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Questions and Answers
If a function $f(x) = 3x^2 - 2x + 5$ is transformed by applying a vertical shift of 4 units upward, what is the new function?
If a function $f(x) = 3x^2 - 2x + 5$ is transformed by applying a vertical shift of 4 units upward, what is the new function?
A rectangle has a length that is 3 times its width. If the perimeter of the rectangle is 48 units, what is the width?
A rectangle has a length that is 3 times its width. If the perimeter of the rectangle is 48 units, what is the width?
What is the area of a triangle with a base of 10 units and a height of 5 units?
What is the area of a triangle with a base of 10 units and a height of 5 units?
A student scored 75%, 85%, and 90% on three tests. What score does the student need on a fourth test to achieve an average of 80%?
A student scored 75%, 85%, and 90% on three tests. What score does the student need on a fourth test to achieve an average of 80%?
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If the equation of a line is given by $y = 2x + 3$, what is the slope of the line?
If the equation of a line is given by $y = 2x + 3$, what is the slope of the line?
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Study Notes
Function Transformation
- Original function: ( f(x) = 3x^2 - 2x + 5 )
- Vertical shift of 4 units upward alters the function to: ( f(x) + 4 = 3x^2 - 2x + 9 )
Rectangle Perimeter and Dimensions
- Rectangle's length is 3 times its width: Let width be ( w ), then length = ( 3w )
- Perimeter formula: ( P = 2(\text{length} + \text{width}) ) gives ( 48 = 2(3w + w) )
- Simplified to ( 48 = 8w ), yielding ( w = 6 ) units for the width
Area of Triangle
- Area formula: ( A = \frac{1}{2} \times \text{base} \times \text{height} )
- For base of 10 units and height of 5 units: ( A = \frac{1}{2} \times 10 \times 5 = 25 ) square units
Average Score Calculation
- Scores: 75%, 85%, 90% on three tests
- Total score from three tests: ( 75 + 85 + 90 = 250 )
- To achieve an average of 80% across four tests: ( \text{Target total score} = 4 \times 80 = 320 )
- Required score on fourth test: ( 320 - 250 = 70 )
Slope of a Line
- Given line equation: ( y = 2x + 3 )
- The slope-intercept form indicates the slope is ( 2 )
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Description
Test your understanding of mathematical concepts with these seven application questions based on Bloom's taxonomy. From transformations of functions to calculating averages, this quiz challenges you to apply what you've learned in practical scenarios. See how well you can solve problems in a mathematical context!
