Answered

When [tex]10b = 5(\sqrt{c} + 2)[/tex] is solved for [tex]c[/tex], one equation is [tex]c = (2b - 2)^2[/tex]. Which of the following is an equivalent equation to find [tex]c[/tex]?

A. [tex]c = 10b - 10 - 5[/tex]
B. [tex]c = (10b - 10 - 5)^2[/tex]
C. [tex]c = \frac{(10b - 2)^2}{25}[/tex]
D. [tex]c = \frac{(10b - 10)^2}{25}[/tex]



Answer :

GinnyAnswer
Alright, let's work through solving for \( c \) given the equation \( 10b = 5(\sqrt{c} + 2) \).

1. Starting with the given equation:

[tex]\[ 10b = 5(\sqrt{c} + 2) \][/tex]

2. First, isolate \(\sqrt{c}\):

[tex]\[ 10b = 5\sqrt{c} + 10 \][/tex]

Subtract 10 from both sides:

[tex]\[ 10b - 10 = 5\sqrt{c} \][/tex]

3. Next, solve for \(\sqrt{c}\):

Divide both sides by 5:

[tex]\[ \frac{10b - 10}{5} = \sqrt{c} \][/tex]

4. Square both sides to solve for \( c \):

[tex]\[ \left(\frac{10b - 10}{5}\right)^2 = c \][/tex]

Simplify the expression inside the square:

[tex]\[ \frac{10b - 10}{5} = 2b - 2 \][/tex]

Therefore:

[tex]\[ c = (2b - 2)^2 \][/tex]

5. Find the equivalent equation:

Notice in this simplified and new expression, the correct form that matches one of the given options would be:

[tex]\[ c = \left( \frac{10b - 10}{5} \right)^2 \][/tex]

This further simplifies to:

[tex]\[ c = \frac{(10b - 10)^2}{25} \][/tex]

Therefore, the equivalent equation to find \( c \) is:

[tex]\[ c = \frac{(10b - 10)^2}{25} \][/tex]

This matches the provided option:

[tex]\[ c = \frac{(10 b - 10)^2}{25} \][/tex]

So the correct answer is:

[tex]\[ c = \frac{(10 b - 10)^2}{25} \][/tex]

Other Questions