🧮 algebra

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

1. The problem involves two inequalities: $x \geq 0$ and $y \geq 0$. 2. These inequalities represent the constraints on the variables $x$ and $y$. Specifically, $x \geq 0$ means $x

1. **State the problem:** Simplify the expression $$\left(\frac{3}{5} - \frac{2}{5} + \frac{1}{4}\right) \div \frac{1}{6}$$ and then evaluate $$\frac{1}{5} + \frac{1}{4}$$, $$\frac

1. **State the problem:** Solve the equation $$\frac{6}{3} = \frac{V + 11}{3V - 12}$$ for $V$. 2. **Simplify the left side:** $$\frac{6}{3} = 2$$, so the equation becomes $$2 = \fr

1. **State the problem:** Simplify the expression $$\frac{1}{8} + \left( \frac{3}{5} + \frac{5}{6} - \frac{1}{3} \right)$$. 2. **Use the order of operations:** First simplify insid

1. The problem asks to determine whether the function is increasing, constant, or decreasing between the points A-B, B-C, C-D, and D-E based on the graph. 2. To determine the behav