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Questions and Answers
If $x = 3$ and $y = 4$, what is the value of $x^2 + y^2$?
If $x = 3$ and $y = 4$, what is the value of $x^2 + y^2$?
- $12$
- $25$ (correct)
- $7$
- $24$
What is the value of the square root of 49?
What is the value of the square root of 49?
- 5
- 7 (correct)
- 10
- -7
What is the median of the following set of numbers: 4, 7, 2, 6, 5?
What is the median of the following set of numbers: 4, 7, 2, 6, 5?
- 5 (correct)
- 6
- 7
- 4
Simplify the expression $3(4 + 5) - 2^2$.
Simplify the expression $3(4 + 5) - 2^2$.
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Study Notes
Mathematical Expressions and Calculations
- Given values: ( x = 3 ) and ( y = 4 ).
- Calculation of ( x^2 + y^2 ):
- ( x^2 = 3^2 = 9 )
- ( y^2 = 4^2 = 16 )
- Therefore, ( x^2 + y^2 = 9 + 16 = 25 ).
Square Roots
- The square root of 49 is calculated as:
- ( \sqrt{49} = 7 ).
Median Calculation
- To find the median of the set: 4, 7, 2, 6, 5:
- Sort the numbers in ascending order: 2, 4, 5, 6, 7.
- The median is the middle number in this ordered list, which is 5.
Expression Simplification
- Simplifying the expression ( 3(4 + 5) - 2^2 ):
- Calculate inside the parentheses: ( 4 + 5 = 9 ).
- Multiply by 3: ( 3 \times 9 = 27 ).
- Calculate ( 2^2 = 4 ).
- Therefore, ( 27 - 4 = 23 ).
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