🧮 algebra

1. Let's start by understanding the number $e = 2.7182818$. 2. The number $e$ is the base of the natural logarithm, which means the logarithm with base $e$ is called the natural lo

1. **Stating the problem:** We need to solve the equation $$\frac{x^2}{3x + 5} = \frac{1}{2}$$ for the possible values of $x$. 2. **Cross-multiply to eliminate the fractions:**

1. The problem is to simplify or understand the expression $$\frac{-8}{x-2}$$. 2. This expression represents a rational function where the numerator is a constant $-8$ and the deno

1. **State the problem:** We have a binary operation defined as $a*b = \frac{a}{b} + \frac{b}{a}$ for real numbers $a$ and $b$. 2. We are given the equation $((\sqrt{x})+1)*((\sqrt

1. The problem involves identifying and continuing patterns in sequences of shapes and numbers. 2. For the numeric sequences:

1. **State the problem:** We have a binary operation $*$ defined on real numbers by the rule $a * b = \frac{a}{b} + \frac{b}{a}$. We want to understand this operation and possibly

1. The problem asks us to find a rational number between $5.01$ and $5.04$. 2. A rational number is any number that can be expressed as a fraction $\frac{p}{q}$ where $p$ and $q$ a

1. The problem asks which numbers are greater than $-0.33$. We will compare each choice to $-0.33$. 2. Choice A: $-0.3$. Since $-0.3$ is greater than $-0.33$ (because $-0.3$ is clo

1. The problem asks which numbers are greater than $$-\frac{185}{100}$$. 2. First, convert $$-\frac{185}{100}$$ to decimal: $$-\frac{185}{100} = -1.85$$.

1. The problem is to calculate $8 \times 6 \frac{1}{4}$ using the distributive law. 2. First, convert the mixed number $6 \frac{1}{4}$ to an improper fraction: $$6 \frac{1}{4} = \f

1. The problem asks to match the given numbers with the correct labels a, b, and c on the number line. 2. The points on the number line are:

1. **State the problem:** Factorise fully the expressions $2(x + 5)$ and $50 - 2y^2$. 2. **Factorise $2(x + 5)$:**

1. **State the problem:** Given the equation $$4^m = p(2^{2m-1}) + p$$, show that for $$p \neq 2$$, it can be rewritten as $$m = \frac{1}{2} \log_2 \left( \frac{2p}{2 - p} \right)$

1. Diketahui barisan geometri dengan suku pertama $u_1 = 6$ dan suku ke-5 $u_5 = 96$. 2. Rumus suku ke-$n$ barisan geometri adalah $$u_n = u_1 \times r^{n-1}$$ dengan $r$ adalah ra

1. The problem asks us to match the labels a, b, c with the correct numbers on the number line and the given decimal or fraction values. 2. The number line points are:

1. The problem is to compare and understand the values of the three numbers: the mixed number $1 \frac{1}{3}$, the decimal $1.4$, and the fraction $\frac{127}{100}$.\n\n2. Convert

1. The problem is to simplify the expression $$\frac{x - 1}{5 (x - 1)^2}$$. 2. First, factor the denominator: $$5 (x - 1)^2 = 5 (x - 1)(x - 1)$$.

1. **State the problem:** Calculate the value of $0.2 - \frac{4}{10} - 1.625$. 2. **Convert all terms to decimals:**

1. Stating the problem: We need to find the number that fits in the blank in the equation $$56 + 40 = \square \times (7 + 5)$$. 2. Simplify the left side: $$56 + 40 = 96$$.

1. The problem is to simplify the expression $$\frac{1}{1} - \frac{2}{15} - \frac{1}{36} - \frac{2}{60}$$. 2. First, find the least common denominator (LCD) of the fractions 1, 15,

1. The problem is to calculate $100\% - \frac{9}{10}$.\n2. Convert $100\%$ to a decimal: $100\% = 1$.\n3. Now subtract $\frac{9}{10}$ from $1$: $$1 - \frac{9}{10} = \frac{10}{10} -