Question

I do not get any of this thing

Answer 1

Answer:  C)  5/2

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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 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

- $\frac{1}{2}$ 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 = $\frac{5}{2}$ → C