🧮 algebra

1. The problem asks us to find which values of $w$ make the inequality $2w > 21$ true. 2. The inequality is $2w > 21$. To solve for $w$, we divide both sides by 2.

1. **Stating the problem:** Simplify the expression \( \frac{8x9z6}{7^4 + z} \). 2. **Understanding the expression:** The numerator is \(8 \times 9 \times z \times 6\) and the deno

1. **State the problem:** Find the y-intercept and slope of the linear equation $$y = -4x - 3$$. 2. **Recall the slope-intercept form:** The equation of a line in slope-intercept f

1. **State the problem:** Verify if the expression $$\frac{2x^{2}y^{4} \cdot 4x^{2}y^{4} \cdot 3x}{3x^{-3} y^{2}}$$

1. The problem shows a table with two columns labeled $p$ and $d$ and three rows of numbers: $p = 9, 7, 8$ and $d = 4, 5, 6$. 2. Since the user did not specify a question, let's as

1. **State the problem:** Determine if the values in the table form a proportional relationship. The table is:

1. The first expression is $(x^{-2} x^{-3})^4$. Using the rule $(a^m a^n)^p = a^{(m+n)p}$, we get: $$ (x^{-2} x^{-3})^4 = (x^{-5})^4 = x^{-20} $$

1. **State the problem:** Simplify the expression $$\frac{(2p^{m-1} q)^{-4} \cdot 2m^{-1} p^3}{2pq^2}$$ and verify if the given process is correct. 2. **Recall the rules:**

1. **State the problem:** We need to find the new price after applying a 16% discount to the original price of 24. 2. **Formula used:** The new price after a discount is given by:

1. **State the problem:** We need to find the new price after applying a 22% discount to the original price of 25. 2. **Formula:** The new price after a discount is given by:

1. **State the problem:** Simplify the expression $$\frac{(2 p m^{-1} q^{0})^{-4} \cdot 2 m^{-1} p^{3}}{2 p q^{2}}$$. 2. **Recall important rules:**

1. **State the problem:** Find the product when the quotient of $5 \frac{1}{4}$ and $3 \frac{1}{2}$ is multiplied by $1 \frac{1}{3}$. 2. **Convert mixed numbers to improper fractio

1. **Stating the problem:** We are given a graph of a proportional relationship passing through the origin and the point approximately $(8, 1050)$. We need to find the equation of

1. **Stating the problem:** Calculate the total salary of a person who has a base salary of 334 and earns an additional 13 for every item sold beyond 100 items. The person sold 193

1. **State the problem:** Determine if the graph showing the relationship between time (hours) and distance (miles) is a proportional relationship. 2. **Recall the definition of pr

1. **Stating the problem:** Calculate the total salary if the base salary is 334 and there is an additional 13 for every item sold beyond 100.

1. The problem asks to write a function for the graph related to $f(x) = 5^x$ where the graph is vertically shifted upwards by a constant $k$. 2. The general form for vertical shif

1. **State the problem:** Write the quadratic function in vertex form $f(x) = a(x-p)^2 + q$ for each graph.

1. **Problem Statement:** We have three graphs of the form $f(x) = ax^2$ labeled $r$, $s$, and $t$. We need to identify which graphs correspond to $a > 0$ and which correspond to $

1. **State the problem:** We need to find the length of a rectangular tank given its volume, width, and height. 2. **Formula:** The volume $V$ of a rectangular prism is given by

1. **Problem statement:** Find the domain and range of the function $$y = (x + 1)(x - 3)$$. 2. **Recall the domain and range definitions:**