If [tex]k(x)=5 x-6[/tex], which expression is equivalent to [tex](k+k)(4)[/tex]?
A. [tex]5(4+4)-6[/tex]
B. [tex]5(5(4)-6)-6[/tex]
C. [tex]54-6+54-6[/tex]
D. [tex]5(4)-6+5(4)-6[/tex]
Answer (2)
The correct option that is equivalent to (k+k)(4) is Option D: 5 ( 4 ) − 6 + 5 ( 4 ) − 6 , which calculates to 28, matching the value of (k+k)(4).
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Calculate k ( 4 ) by substituting x = 4 into k ( x ) = 5 x − 6 , which gives k ( 4 ) = 5 ( 4 ) − 6 = 14 .
Determine ( k + k ) ( 4 ) by adding k ( 4 ) + k ( 4 ) = 14 + 14 = 28 .
Evaluate the given expressions to find the one that equals 28.
The expression 5 ( 4 ) − 6 + 5 ( 4 ) − 6 is equivalent to ( k + k ) ( 4 ) , since 5 ( 4 ) − 6 + 5 ( 4 ) − 6 = 14 + 14 = 28 .
Explanation
Understanding the problem We are given the function k ( x ) = 5 x − 6 , and we want to find an expression equivalent to ( k + k ) ( 4 ) . The expression ( k + k ) ( 4 ) means k ( 4 ) + k ( 4 ) .
Calculating k(4) First, let's find the value of k ( 4 ) . We substitute x = 4 into the function k ( x ) = 5 x − 6 :
k ( 4 ) = 5 ( 4 ) − 6 = 20 − 6 = 14.
Calculating (k+k)(4) Now, we need to find ( k + k ) ( 4 ) , which is k ( 4 ) + k ( 4 ) . Since we found that k ( 4 ) = 14 , we have: ( k + k ) ( 4 ) = k ( 4 ) + k ( 4 ) = 14 + 14 = 28.
Comparing with the options Now we need to find which of the given expressions is equal to 28.
5 ( 4 + 4 ) − 6 = 5 ( 8 ) − 6 = 40 − 6 = 34 . This is not equal to 28.
5 ( 5 ( 4 ) − 6 ) − 6 = 5 ( 20 − 6 ) − 6 = 5 ( 14 ) − 6 = 70 − 6 = 64 . This is not equal to 28.
54 − 6 + 54 − 6 = 48 + 48 = 96 . This seems to be a typo, it should be 5 ( 4 ) − 6 + 5 ( 4 ) − 6 . This is not equal to 28.
5 ( 4 ) − 6 + 5 ( 4 ) − 6 = ( 20 − 6 ) + ( 20 − 6 ) = 14 + 14 = 28 . This is equal to 28.
Examples
Understanding function notation and evaluation is crucial in many real-world applications. For example, in economics, a cost function might describe the cost of producing a certain number of items. If C ( x ) = 2 x + 5 represents the cost of producing x items, then C ( 10 ) would tell you the cost of producing 10 items. Similarly, in physics, a function might describe the position of an object at a given time. Evaluating these functions at specific points helps us understand and predict real-world phenomena.
