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Explanation:
The term "zero" is the same as "root".
The root of f(x) is found by replacing f(x) with 0 and solving for x.
f(x) = 4x-20
0 = 4x-20
0+20 = 4x
20 = 4x
4x = 20
x = 20/4
x = 5
The root of f(x) is 5. If you plugged in x = 5, then you'll land on f(5) = 0.
Your teacher then wants to know what value of k will have g(x) get the same root of 5. In other words, we need to find k that will allow g(5) = 0.
We'll replace g(x) with 0 and plug in x = 5. Solving for k leads to...
g(x) = -0.5x+k
0 = -0.5*5+k
0 = -2.5+k
0+2.5 = k
2.5 = k
k = 2.5
k = 5/2
Answer:
C
Step-by-step explanation:
To find the zero of f(x) , let f(x) = 0 , that is
4x - 20 = 0 ( add 20 to both sides )
4x = 20 ( divide both sides by 4 )
x = 5 ← is the zero of f(x)
To find the zero of g(x) , let g(x) = 0 , that is
- [tex]\frac{1}{2}[/tex] x + k = 0 ( multiply through by 2 to clear the fraction )
- x + 2k = 0 ( subtract 2k from both sides )
- x = - 2k ( multiply both sides by - 1 )
x = 2k ← is the zero of g(x)
Equating the 2 zeros
2k = 5 ( divide both sides by 2 )
k = [tex]\frac{5}{2}[/tex] → C
