🧮 algebra

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.

1. **State the problem:** Apples cost $x$ cents each and oranges cost $(x + 2)$ cents each.

1. The problem asks for an expression representing the total amount of drink Sandra has in millilitres, given she buys $p$ cans and $q$ bottles. 2. Each can contains 330 ml, so $p$

1. **State the problem:** Dylan buys apples costing $x$ cents each and oranges costing $(x+2)$ cents each.

1. **State the problem:** Solve the cubic equation $$x^3 + 3x^2 + 2x - 210 = 0$$. 2. **Try to find rational roots using the Rational Root Theorem:** Possible roots are factors of 2

1. **State the problem:** We have four points A, B, C, and D representing integers on a number line. We need to arrange these integers in order using given clues. 2. **Identify the

1. Let's start by understanding what negative and positive integers are. 2. Negative integers are numbers less than zero, such as $-1, -2, -3, \ldots$.

1. প্রথম সেটের বীজগণিতীয় ভগ্নাংশগুলি হল: - $\frac{a}{a^2 - 6a + 5}$

1. প্রথম ভগ্নাংশের হারকে উপপাদকে বিশ্লেষণ কর। প্রথম ভগ্নাংশ: $\frac{5}{a^2 - 6a + 5}$

1. The problem is to simplify the expression $[3X] - 3$. 2. Here, $[3X]$ denotes the greatest integer function (floor function) applied to $3X$, which means it is the greatest inte