🧮 algebra

1. **State the problem:** We have two rectangles, one inside the other. The larger rectangle has side lengths $2x + 1$ and $4x + 3$. The smaller rectangle inside has side lengths $

1. Masalah yang diberikan adalah menghitung jumlah dari rumus $P_n = P_0 (1+r)^n - o$. 2. Rumus ini biasanya digunakan untuk menghitung nilai suatu jumlah setelah $n$ periode denga

1. The problem shows pairs of numbers stacked vertically in rectangles: (1,2), (3,2), (7,4), (19,24), and asks for the next pair. 2. We need to find a pattern or rule that relates

1. Stating the problem: Solve the linear equation $3x - 4 \frac{1}{2} = -19 \frac{1}{2}$. 2. Convert mixed numbers to improper fractions or decimals for easier calculation:

1. **State the problem:** Solve the linear equation $-5m - 10 = 0$ for $m$. 2. **Formula and rules:** To solve for $m$, isolate the variable by performing inverse operations. Remem

1. **State the problem:** Simplify the expression $4(-23x + 8b)$. 2. **Formula used:** Use the distributive property $a(b + c) = ab + ac$ to multiply each term inside the parenthes

1. **State the problem:** We are given the expression $-5m - 10$ and asked to find the value of $m$. However, the problem as stated is incomplete because it does not provide an equ

1. **State the problem:** Simplify the expression $4(-x-16)$. 2. **Formula and rules:** Use the distributive property which states $a(b+c) = ab + ac$.

1. **State the problem:** Simplify the expression $3(-9x - 6y)$. 2. **Formula and rules:** Use the distributive property which states $a(b + c) = ab + ac$. Here, $a=3$, $b=-9x$, an

1. **State the problem:** Solve the equation $3x + 10 = 2x - 5m$ for $x$. 2. **Isolate the variable $x$:** To solve for $x$, we want to get all terms containing $x$ on one side and

1. **Problem:** One root of the quadratic equation $x^2 - (k^2 - 4k + 4)x + 9 = 0$ is the additive inverse of the other. Find $k$. 2. **Formula and rules:** For a quadratic equatio

1. **State the problem:** Simplify the expression $11(-5-3m)$. 2. **Formula and rules:** Use the distributive property: $a(b+c) = ab + ac$.

1. **State the problem:** Simplify the expression $5(y+4)$. 2. **Formula used:** Use the distributive property of multiplication over addition:

1. **State the problem:** Simplify the expression $3(x-9)$. 2. **Formula used:** Use the distributive property $a(b+c) = ab + ac$.

1. The problem states that we divided a number and received 378,000 as the result. 2. To find the original number, we need to know what number we divided by. Since the divisor is n

1. The problem is to simplify the expression $6a + a^{\frac{1}{2}} b^{\frac{1}{3}} - 15 b^{\frac{2}{3}}$. 2. This expression contains terms with variables $a$ and $b$ raised to fra

1. The problem is to find the unit prices for each item in the table by dividing the total price by the quantity, then sum all unit prices to verify the total price $379,673.01$. 2

1. **Problem statement:** Simplify the expression $(-5q^2 + 3p - 2q + p^2) + (4p + q + pq)$. 2. **Formula and rules:** To simplify, combine like terms. Like terms have the same var

1. **State the problem:** Simplify the expression $ (6 - 7x + x^2) + (6x - 6x^2 + 10) $. 2. **Write down the expression:**

1. **Problem 1a: Analyze the equation $|y| = x$.** - The equation states that the absolute value of $y$ equals $x$.

1. **State the problem:** Simplify the expression $$(-7p - 3) + (p^2 + 5)$$. 2. **Recall the rules:** When adding algebraic expressions, combine like terms. Like terms have the sam