Tunge \( h \) dinyatakan dengan lumus \( k(x)=P x+q \) ika \( h(4)=-28 \) dan \( h(-5)=2 \), maka \( h(-12) \)

Given that \( h \) is represented by the function \( k(x) = P x + q \) and we are given that \( h(4) = -28 \) and \( h(-5) = 2 \), we need to find \( h(-12) \). To find \( h(-12) \), we first need to determine the values of \( P \) and \( q \) in the function \( k(x) = P x + q \) using the given information. From the given information: 1. \( h(4) = -28 \) implies \( k(4) = -28 \) 2. \( h(-5) = 2 \) implies \( k(-5) = 2 \) Substitute the values of \( x \) and \( h(x) \) into the function \( k(x) = P x + q \) to form a system of equations: 1. \( 4P + q = -28 \) 2. \(-5P + q = 2 \) Now, we can solve this system of equations to find the values of \( P \) and \( q \). Let's solve the system of equations. Solve the system of equations by following steps: - step0: Solve using the substitution method: \(\left\{ \begin{array}{l}4P+q=-28\\-5P+q=2\end{array}\right.\) - step1: Solve the equation: \(\left\{ \begin{array}{l}q=-28-4P\\-5P+q=2\end{array}\right.\) - step2: Substitute the value of \(q:\) \(-5P-28-4P=2\) - step3: Subtract the terms: \(-9P-28=2\) - step4: Move the constant to the right side: \(-9P=2+28\) - step5: Add the numbers: \(-9P=30\) - step6: Change the signs: \(9P=-30\) - step7: Divide both sides: \(\frac{9P}{9}=\frac{-30}{9}\) - step8: Divide the numbers: \(P=-\frac{10}{3}\) - step9: Substitute the value of \(P:\) \(q=-28-4\left(-\frac{10}{3}\right)\) - step10: Simplify: \(q=-\frac{44}{3}\) - step11: Calculate: \(\left\{ \begin{array}{l}P=-\frac{10}{3}\\q=-\frac{44}{3}\end{array}\right.\) - step12: Check the solution: \(\left\{ \begin{array}{l}P=-\frac{10}{3}\\q=-\frac{44}{3}\end{array}\right.\) - step13: Rewrite: \(\left(P,q\right) = \left(-\frac{10}{3},-\frac{44}{3}\right)\) The solution to the system of equations is \( P = -\frac{10}{3} \) and \( q = -\frac{44}{3} \). Therefore, the function \( h(x) = -\frac{10}{3}x - \frac{44}{3} \). Now, we can find \( h(-12) \) by substituting \( x = -12 \) into the function \( h(x) \). Evaluate the expression by following steps: - step0: Evaluate: \(-\frac{10}{3}x-\frac{44}{3}\) - step1: Substitute: \(-\frac{10}{3}\left(-12\right)-\frac{44}{3}\) - step2: Multiply the numbers: \(40-\frac{44}{3}\) - step3: Reduce fractions to a common denominator: \(\frac{40\times 3}{3}-\frac{44}{3}\) - step4: Calculate: \(\frac{120}{3}-\frac{44}{3}\) - step5: Transform the expression: \(\frac{120-44}{3}\) - step6: Subtract the numbers: \(\frac{76}{3}\) The value of \( h(-12) \) is \( \frac{76}{3} \) or \( 25\frac{1}{3} \) or \( 25.\dot{3} \).