Answered

Westonci.ca offers quick and accurate answers to your questions. Join our community and get the insights you need today. Connect with professionals ready to provide precise answers to your questions on our comprehensive Q&A platform. Connect with a community of professionals ready to help you find accurate solutions to your questions quickly and efficiently.

Which equation is the inverse of [tex]2(x-2)^2 = 8(7 + y)[/tex]?

A. [tex]-2(x-2)^2 = -8(7 + y)[/tex]

B. [tex]y = \frac{1}{4} x^2 - x - 6[/tex]

C. [tex]y = -2 \pm \sqrt{28 + 4x}[/tex]

D. [tex]y = 2 \pm \sqrt{28 + 4x}[/tex]

Sagot :

GinnyAnswer
To find the inverse of the given equation \(2(x-2)^2 = 8(7+y)\), we need to isolate \(y\) in terms of \(x\). Here’s a step-by-step process to do this:

1. Start with the given equation:
[tex]\[ 2(x-2)^2 = 8(7+y) \][/tex]

2. Divide both sides by 8 to simplify:
[tex]\[ \frac{2(x-2)^2}{8} = 7 + y \][/tex]
[tex]\[ \frac{(x-2)^2}{4} = 7 + y \][/tex]

3. Subtract 7 from both sides to isolate \(y\):
[tex]\[ \frac{(x-2)^2}{4} - 7 = y \][/tex]

Thus, the equation for \(y\) in terms of \(x\) is:
[tex]\[ y = \frac{(x-2)2}{4} - 7 \][/tex]

From the options provided, the correct inverse equation is:
[tex]\[ \boxed{[(x - 2)^2/4 - 7]} \][/tex]
Thanks for using our platform. We aim to provide accurate and up-to-date answers to all your queries. Come back soon. Thank you for your visit. We're dedicated to helping you find the information you need, whenever you need it. Your questions are important to us at Westonci.ca. Visit again for expert answers and reliable information.