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Justin and Kira use functions to model the heights, in centimeters, of two sunflower plants [tex]\(x\)[/tex] weeks after transplanting them to the school garden.

Function [tex]\(j\)[/tex] models the height of Justin's plant:
[tex]\[ j(x) = 18 + 6x \][/tex]

Function [tex]\(k\)[/tex] models the height of Kira's plant:
[tex]\[ k(x) = 12 + 4x \][/tex]

Which function correctly represents how much taller Justin's plant is than Kira's plant, [tex]\(x\)[/tex] weeks after they were transplanted to the school garden?

A. [tex]\((j-k)(x) = 6 + 2x\)[/tex]

B. [tex]\((j-k)(x) = 30 + 2x\)[/tex]

C. [tex]\((j-k)(x) = 6 + 10x\)[/tex]

D. [tex]\((j-k)(x) = 30 + 10x\)[/tex]

Sagot :

GinnyAnsweridn
To determine which function correctly represents how much taller Justin's plant is compared to Kira's plant [tex]\( x \)[/tex] weeks after transplanting, we need to find the difference between the heights of the two plants.

The function [tex]\( j \)[/tex] for Justin's plant is given by:
[tex]\[ j(x) = 18 + 6x \][/tex]

The function [tex]\( k \)[/tex] for Kira's plant is given by:
[tex]\[ k(x) = 12 + 4x \][/tex]

To find how much taller Justin's plant is than Kira's plant, we need to calculate [tex]\( (j - k)(x) \)[/tex], which is the difference between the two functions:
[tex]\[ (j - k)(x) = j(x) - k(x) \][/tex]

Substitute the expressions for [tex]\( j(x) \)[/tex] and [tex]\( k(x) \)[/tex] into the equation:
[tex]\[ (j - k)(x) = (18 + 6x) - (12 + 4x) \][/tex]
[tex]\[ (j - k)(x) = 18 + 6x - 12 - 4x \][/tex]
[tex]\[ (j - k)(x) = (18 - 12) + (6x - 4x) \][/tex]
[tex]\[ (j - k)(x) = 6 + 2x \][/tex]

Therefore, the function representing how much taller Justin's plant is than Kira's plant [tex]\( x \)[/tex] weeks after transplanting is:
[tex]\[ (j - k)(x) = 6 + 2x \][/tex]

The correct answer is:
A. [tex]\( (j - k)(x) = 6 + 2x \)[/tex]
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