sum of the fractions $\frac{2}{-9} + \frac{-8}{9}$ and $\frac{9}{32} - \frac{-5}{-8}$.\n\n2. **Calculate the first expression:** $\frac{2}{-

1. **Problem:** Calculate $-\frac{5}{16} + \frac{7}{4}$. 2. **Formula:** To add fractions, use the formula $$\frac{a}{b} + \frac{c}{d} = \frac{ad + bc}{bd}$$ where $a,b,c,d$ are in

1. The problem involves understanding the expression with a minus sign next to the 9 and the number 2, resulting in -8, not 8. 2. Let's clarify the expression: if you have $9 - 2$,

1. Calculate $-\frac{2}{7} + \frac{9}{7}$. Since denominators are the same, add numerators:

1. Problema: Multiplicar monomios por monomios. 2. Regla: Para multiplicar monomios, multiplicamos los coeficientes y sumamos los exponentes de las variables iguales.

1. **Simplify** $\frac{5}{63} = \frac{5 \times 8}{9 \times 7} = \frac{5}{7}$ - The original fraction is $\frac{5}{63}$.

1. Énoncé du problème : Simplifier les fractions suivantes au maximum : $$\frac{21}{14}, \frac{36}{42}, \frac{24}{-22}, \frac{-15}{-18}, \frac{-25}{55}, \frac{25}{200}$$

1. **State the problem:** Simplify the expression $$\frac{10(p^3 q^2 r^0)^{-3}}{(8p^{-3} q^5 r^3)^{-2}}$$. 2. **Recall the rules:**

1. **State the problem:** We need to graph the inequality $$5x + 4y > -8$$ on the Cartesian plane. 2. **Rewrite the inequality in slope-intercept form:** To graph, first express th

1. The problem asks to verify the correctness of the answers given for the polynomial function $h(x) = 2(x - 1)^3 (x + 4)^2$. 2. First, check the degree and leading coefficient.

1. **Problem:** Determine which ratios are correct based on the number of children riding bicycles and scooters at the park. 2. **Given:**

1. The problem asks to write equations for three lines given their descriptions and points. 2. For line l (red), it is a horizontal line crossing the y-axis at $y=3$. The equation

1. **Problem Statement:** We are given the equation for the total cost of notebooks and pencils: $$1.00 n + 0.25 p = 10.00$$

1. **Problem Statement:** Identify the slope and y-intercept of the line passing through points approximately $(-3,-2)$ and $(2,2)$. 2. **Formula for slope:** The slope $m$ of a li

1. **State the problem:** We have a system of equations with symbols representing unknown values: $$\text{pirate} + \text{pirate} + \text{squid} = 21$$

1. The problem asks to express 0.60 dollars as a fraction of a dollar. 2. Recall that 1 dollar equals 1 whole, so 0.60 dollars is 0.60 out of 1.

1. The problem asks to write $0.40 as a fraction of a dollar. 2. Recall that 1 dollar equals 1 whole, so $0.40 means 40 cents out of 100 cents.

1. **State the problem:** We need to find all x-intercepts of the function $$f(x) = x^5 - 36x^3$$. The x-intercepts occur where $$f(x) = 0$$. 2. **Set the function equal to zero:**

1. **State the problem:** We need to find all x-intercepts of the function $$f(x) = -2x^4 + 2x$$. The x-intercepts occur where $$f(x) = 0$$. 2. **Set the function equal to zero:**

1. **State the problem:** We need to find the average rate of change of the function $f(x)$ on the interval $-3 \leq x \leq 3$. 2. **Recall the formula:** The average rate of chang