The formula N=(t^2-t)/(2) describes the number of football...

The formula $$N=\frac{t^{2}-t}{2}$$ describes the number of football games, $N$, that must be played in a league with $t$ teams if each team is to play every other team once. Use this information to solve Great white sharks have triangular teeth with a height that is 1 centimeter longer than the base. If the area of one tooth is 15 square centimeters, find its base and height. (IMAGE CAN'T COPY)

The formula
$$N=\frac{t^{2}-t}{2}$$
describes the number of football games, $N$, that must be played in a league with $t$ teams if each team is to play every other team once. Use this information to solve
Great white sharks have triangular teeth with a height that is 1 centimeter longer than the base. If the area of one tooth is 15 square centimeters, find its base and height.
(IMAGE CAN'T COPY)

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Key Concepts

Quadratic Equations

This concept involves equations in which the highest exponent of the variable is two. Solving quadratic equations is a key algebraic skill, as they frequently arise when modeling relationships in various contexts, such as in geometric problems where changing one variable affects another in a squared relationship. Techniques such as factoring, completing the square, or using the quadratic formula are typically employed.

Combinatorial Counting

This concept involves determining the number of ways to form pairs from a set of items without considering the order of selection. It often appears in problems such as scheduling matches in a league or creating connections among elements, and it is typically modeled by a formula that calculates the total number of unique pairings (often referred to as triangular numbers).

Area Calculation of Triangles

This concept focuses on computing the area of a triangle using the formula (1/2) × base × height. It is a fundamental aspect of geometry, where understanding the relationship between the dimensions of a triangle allows one to determine its area when either or both dimensions are expressed in relation to one another.

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