🧮 algebra

1. **State the problem:** A hammock costs $50.40 before tax and $52.92 after tax. We need to find the sales tax percentage.

1. **Problem statement:** We have a cubic function $$f(x) = ax^3 + bx^2 + cx - 8$$ with zeros at $$x = -1$$ and $$x = 2$$, and it passes through the point $$(1, -2)$$. We need to:

1. **State the problem:** We need to find the sales tax percentage when a chess board priced at 21.70 costs 23.87 after tax. 2. **Formula:** Sales tax percentage is calculated by \

1. The problem asks to find the equation in slope-intercept form $y=mx+b$ that matches the given table of values: | x | y |

1. **State the problem:** Determine the slope and y-intercept of the line described by the points given in the graph. 2. **Identify points from the graph:** From the description, t

1. **State the problem:** We need to calculate $$(4.9 \times 10^7) + (3.1 \times 10^6)$$ and express the answer in standard form. 2. **Rewrite the first term:** Given that $$4.9 \t

1. **State the problem:** There are 30 bikers in total. Some ride bicycles (1 person each), others ride tandems (2 people each). The total number of bicycles and tandems combined i

1. **State the problem:** We need to find the function $(f - g)(x)$ given $f(x) = -2x^2 - 7x$ and $g(x) = x^2 + 9x$. 2. **Recall the formula:** The difference of two functions is d

1. The problem is to graph the line given by the equation $y = 4x + 1$ using the slope and y-intercept. 2. The slope-intercept form of a line is $y = mx + b$, where $m$ is the slop

1. **State the problem:** We need to find the ticket price that maximizes revenue for a minor league hockey team. 2. **Define variables:** Let $x$ be the number of $1$ dollar incre

1. The problem asks to find the value of the function $f(x)$ at $x = -3$. 2. From the graph, we see the curve passes through the point $(-3, 5)$.

1. **State the problem:** Ricardo ran a 400-meter race 3 times. His fastest time was 54.3 seconds, his slowest time was 56.1 seconds, and his average time was 55.0 seconds. We need

1. The problem asks to find the value of the function $f(x)$ at $x = -4$ for a piecewise linear function described by a triangular shape. 2. The function increases linearly from $y

1. The problem asks which set of ordered pairs $(x, y)$ could represent a linear function. 2. A linear function has a constant rate of change or slope between any two points.

1. The problem asks which table of values represents a linear function. 2. A linear function has a constant rate of change (slope) between any two points.

1. **State the problem:** We are given the tuition in 2001 as $4448$ and the percentage increase from 2001 to 2009 as $77.3\%$. We need to find the increase amount and the tuition

1. The problem is to solve the equation $30 - 7 \frac{1}{4} = 21 \frac{2}{3}$ and verify if it is true. 2. First, convert the mixed numbers to improper fractions for easier calcula

1. **Problem 1.1:** Find the sum of the first 15 terms of the arithmetic series 3 + 7 + 11 + 15 + ... 2. The formula for the sum of the first $n$ terms of an arithmetic series is:

1. **State the problem:** Solve for the unknown value represented by "?" in the equation $$\frac{5}{12} - ? + \frac{5}{4} = \frac{2}{3}$$. 2. **Isolate the unknown:** We want to fi

1. **State the problem:** Find the vertical and horizontal asymptotes of the function $$f(x) = \frac{x^3 - x^2 - 12x}{-3x^2 + 6x}$$. 2. **Vertical asymptotes:** Vertical asymptotes

1. **State the problem:** Solve the two-step equation $$3x + 1 = 7$$. 2. **Identify the goal:** We want to isolate the variable $x$ on one side of the equation.