Answered

IDNLearn.com is your trusted platform for finding reliable answers. Ask any question and get a detailed, reliable answer from our community of experts.

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 solve this step-by-step and express the given equation in the proper function notation with [tex]\(c\)[/tex] as the independent variable.

Given Equation:
[tex]\[ 6c = 2p - 10 \][/tex]

We need to solve this equation for [tex]\(p\)[/tex] in terms of [tex]\(c\)[/tex].

Step 1: Isolate the [tex]\(2p\)[/tex] term.
[tex]\[ 6c + 10 = 2p \][/tex]

Step 2: Solve for [tex]\(p\)[/tex] by dividing both sides by 2.
[tex]\[ p = 3c + 5 \][/tex]

Now, we need to write this in function notation. Since [tex]\(c\)[/tex] is the independent variable and we have [tex]\(p\)[/tex] expressed in terms of [tex]\(c\)[/tex], we can rewrite the equation in the form [tex]\(f(c) = 3c + 5\)[/tex].

However, we notice that the function notation given in the choices involves [tex]\(p\)[/tex], so let's revise our approach.

Revisiting the choices:
- This suggests that we express function in terms of [tex]\(f(p)\)[/tex].

Given that we have [tex]\(p = 3c + 5\)[/tex], we can restate that:
[tex]\[ p \to 3c + 5 \][/tex]

Therefore, the fourth option,
[tex]\[ f(p) = 3c + 5 \][/tex]
is the one that correctly represents the equation in function notation where [tex]\(c\)[/tex] is the independent variable.

So, the answer is:
[tex]\[ f(p) = 3c + 5 \][/tex]
Thank you for being part of this discussion. Keep exploring, asking questions, and sharing your insights with the community. Together, we can find the best solutions. IDNLearn.com has the answers you need. Thank you for visiting, and we look forward to helping you again soon.