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Sagot :
To find out how much more money is in Joel's account compared to Kevin's account [tex]\(x\)[/tex] weeks after the start of the year, we need to calculate the difference between the two functions [tex]\( j(x) \)[/tex] and [tex]\( k(x) \)[/tex].
Given:
[tex]\[ j(x) = 25 + 3x \][/tex]
[tex]\[ k(x) = 15 + 2x \][/tex]
We need to find the function [tex]\((j-k)(x)\)[/tex], which represents the difference between [tex]\(j(x)\)[/tex] and [tex]\(k(x)\)[/tex].
[tex]\[ (j - k)(x) = j(x) - k(x) \][/tex]
[tex]\[ = (25 + 3x) - (15 + 2x) \][/tex]
Now, we will simplify the expression step-by-step:
1. Distribute the negative sign through the [tex]\(k(x)\)[/tex] term:
[tex]\[ = 25 + 3x - 15 - 2x \][/tex]
2. Combine like terms:
[tex]\[ = (25 - 15) + (3x - 2x) \][/tex]
[tex]\[ = 10 + x \][/tex]
So, the function that correctly represents how much more money is in Joel's account than in Kevin's account [tex]\(x\)[/tex] weeks after the start of the year is:
[tex]\[ (j - k)(x) = 10 + x \][/tex]
Therefore, the correct answer is:
B. [tex]\((j - k)(x) = 10 + x\)[/tex]
Given:
[tex]\[ j(x) = 25 + 3x \][/tex]
[tex]\[ k(x) = 15 + 2x \][/tex]
We need to find the function [tex]\((j-k)(x)\)[/tex], which represents the difference between [tex]\(j(x)\)[/tex] and [tex]\(k(x)\)[/tex].
[tex]\[ (j - k)(x) = j(x) - k(x) \][/tex]
[tex]\[ = (25 + 3x) - (15 + 2x) \][/tex]
Now, we will simplify the expression step-by-step:
1. Distribute the negative sign through the [tex]\(k(x)\)[/tex] term:
[tex]\[ = 25 + 3x - 15 - 2x \][/tex]
2. Combine like terms:
[tex]\[ = (25 - 15) + (3x - 2x) \][/tex]
[tex]\[ = 10 + x \][/tex]
So, the function that correctly represents how much more money is in Joel's account than in Kevin's account [tex]\(x\)[/tex] weeks after the start of the year is:
[tex]\[ (j - k)(x) = 10 + x \][/tex]
Therefore, the correct answer is:
B. [tex]\((j - k)(x) = 10 + x\)[/tex]
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