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A team scores n goals and the other team scores n+5 goals. The total number of goals is less than 15. What is the possible range of n?
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Step-by-step solution
8 stepsFormulate the total number of goals.
Team A scores goals.
Team B scores goals.
The total number of goals scored by both teams is the sum of their individual scores:Formulate the inequality.
The total number of goals is less than 15.
Solve the inequality for .
Combine like terms:
Subtract 5 from both sides:
Divide by 2:
The inequality is .
Identify the properties of a parallelogram.
In a parallelogram RSTU, opposite angles are equal, and consecutive angles are supplementary (add up to ).
Given:
Use the property of opposite angles to find .
Angles (at vertex U) and (at vertex S) are opposite angles in the parallelogram RSTU. Therefore, they are equal.
Solve for .
Subtract from both sides:
Add 25 to both sides:
Divide by 5:
Calculate the measure of .
Substitute into the expression for :
Calculate the value of .
Angles (at vertex T) and (at vertex S) are consecutive angles in the parallelogram RSTU. Therefore, they are supplementary.
Substitute the value of :
Subtract from both sides:
The value of angle STU is .
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