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Consider the function represented by the equation [tex]6c = 2p - 10[/tex].

Write the equation in function notation, where [tex]c[/tex] is the independent variable.

A. [tex]f(c) = \frac{1}{3} p + \frac{5}{3}[/tex]
B. [tex]f(c) = 3c + 5[/tex]
C. [tex]f(p) = \frac{1}{3} p + \frac{5}{3}[/tex]
D. [tex]f(p) = 3c + 5[/tex]

Sagot :

GinnyAnsweridn
Sure! Let's convert the given equation [tex]\( 6c = 2p - 10 \)[/tex] into function notation. Here we are to express it with [tex]\( c \)[/tex] as the independent variable and rewrite the equation to represent a function of [tex]\( p \)[/tex].

1. Start with the given equation:
[tex]\[ 6c = 2p - 10 \][/tex]

2. To isolate [tex]\( p \)[/tex], we divide both sides of the equation by 2:
[tex]\[ 3c = p - 5 \][/tex]

3. Next, we solve for [tex]\( p \)[/tex] by adding 5 to both sides of the equation:
[tex]\[ 3c + 5 = p \][/tex]

4. Rewrite in function notation, where [tex]\( f(p) \)[/tex] represents [tex]\( p \)[/tex] in terms of [tex]\( c \)[/tex]:
[tex]\[ f(p) = 3c + 5 \][/tex]

Therefore, the function notation for the given equation [tex]\( 6c = 2p - 10 \)[/tex], where [tex]\( c \)[/tex] is the independent variable, is:
[tex]\[ f(p) = 3c + 5 \][/tex]
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