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Reptile
11 days ago
15

On a number line, a number, b, is located the same distance from 0 as another number, a, but in the opposite direction. The numb

er b varies directly with the number a. For example b = 2a equals negative 2 and StartFraction 3 Over 4 EndFraction. when a = –2a equals negative 2 and StartFraction 3 Over 4 EndFraction.. Which equation represents this direct variation between a and b?
Mathematics
1 answer:
Leona [9.2K]11 days ago
5 0
b Step-by-step explanation: On a number line, the number b is placed at an equal distance from 0 as another number a, but in the opposite direction. The number b varies directly with a. For instance, if b = 2a equals -2 and 3/4 when a = -2, then we find a = -2 equals -2 and 3/4. Therefore, what equation reflects this direct variation between a and b?
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Response:

f(g(x))=6x^3+4, indicating the amount of earnings per working hours, designated as x

Detailed Explanation:

We have two distinct functions to analyze:

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Then the second function is

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which illustrates the quantity of gallons of ice cream produced by Barrett each hour, with x representing the hours worked.

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By substituting g(x) into the x variable of f(x), we obtain:

f(g(x))=2(g(x))^2+4=2(\sqrt{3x^3})^2+4=2(3x^3)+4=6x^3+4

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