🧮 algebra

1. **State the problem:** Solve the quadratic equation $x^2 + 12x - 8 = 0$ using the quadratic formula. 2. **Quadratic formula:** For any quadratic equation $ax^2 + bx + c = 0$, th

1. The problem asks to find the position of $\sqrt{89}$ on the number line. 2. We know that $\sqrt{89}$ is the positive number which when squared gives 89.

1. The problem asks to find which point on the number line corresponds to $\sqrt{89}$. 2. Recall that $\sqrt{89}$ is the positive number which when squared gives 89.

1. The problem is to solve for $x$ in the equation $x + 5 = 12$. 2. The formula used here is to isolate $x$ by subtracting 5 from both sides of the equation.

1. Задача: Реши нееднаквоста $$x^2 + x - 12 < 0$$. 2. Формула и правила: За квадратична нееднаквост од обликот $$ax^2 + bx + c < 0$$, прво ја наоѓаме дискриминантата $$\Delta = b^2

1. **Problem 1: Add the fractions $\frac{3}{2}$ and $\frac{5}{6}$.** 2. To add fractions, they must have a common denominator.

1. **Problem Statement:** Transform the equation $-2x + 5y = 10$ into four different forms: (i) Two points form, (ii) Two intercepts form, (iii) Symmetric form, and (iv) Normal for

1. **State the problem:** We are given a polynomial and have found one rational zero using synthetic division. Now, we need to find the quadratic factor from the division and solve

1. **State the problem:** A train travels a track measured as 270 km (nearest 10 km assumed initially) in 110 minutes (nearest 5 minutes). We want to check if the average speed cou

1. **State the problem:** A man travelled along a track in 110 minutes, measured to the nearest 5 minutes. The track length is given as 270 km, with half the track assumed to be me

1. The problem is to find the value of $x$ in the equation $\text{la } 2$.\n\n2. It seems there might be a typo or missing information in the problem statement. Assuming you meant

1. The problem is to find the shortcut or simplified method to solve a given algebraic expression or equation. 2. Generally, shortcuts involve recognizing patterns such as differen

1. **State the problem:** Calculate $\frac{2}{5} - \frac{3}{10}$. 2. **Find a common denominator:** The denominators are 5 and 10. The least common denominator (LCD) is 10.

1. **State the problem:** Add the fractions $\frac{1}{8}$ and $\frac{1}{16}$. 2. **Formula and rules:** To add fractions, they must have a common denominator. The sum is given by $

1. **State the problem:** Simplify the expression $$\frac{1}{1 - 3y} + \frac{21y - 9}{1 - 9y^2}$$. 2. **Identify the formula and rules:** To add these fractions, we need a common d

1. **State the problem:** Simplify the expression $$\frac{4r}{5r^2} - \frac{2}{3r}$$. 2. **Rewrite each term:**

1. **Stating the problem:** We start with the base graph $y = x^2$ and need to find the equations of graphs A, B, C, and D by considering transformations of this base graph. 2. **R

1. **Problem:** Solve the system of linear equations using the substitution method and check the answer. ---

1. **State the problem:** Simplify the expression $$\frac{20x - 30}{12x - 42} - \frac{4x + 26}{12x - 42}$$ where both fractions have the same denominator. 2. **Formula and rule:**

1. **State the problem:** Simplify the expression $$\frac{6p^2 - 15p}{25 - 4p^2}$$. 2. **Factor numerator and denominator:**

1. **State the problem:** Simplify the expression and solve the equation given by $$k - 8 = 8$$