Which value for the constant c makes z=-(5)/(4) an extraneous solution in the following equation? {:[sqrt(4z+9)=cz+8],[c=]:}

Given equation and extraneous solution: We are given that z=-(5)/(4) is an extraneous solution to the equation sqrt(4z+9)=cz+8. To find the value of c that makes this true, we need to substitute z=-(5)/(4) into the equation and solve for c.Substitute and simplify left side: First, substitute z=-(5)/(4) into the left side of the equation sqrt(4z+9). sqrt(4*(-(5)/(4)) + 9) = sqrt(-5 + 9) = sqrt(4) = 2.Substitute and simplify right side: Now, substitute z=-(5)/(4) into the right side of the equation cz+8. c*(-(5)/(4)) + 8 = -(5c)/(4) + 8.Set expressions equal to find contradiction: Since z=-(5)/(4) is an extraneous solution, the two sides of the equation will not be equal. Therefore, we set the two expressions equal to each other and look for a contradiction. 2 = -(5c)/(4) + 8.Isolate term with c: To solve for c, we first isolate the term with c on one side. -(5c)/(4) = 2 - 8 = -6.Solve for c: Now, multiply both sides by -4/5 to solve for c. c = (-4/5) * (-6) = 24/5 = 4.8.

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Which value for the constant
c makes
z=-(5)/(4) an extraneous solution in the following equation?

{:[sqrt(4z+9)=cz+8],[c=]:}

Which value for the constant $c$ makes $z=-\frac{5}{4}$ an extraneous solution in the following equation? $\newline$ $\begin{array}{l} \sqrt{4 z+9}=c z+8 \\ c=\square \end{array}$

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Q. Which value for the constant

c

makes

z=-\frac{5}{4}

an extraneous solution in the following equation?

\newline

\begin{array}{l} \sqrt{4 z+9}=c z+8 \\ c=\square \end{array}

Given equation and extraneous solution: We are given that $z=-\frac{5}{4}$ is an extraneous solution to the equation $\sqrt{4z+9}=cz+8$ . To find the value of $c$ that makes this true, we need to substitute $z=-\frac{5}{4}$ into the equation and solve for $c$ .
Substitute and simplify left side: First, substitute $z=-\frac{5}{4}$ into the left side of the equation $\sqrt{4z+9}$ . $\sqrt{4\left(-\frac{5}{4}\right) + 9} = \sqrt{-5 + 9} = \sqrt{4} = 2$ .
Substitute and simplify right side: Now, substitute $z=-\frac{5}{4}$ into the right side of the equation $cz+8$ . $c\left(-\frac{5}{4}\right) + 8 = -\frac{5c}{4} + 8$ .
Set expressions equal to find contradiction: Since $z=-\frac{5}{4}$ is an extraneous solution, the two sides of the equation will not be equal. Therefore, we set the two expressions equal to each other and look for a contradiction. $2 = -\frac{5c}{4} + 8.$
Isolate term with c: To solve for c, we first isolate the term with c on one side. $\newline$ $-\frac{5c}{4} = 2 - 8 = -6$ .
Solve for c: Now, multiply both sides by $-\frac{4}{5}$ to solve for c. $\newline$ $c = \left(-\frac{$4$}{$5$}\right) \times ($-6$) = \frac{$24$}{$5$} = $4$.$8$.