🧮 algebra

1. We are asked to find the quadratic function $f(x) = ax^2 + bx + c$ that passes through the points $(3,0)$, $(-2,0)$, and $(1,7)$. 2. Since the points $(3,0)$ and $(-2,0)$ are ze

1. **State the problem:** We are given three points A(2,5), B(9,-2), and J(4,h) that lie on the same straight line. We need to find the value of $h$. 2. **Find the slope of the lin

1. **State the problem:** We have a linear function $f$ such that $f(0) = \frac{1}{2}$ and $f(-3) = -\frac{3}{2}$. We need to find the value of $f(3)$. 2. **Recall the form of a li

1. **State the problem:** Find the equation of the line perpendicular to the line given by $$2x - 3y = -1$$ and passing through the midpoint of segment $$\overline{AB}$$ where $$A(

1. The problem asks us to find which taxi company offers the cheapest total cost for traveling 500 Km. 2. Each taxi company charges a fixed amount plus an additional amount per 25

1. **State the problem:** We are given the equation of a line $$\frac{2}{x} - \frac{3}{y - 1} = 0$$ and need to find its slope. 2. **Rewrite the equation:** Move terms to isolate o

1. **Problem:** Analyze the function $f(x) = \frac{x}{x-1}$. - The function is a rational function with a vertical asymptote at $x=1$ because the denominator is zero there.

1. The problem asks for the slope of the line $m$ passing through points $(2a, a^2)$ and $(2b, b^2)$ where $a \neq b$. 2. Recall the formula for the slope $m$ of a line through two

1. **State the problem:** Find the equation of line $d$ that passes through the origin $O(0,0)$ and is perpendicular to line $k$ which passes through points $A(0,3)$ and $B(2,0)$.\

1. **State the problem:** Find the equation of line $d$ that passes through the origin $O(0,0)$ and is perpendicular to line $k$ which passes through points $A(0,3)$ and $B(2,0)$.\

1. The problem is to simplify the expression $\sqrt{12}$. 2. Start by factoring 12 into its prime factors: $12 = 4 \times 3$.

1. **State the problem:** We are given the equation of line L as $$2mx - 2y + 12 = 0$$ and need to find its slope (gradient). 2. **Rewrite the equation in slope-intercept form:** T

1. **State the problem:** We want to find a function $f(m)$ that gives the number of miles of paved roads in country Y $m$ years after 2017. 2. **Identify given information:**

1. The problem is to simplify the expression \(\sqrt{x}12\). 2. We interpret this as \(12 \times \sqrt{x}\).

1. **State the problem:** We have a linear function $f$ with values given in a table: $$\begin{array}{c|c}

1. **Masalah 1: Menentukan nilai a + b dari polinomial P(x) = x^4 + x^3 - 13x^2 + ax + b yang habis dibagi oleh (x - 2) dan (x + 3).** Karena P(x) habis dibagi oleh (x - 2), maka P

1. Factorize $p^2 - 8p + 16$. Step 1: Recognize this as a quadratic trinomial.

1. Diberikan vektor $\mathbf{a} = 3\mathbf{i} - 2\mathbf{j} + 4\mathbf{k}$ dan $\mathbf{b} = -\mathbf{i} + 5\mathbf{j} - 2\mathbf{k}$. Kita diminta menentukan vektor $\mathbf{c} =

1. **Find the two prime factors of 323.** To factor 323, we test divisibility by prime numbers.

1. The problem is to calculate the relative error for each pair of values $(x, y)$ given in the table. 2. Relative error is defined as:

1. The problem is to find the prime factors of 323. 2. Start by checking divisibility by small prime numbers.