🧮 algebra

1. State the problem: Calculate $0.02^3 \times 10^{-1}$.\n\n2. Calculate $0.02^3$: Since $0.02 = \frac{2}{100} = \frac{1}{50}$, we have \n$$0.02^3 = \left(\frac{1}{50}\right)^3 = \

1. We start with the expression: $$15a^2 - 15ab + 2a - 3b$$. 2. Group terms to factor by grouping: $$(15a^2 - 15ab) + (2a - 3b)$$.

1. **Problem 1:** Solve the equation $$-52 = 8(x + 3)$$ for $$x$$. 2. **Step 1:** Distribute the 8 on the right side:

1. El problema parece referirse a una sustitución en una expresión o ecuación, cambiando el número 5 por 6. 2. Para resolver esto, se debe identificar dónde está el número 5 y reem

1. Solve the system \(\begin{cases} 7 = y + \frac{5}{x} \\ 13 = 5y - 3x \end{cases}\) Step 1: From the first equation, express \(y\):

1. The problem is to analyze and understand the function given by the equation $y = x^2 + 2x + 1$.\n\n2. First, recognize that the expression is a quadratic polynomial. We can fact

1. We are asked to convert the fraction $\frac{128}{495}$ into a decimal. 2. To do this, we perform the division $128 \div 495$.

1. The problem is to factor the quadratic expression $$x^2 + 5x + 6$$. 2. To factor a quadratic, look for two numbers that multiply to the constant term ($6$) and add up to the coe

1. **State the problem:** Convert the fraction $\frac{128}{495}$ into its decimal form. 2. **Understand what is asked:** We want to divide 128 by 495 to get a decimal number.

1. The problem is to simplify the fraction $\frac{256}{990}$.\n2. Start by finding the greatest common divisor (GCD) of 256 and 990.\n3. Prime factorization of 256 is $2^8$.\n4. Pr

1. The problem states the side lengths of an equilateral triangle as expressions: $$3w + 8$$, $$5w - 14$$, and $$2w + 19$$. 2. Since all sides of an equilateral triangle are equal,

**Problem:** There are 12 more giraffes than tigers.

1. We are asked to multiply the fractions $\frac{12}{7}$ and $\frac{9}{5}$. 2. Multiply the numerators: $12 \times 9 = 108$.

1. The logarithm is the inverse operation of exponentiation. 2. It answers the question: To what power must the base $b$ be raised, to produce the number $x$?

1. Masalani bayon qilamiz: Funksiyani grafigini chizish va o’sish, kamayish oralig’ini aniqlash. 2. Funksiya: $y=2x+3$

1. Let's clarify the problem statement first: it appears you are asking why the value of \( d \) is \( \frac{3}{4} \).\n\n2. Typically, \( d = \frac{3}{4} \) arises from solving an

1. The problem asks for the 5th term of a harmonic sequence given the 2nd term is $\frac{1}{2}$ and the 6th term is $\frac{1}{5}$. 2. A harmonic sequence is a sequence whose terms

1. We are given a harmonic sequence where the 2nd term is $\frac{1}{2}$ and the 6th term is $\frac{1}{5}$. We need to find the 5th term. 2. Recall that a harmonic sequence is a seq

1. The problem states that the shopkeeper makes a profit of 30% on the cost price by selling a book and the profit amount is Rs. 240. We need to find the cost price of the book. 2.

1. Simplify each expression: i. $(x^5)^1 = x^5$ because any power raised to 1 remains the same.

1. **State the problem:** Solve the equation $$\frac{75 - 15y}{4} + 4y = 19$$ for $y$. 2. **Rewrite the equation:** The equation is already written as $$\frac{75 - 15y}{4} + 4y = 1