🧮 algebra

1. **State the problem:** We have a rational function which is a quotient of linear functions. It has a vertical asymptote at $x=-4$, a horizontal asymptote at $y=3$, and an $x$-in

1. The problem is to solve the equation $2x + 3 = 7$ for $x$. 2. The formula used here is to isolate $x$ by performing inverse operations. We subtract 3 from both sides to undo the

1. Problem 2.98: Klient banku spłacił pożyczkę w wysokości 13923 w czterech ratach, z których każda następna była o 10% większa od poprzedniej. Oblicz kwotę pierwszej i czwartej ra

1. The problem asks if the ratios 6 staff members to 10 campers and 3 staff members to 5 campers are equivalent. 2. To check if two ratios are equivalent, we can write them as frac

1. **State the problem:** We need to determine if the ratios 10 large bookmarks to 4 small bookmarks and 15 large bookmarks to 6 small bookmarks are equivalent. 2. **Formula and ru

1. **Problem Statement:** Given the function $f(x) = -x^2 - 3x + 28$, we need to find: a) The $x$ and $y$ intercepts.

1. **Problem Statement:** Given the function $f(x) = -x^2 - 3x + 28$, find the X and Y intercepts, compute the vertex coordinates and its nature, plot the function, and draw the ax

1. **State the problem:** We need to divide the polynomial $6x^3 - 5x^2 - 2x + 1$ by a divisor using long division. Since the divisor is not specified, we assume the divisor is $x

1. The problem asks for the rate of change in boxes of cookies sold between Thursday and Friday. 2. The rate of change formula is:

1. **State the problem:** We need to find the rate of change in the number of sandwiches sold between Thursday and Friday. 2. **Formula:** The rate of change between two points is

1. **State the problem:** Solve the system of equations: $$3x - 8y = 24$$

1. **State the problem:** Solve the linear system by graphing and checking the solution for the first system: $$y = -x + 3$$

1. **Problem Statement:** Given the function $f(x) = -x^2 - 3x + 28$, find the x- and y-intercepts, the vertex coordinates and its nature, plot the function, and find the axis of s

1. **State the problem:** Solve the linear equation $-13 - 4x = x + 7$ for $x$. 2. **Write down the equation:**

1. **State the problem:** Solve the equation $-10 - 7x = -3x - 2$ for $x$. 2. **Write down the equation:**

1. **State the problem:** We analyze a parabola with vertex at approximately (0, -9), opening upwards, crossing the y-axis at (0, -9), and intersecting the x-axis near -3 and 3. 2.

1. **State the problem:** Solve the equation $x - 11 = 16 + 4x$ for $x$. 2. **Write down the equation:**

1. **State the problem:** We analyze a parabola that opens downward, symmetric about the vertical line $x=2$, with x-intercepts near 0 and 4, vertex at $(2,9)$, and y-intercept nea

1. **State the problem:** Solve the equation $5 - 6x = 17 - 8x$ for $x$. 2. **Write down the equation:**

1. **Problem Statement:** We are given a parabola that opens upward with vertex near $(-1, -9)$ and need to find: (a) Whether it opens upward or downward.

1. **State the problem:** Factor the quadratic expression $$15x^2 + 14x + 3$$ by grouping using the ac-method. 2. **Formula and rules:** The ac-method involves multiplying the coef