🧮 algebra

1. **State the problem:** Write the expression $$\frac{4 - \sqrt{3}}{\sqrt{3}}$$ in the form $$\frac{a\sqrt{3} + b}{c}$$ where $a$, $b$, and $c$ are integers. 2. **Start with the g

1. **State the problem:** Write $\frac{3\sqrt{3}}{4} - \frac{2}{\sqrt{3}}$ in the form $a\sqrt{3} + \frac{b}{c}$ where $a$, $b$, and $c$ are integers. 2. **Rewrite the expression:*

1. Problem: Factorise each expression. (a) $x^3 + 2x^2$

1. The first problem is to simplify the expression $\frac{3\sqrt{3}}{2} - 2$.\n\n2. The second problem is to write $4 - \sqrt{3} - \sqrt{5}$ in the form $a\sqrt{3} + b\sqrt{5} + c$

1. The problem asks to fill in the missing terms for sequences B and C based on the given terms and nth term formulas. 2. For Sequence A, the nth term is given as $21 - n$. The ter

1. **State the problem:** We want to write the expression $$\frac{2\sqrt{3}}{4 - \sqrt{5}} - 2$$ in the form $$a\sqrt{3} + b$$ where $a$, $b$, and $c$ are integers. 2. **Rationaliz

1. **State the problem:** Write $\frac{4 - \sqrt{3}}{\sqrt{3}}$ in the form $\frac{a\sqrt{3} + b}{c}$ where $a$, $b$, and $c$ are integers. 2. **Start with the given expression:**

1. **State the problem:** We know that one recycled glass bottle saves enough energy to power a computer for 25 minutes. 2. We want to find how many recycled glass bottles are need

1. The problem involves understanding the domain of the function $f(x) = \sqrt{4 - x}$. 2. The square root function requires the radicand (expression inside the root) to be non-neg

1. Stating the problem: Simplify the expression $$\frac{\frac{X^2}{16000}}{X}$$. 2. Rewrite the expression as a single fraction: $$\frac{X^2}{16000} \div X = \frac{X^2}{16000} \tim

1. **Work out the following, giving answers as mixed numbers in simplest form:** (1) $\frac{1}{2} + \frac{3}{4}$

1. The problem is to calculate the expression $\frac{15}{9} - 1 \frac{5}{18}$.\n\n2. Convert the mixed number $1 \frac{5}{18}$ to an improper fraction.\n\n$$1 \frac{5}{18} = \frac{

1. **State the problem:** Solve the quadratic equation $$x^2 + 2x = 28$$. 2. **Rewrite the equation:** Move all terms to one side to set the equation to zero:

1. Stating the problem: A notary receives 3000 for each property deed and 2000 for each incorporation minute. He made a total of 22 operations (deeds and minutes) with a total inco

1. The problem is to solve the quadratic equation $$2x^2 - 4x - 6 = 0$$. 2. First, identify the coefficients: $$a = 2$$, $$b = -4$$, and $$c = -6$$.

1. The problem is to solve the quadratic equation $$x^2 - 5x + 6 = 0$$. 2. We start by factoring the quadratic expression. We look for two numbers that multiply to 6 and add to -5.

1. The problem is to solve the equation $$2x + 3 = 7$$ for $x$. 2. Start by isolating the variable term on one side. Subtract 3 from both sides:

1. The problem asks: What percent is 60 of 80? 2. To find what percent one number is of another, use the formula:

1. The problem is to convert the fraction $\frac{5}{40}$ into a decimal. 2. To convert a fraction to a decimal, divide the numerator by the denominator.

1. **Problem:** Which of the following numbers is not a real number? Options: (a) $\frac{22}{7}$, (b) $\sqrt{25}$, (c) $\sqrt{-25}$, (d) 25

1. **Write down the order of each matrix:** 1.a) Matrix \( A = \begin{pmatrix} -3 & 4 & 2 \\ 1 & 5 & -1 \end{pmatrix} \) has 2 rows and 3 columns.