🧮 algebra

1. **State the problem:** Find the system of linear equations for two lines intersecting at the point $(-2, -1)$. 2. **Identify points and slopes:**

1. **State the problem:** Find the equations of two parallel lines given points on each line. 2. **Formula and rules:** The equation of a line in slope-intercept form is $$y = mx +

1. Problemet: Vi har funktionen $f(x) = 3x^2 + 4x$ och en tangentlinje vid punkten där $x=2$. Tangentens ekvation är $y = kx - 12$. Vi ska bestämma lutningen $k$. 2. Formeln för lu

1. **State the problem:** Solve the system of equations: $$0 = 2x_2 - 2x_1 - 4$$

1. **State the problem:** Last year, there were $z$ zebra mussels in a river section. This year, there are $z^3$ zebra mussels, and this year the number is 729. Find $z$. 2. **Writ

1. **State the problem:** Solve the rational equation $$\frac{1}{5 - x^4} + \frac{1}{x^4 - 3} = 2$$. 2. **Rewrite the equation:** Notice that the denominators are $$5 - x^4$$ and $

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: