🧮 algebra

1. **State the problem:** Simplify the expression $$\frac{x^4 - 9x^2}{x^2 - 1 + 5}$$. 2. **Rewrite the denominator:** Combine like terms in the denominator:

1. **State the problem:** Determine the domain on which the function represented by a downward-opening parabola with vertex at approximately $(-1,7)$ is increasing. 2. **Recall the

1. **State the problem:** We need to determine the domain on which the given quadratic function is decreasing. 2. **Identify the function type:** The graph is a downward-opening pa

1. **State the problem:** Divide the fraction $\frac{3}{4}$ by the mixed number $3 \frac{1}{3}$. Write the answer as a fraction or mixed number in simplest form. 2. **Convert the m

1. **State the problem:** Solve the system of equations: $$\begin{cases} 2x - 4y = -8 \\ -4x + y = -12 \end{cases}$$

1. **State the problem:** Solve the system of equations using elimination: $$\begin{cases} 3x + 2y = 8 \\ -3x + 2y = 8 \end{cases}$$

1. **Problem:** Check if the function $f(x) = \frac{x - 3}{x + 3}$ matches the description: "Vertical asymptote at $x = 3$, horizontal asymptote at $y = 1$, $x$-intercept of $x = -

1. **Problema:** Resolver la ecuación $2x - 34 = -20$. 2. **Fórmula y reglas:** Para resolver ecuaciones lineales, se busca aislar la variable $x$ en un lado de la ecuación. Esto s

1. **Problema:** Resuelve la ecuación $2x - 34 = -20$. 2. **Fórmula y reglas:** Para resolver ecuaciones lineales, el objetivo es aislar la variable $x$ en un lado de la ecuación.

1. **State the problem:** We need to graph the piecewise function $$f(x) = \begin{cases} -3x - 15 & \text{if } x < -5 \\ 3x + 15 & \text{if } x \geq -5 \end{cases}$$

1. **State the problem:** Find the ordered pair $(x,y)$ that satisfies both equations: $$x = -5y + 27$$

1. The scatterplot shows a **positive** and **linear** relationship. 2. To find how many pencils Mrs. Davis will have after 35 days, we use the graph data points to find the rate o

1. **State the problem:** Solve the equation $$\frac{2}{n^2 - n - 20} = \frac{1}{n^2 - n - 20} + \frac{1}{n + 4}$$ and find the solution set. 2. **Identify the domain restrictions:

1. **State the problem:** Solve the linear equation $5x - 80 = 0$ for $x$. 2. **Formula and rules:** To solve for $x$, isolate $x$ by performing inverse operations. The goal is to

1. **Simplify the expression** \(\frac{x-1}{x+3} - \frac{2(x-1)}{x+3}\). Since the denominators are the same, subtract the numerators:

1. Find four consecutive even integers such that 4 times the sum of the first and fourth is 8 greater than 12 times the third. Let the four consecutive even integers be $x$, $x+2$,

1. **Problem:** Find four consecutive even integers such that 4 times the sum of the first and fourth is 8 greater than 12 times the third. 2. **Step 1: Define variables.** Let the

1. **Problem:** Find four consecutive even integers such that 4 times the sum of the first and fourth is 8 greater than 12 times the third. 2. **Step 1: Define variables.** Let the

1. **State the problem:** Simplify or factor the quadratic expression $4y^2 - 3y - 27$. 2. **Formula and rules:** To factor a quadratic expression $ay^2 + by + c$, we look for two

1. **State the problem:** Calculate the value of the expression $$\frac{735 + \sqrt{987,654,321} - 293,847 \times 476}{1,829} + 37^4$$. 2. **Recall formulas and rules:**

1. Planteamos el problema: calcular los valores de $K_1$ y $K_2$ para el tiempo $40$ minutos. 2. Para resolverlo, necesitamos la fórmula o relación que vincule $K_1$, $K_2$ y el ti