🧮 algebra

1. Problem 21: Given the equation $y = 3x - 2$, find $y$ when $x = 10$. 2. Substitute $x = 10$ into the equation:

1. Calculate $2 \left( \frac{3}{5} \right)^2$. First, square $\frac{3}{5}$:

1. Express $\frac{12}{5}$ as a mixed fraction. - Divide 12 by 5: $12 \div 5 = 2$ remainder $2$.

1. The problem is to simplify the expression \(\frac{0,(7) + 1}{0,(7) + 2} - \frac{7}{176} \div \frac{0,(81) + 1}{0,(81) + 2}\). 2. First, convert the repeating decimals to fractio

1. Problem: Simplify $ (4n^7)^5$.\n 2. Formula and rules: Use the power-of-a-product rule $ (ab)^m = a^m b^m$ and the power-of-a-power rule $ (a^m)^n = a^{mn}$.\n

1. **Express 12/5 as a mixed fraction in the form a (b/c)** Step 1: Divide 12 by 5 to find the whole number part.

1. **State the problem:** Simplify the expression $12 \cdot 2 \left(\frac{3}{5}\right)^2$. 2. **Recall the order of operations:** First, calculate the exponent, then multiplication

1. **State the problem:** Solve the equation $m + 13 = 20$ for $m$. 2. **Formula and rules:** To isolate $m$, subtract 13 from both sides of the equation. This uses the property th

1. Express $\frac{12}{5}$ as a mixed fraction in the form $a \frac{b}{c}$. Step 1: Divide 12 by 5.

1. **State the problem:** Simplify the expression $$\frac{6 + 4(7 + 4)}{5^3 + 9}$$. 2. **Apply the order of operations (PEMDAS):** Parentheses, Exponents, Multiplication and Divisi

1. **State the problem:** Simplify the expression $$\frac{6 + 4(7 + 4)}{5^3 + 9}$$. 2. **Apply the order of operations:** First, solve inside the parentheses.

1. **State the problem:** Find the domain and range of the inverse function of $f(x) = \frac{1}{x} - 2$. 2. **Recall the inverse function:** To find the inverse, swap $x$ and $y$ a

1. **State the problem:** We are given the function $f(x) = \frac{1}{x} - 2$ and want to understand its behavior. 2. **Rewrite the function:** The function can be written as a sing

1. **State the problem:** Solve the equation $$\frac{x-6}{3} + x + \frac{2}{4} = 32$$ for $x$. 2. **Identify the formula and rules:** To solve for $x$, we need to combine like term

1. **State the problem:** Solve the equation $x - 63 + x + 24 = 32$ for $x$. 2. **Combine like terms:** Group the $x$ terms and the constants separately.

1. The problem is to solve the first question from the worksheet. Since the worksheet is not provided, I will solve a common algebra problem: Solve for $x$ in the equation $2x + 3

1. **Problem Statement:** We are given a piecewise function:

1. **State the problem:** We have an arithmetic sequence with terms $t(7) = 1056$ and $t(12) = 116$. We need to find $t(4)$. 2. **Recall the formula for the $n$-th term of an arith

1. **State the problem:** Factor the expression $$3x^2 + 6x^2 - 4x - 8$$. 2. **Combine like terms:** First, combine the terms with $$x^2$$.

1. **State the problem:** We want to find the snowfall rate per hour given that 3 inches of snow fell from 1:00 pm to 12:00 am the next day. 2. **Identify the time interval:** From

1. **State the problem:** Simplify the expression $\left(\frac{3}{5} - \frac{2}{5} + \frac{1}{4}\right) + \frac{1}{6}$.\n\n2. **Combine the fractions inside the parentheses:** Sinc