🧮 algebra

1. The problem is to simplify or solve the expression $16x^3 - 2x^6$ using indices (exponents). 2. The expression is a subtraction of two terms with powers of $x$: $16x^3$ and $2x^

1. **State the problem:** Multiply $-68$ by $-92$. 2. **Recall the multiplication rule for signs:**

1. **State the problem:** We need to divide the expression $x + p - 222222222222999993002939e0848475556$ by 51. 2. **Understand the expression:** The expression contains variables

1. **State the problem:** Complete the expression given values $x=7$, $p=3$, $q=9$, and $r=2$ for the expression $x - 9x + 4x \times (pqr)$. 2. **Write the expression:** The expres

1. **State the problem:** Solve the equation $x + x = y$ for $x$. 2. **Understand the equation:** The equation $x + x = y$ means adding $x$ to itself equals $y$.

1. **State the problem:** Kristian spends 45% of his 72 dollars on a computer game. We need to find the price of the game. 2. **Formula used:** To find the part of a total amount c

1. Masalah yang diberikan adalah mencari bentuk baku dari penjumlahan angka 14 + 2,1 + 0,763 + 0,041. 2. Bentuk baku adalah cara menulis angka dalam bentuk $a \times 10^n$ di mana

1. **Stating the problem:** Kristian and Stephanie share money in the ratio 3:2. Kristian receives 72 dollars. We need to find how much Stephanie receives. 2. **Understanding the r

1. **Énoncé du problème :** Soit la suite $(u_n)_n$ définie par $u_0 = \frac{5}{2}$ et $u_{n+1} = \frac{u_n - 6}{u_n - 4}$ pour tout $n \in \mathbb{N}$.

1. **State the problem:** Solve the linear equation $$6x + 9y - 12 = 0$$ for $y$ in terms of $x$. 2. **Rewrite the equation:** The goal is to isolate $y$. Start by moving all terms

1. **State the problem:** Solve the linear equation $$6x + 9y - 12 = 0$$ for $y$ in terms of $x$. 2. **Rewrite the equation:** The goal is to isolate $y$. Start by moving all terms

1. **Problem Statement:** Calculate the percentage increase when a quantity changes from 120 to 150. 2. **Formula:** Percentage Increase = $$\frac{\text{New Value} - \text{Original

1. **Problem Statement:** Find the value of the series $$100 - 99 + 98 - 97 + 96 - 95 + \cdots + 2 - 1$$. 2. **Understanding the series:** The series alternates between subtracting

1. **Problem Statement:** We are given the function $f(x) = 2x - 3 \sin(x)$ and asked to analyze it. 2. **Formula and Explanation:** The function combines a linear term $2x$ and a

1. **Problem:** Solve the recurrence relation $$S(n) - 2S(n - 1) + S(n - 2) = 0$$ with initial conditions $$S(0) = 9$$ and $$S(1) = 10$$. 2. **Formula and approach:** This is a lin

1. **State the problem:** Find the value of $x$ such that $$\frac{x - 2}{x - 3} + \frac{x + 3}{x + 2} = 2.$$\n\n2. **Formula and rules:** To solve equations involving rational expr

1. **State the problem:** We have a line segment AB with points C and D between A and B. Car X travels \(\frac{3}{4}\) of AB from A to C, and Car Y travels \(\frac{1}{8}\) of BA fr

1. **State the problem:** Arrange the numbers 17%, \(\frac{3}{20}\), 0.14, and \(\frac{5}{36}\) in ascending order. 2. **Convert all numbers to decimals for easy comparison:**

1. The problem is to find the value of $x$ in the equation $$\frac{2x+3}{5} = 7.$$\n\n2. The formula used here is to solve linear equations by isolating the variable $x$.\n\n3. Fir

1. The problem asks for the exponential form of the product $108 \times 192$. 2. To express a number in exponential form, we first find its prime factorization.

1. The problem is to express the number $\frac{5}{2} \times 3.54$ as a product of prime factors with positive exponents. 2. First, calculate the product: