🧮 algebra

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} -

1. **State the problem:** Calculate the value of $-1.75 - \frac{22}{20}$.\n\n2. **Convert decimals and fractions:** Note that $-1.75$ is a decimal and $\frac{22}{20}$ is a fraction

1. **State the problem:** We have two drones at points C and D on the ground. The drone at C follows the path $f(x) = -x^2 + 2x + q$, and the drone at D follows $g(x) = mx + 5$. We

1. **State the problem:** We need to find scalars $a$, $b$, and $c$ such that every point $(x,y)$ on the line $ax + by = c$ is equidistant from the points $(2,-1)$ and $(3,2)$. 2.

1. Problem: Simplify the expression $$\frac{2}{5} + \frac{1}{3} + \frac{1}{12} - \frac{2}{180}$$. 2. Find the least common denominator (LCD) of 5, 3, 12, and 180.

1. **State the problem:** Calculate the value of $-1.2 - \frac{29}{20}$.\n\n2. **Convert decimals and fractions to a common form:** Convert $-1.2$ to a fraction. Since $1.2 = \frac

1. The problem is to find the domain of the function $$f(x) = \frac{x - 1}{x^2 + 1}$$. 2. The domain of a function is the set of all real numbers for which the function is defined.

1. The problem is to verify the identity for the square of a sum, which states that $$(a+b)^2 = a^2 + 2ab + b^2.$$\n\n2. Start with the left-hand side (LHS): $$(a+b)^2.$$\n\n3. Exp

1. The problem is to understand the concept of an identity in algebra. 2. An identity is an equation that is true for all values of the variable involved.

1. The property used in expansion is the **distributive property** of multiplication over addition. 2. This property states that for any numbers $a$, $b$, and $c$, we have $$a(b+c)

1. נניח שהאיבר הראשון בסדרה החשבונית הוא $a_1 = a$ והפרש הסדרה הוא $d$. 2. מספר האיברים בסדרה הוא $3n$.

1. The problem is to understand the transformation from the base function $y=x^2$ to the transformed function $y=(x-2)^2$. 2. The base function $y=x^2$ is a parabola with its verte

1. Stating the problem: Solve the equation $$3(x + 1)^2 + 2(x - 3)^2 = (5x - 2)(x - 1) + 30$$ for $x$. 2. Expand each term: