🧮 algebra

1. **State the problem:** Find the equation of the line passing through the point $(5,8)$ with slope $\frac{5}{3}$. 2. **Formula used:** The point-slope form of a line is given by

1. **State the problem:** Find the equation of the line passing through the point $(-6,-4)$ with slope $\frac{3}{1}$. 2. **Formula used:** The point-slope form of a line is given b

1. **State the problem:** Find the equation of the line passing through the points $(-2, 8)$, $(-1, 2)$, $(0, -4)$, and $(1, -10)$ in slope-intercept form $y = mx + b$. 2. **Formul

1. **State the problem:** We need to find the equation of the line passing through the points $(0, 5)$ and $(5, 0)$ in slope-intercept form, which is $$y = mx + b$$ where $m$ is th

1. **State the problem:** Find the equation of the line passing through the points given, in slope-intercept form $y=mx+b$. 2. **Identify points:** We have points $(0,-2)$ and $(1,

1. **Stating the problem:** Calculate the factorial of $342$, denoted as $342!$. 2. **Formula and explanation:** The factorial of a positive integer $n$ is defined as the product o

1. **State the problem:** We are given two one-to-one functions:

1. **State the problem:** We are given two functions $g(x) = 4x^3$ and $h(x) = x^2$ and need to find the sum, product, and difference of these functions at specified inputs. 2. **S

1. **State the problem:** We are given two functions $r(x) = 2x^2$ and $s(x) = x + 3$. We need to find the sum $(s + r)(x)$, the difference $(s - r)(x)$, and the product $(s \cdot

1. **State the problem:** We are given two functions $r(x) = 2x^2$ and $s(x) = x + 3$. We need to find the sum $(s + r)(x)$, the difference $(s - r)(x)$, and the product $(s \cdot

1. **State the problem:** Simplify the given expressions involving $x$ and powers of $i$. 2. **Solve for $x$:**

1. **State the problem:** Solve the quadratic equation $$y^2 - 4y + 4 = 0$$ for $y$. 2. **Recall the formula:** For a quadratic equation $$ay^2 + by + c = 0$$, the roots are given

1. **State the problem:** We need to find the roots of the quadratic equation $$y^2 - 3y - 18 = 0$$. 2. **Recall the quadratic formula:** For an equation $$ay^2 + by + c = 0$$, the

1. **State the problem:** We need to find the roots of the quadratic equation $$w^2 - 8w + 16 = 0$$. 2. **Recall the quadratic formula:** For an equation $$aw^2 + bw + c = 0$$, the

1. **State the problem:** Calculate the value of the expression $$(20-5) \times 15 + 130$$. 2. **Apply the order of operations:** According to the rules, perform operations inside

1. **State the problem:** We need to find the least possible degree of a polynomial whose graph is a straight line crossing the y-axis at $-1$ and the x-axis at $2$. 2. **Understan

1. **State the problem:** We need to find all real solutions to the cubic equation $$x^3 - 2.1x^2 - 21.16x + 8.736 = 0$$ by graphing the function $$y = x^3 - 2.1x^2 - 21.16x + 8.73

1. **Postavka problema:** Treba odrediti koeficijente $a$, $b$ i $c$ kvadratne funkcije $f(x) = ax^2 + bx + c$ tako da funkcija prolazi kroz tačke $A(1, 2)$, $B(2, 10)$ i $C(-1, -8

1. The problem is to understand the Fibonacci sequence and find its terms. 2. The Fibonacci sequence is defined by the recurrence relation:

1. **State the problem:** Find the real values of $x$ and $y$ such that the complex fractions $\frac{2x - yi}{1 + 2i}$ and $\frac{3 - i}{1 - i}$ are conjugates.

1. **The problem is:** show how $-1$ creates $2$ in the expression $1-\frac{1}{x}$. 2. **Use the rule for this expression.**