🧮 algebra

1. The problem is to find the formula to determine the number of terms in an arithmetic series. 2. An arithmetic series is the sum of terms in an arithmetic sequence, where each te

1. **State the problem:** Solve for $x$ in the equation $$\frac{x - 3}{6} = \frac{x - 2}{4} - 36.$$\n\n2. **Identify the formula and rules:** To solve equations with fractions, mul

1. **State the problem:** Simplify the expression $$\frac{x^3 - 7x + 6}{x^2 + 4x - 5} \times \frac{x^2 + 9x + 20}{x^3 - 4x^2 + 5x - 2}$$. 2. **Factor each polynomial:**

1. **State the problem:** 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 want to find the

1. **State the problem:** Solve the equation $$\frac{3}{x+2} = 1 + \frac{2}{x-3}$$ for $x$. 2. **Rewrite the equation:**

1. **State the problem:** A watch costs 86 before tax and 87.72 after tax. We need to find the sales tax percentage.

1. **State the problem:** We need to identify the slope of the line that represents the relationship between the height the elevator rises in feet and the number of floors it passe

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.