🧮 algebra

1. The problem is to understand the inequality $a - b > 0$. 2. Start by isolating $a$ on one side by adding $b$ to both sides:

1. Die probleem: Vereenvoudig die breuk $\frac{25}{50}$ na sy eenvoudigste vorm. 2. Vind die grootste gemene deler (GGD) van 25 en 50. Die delers van 25 is 1, 5, 25 en die delers v

1. The problem is to add the fractions $\frac{1}{10}$ and $\frac{5}{10}$. 2. Since both fractions have the same denominator, we can directly add the numerators: $1 + 5 = 6$.

1. مسئله: تابع‌ها به صورت زیر داده شده‌اند:

1. The problem asks to find \frac{1}{6} van 24, which means \frac{1}{6} of 24. 2. To calculate \frac{1}{6} of 24, multiply 24 by \frac{1}{6}:

1. **State the problem:** There are 3 more girls than boys in the school and the total number of students (boys + girls) is 515. We need to find the number of boys and girls using

1. **Task 1: Definitions and Examples of Matrices** - Row matrix: A matrix with only one row. Example: $$\begin{bmatrix}1 & 2 & 3\end{bmatrix}$$

1. Problem statement: Prove that the normal chord at the point on a parabola where the ordinate equals the abscissa subtends a right angle at the focus. 2. Let's consider the stand

1. **State the problem:** Simplify the expression $$\sqrt{(x^3 - x^2)}$$. 2. **Factor the expression inside the square root:** Notice both terms have a common factor of $$x^2$$.

1. **Problem 01**: Given the function $f(x) = 3x^2 - x + 3$, find the following values: (a) $f(2)$

1. Simplify \(\frac{27}{27x + 18}\):\nFactor denominator: \(27x + 18 = 9(3x + 2)\). Simplified: \(\frac{27}{9(3x + 2)} = \frac{3}{3x + 2}\).\n\n2. Simplify \(\frac{45}{10a - 10}\):

1. Problem statement: Given graphs of functions $f$ and $g$, answer parts a through e based on the graph descriptions. 2. (a) Find $f(-4)$ and $g(3)$:

1. **Problem statement:** Given the function $f(x) = (1 + 2x)^{32}$, find the first 4 terms in the power series expansion and state when the expansion is valid. 2. **Use the binomi

1. The problem asks us to find the smallest number by which 243 must be multiplied to become a perfect cube. 2. First, factorize 243 into its prime factors. Since 243 is $3^5$, we

1. The problem is to simplify the fraction $\frac{19265}{7475}$ to its simplest form and find out how much was "taken out" or factored out from the numerator and denominator. 2. Fi

1. State the problem: Solve the equation $$\frac{2x+7}{3} - 4 = \frac{x-7}{4}$$ for $x$. 2. Eliminate the denominators by multiplying both sides by the least common multiple of 3 a

1. Masalahnya adalah menyederhanakan ekspresi $$\binom{81x^{\frac{3}{4}}yz^{\frac{3}{2}}}{27x^{\frac{1}{2}}y^{\frac{1}{4}}z^{\frac{1}{2}}}$$ yang melibatkan pembagian dua suku deng

1. Masalah yang diberikan adalah menyederhanakan ekspresi $$5\sqrt{243} + 2\sqrt{27} - \sqrt{75} - 3\sqrt{48}$$ dengan cara memfaktorkan dan menyederhanakan akar kuadrat yang ada.

1. Kita diberikan ekspresi $5\sqrt{243} + 2\sqrt{27} - \sqrt{75} - 3\sqrt{48}$. Tujuan kita adalah menyederhanakan bentuk ini. 2. Faktorkan dan sederhanakan masing-masing akar kuad

1. The problem asks us to find the cube root of 512, which means finding a number $x$ such that $x^3 = 512$. 2. We start by finding prime factors of 512. Since $512 = 2^9$, we have

1. Simplify (a) $\frac{9}{11} + \frac{10}{22}$ Step 1: Find common denominator.