Question

1. for an angle with measure α in a right triangle, sinα = 5/13 and tanα = 5/12. what is the value of cosα? a. 12/13 b. 12/√194 c. 12/√119 d. 13/12 14. which of the following values, if any, is the y - value of the solution set to the system of equations below? 2x - y = 7 - 4x + 2y = 2 f. 2 g. 5 h. 9 j. there is no such value for y.

Explanation:

Question 13

Step1: Recall the trigonometric identity

We know that \(\tan\alpha=\frac{\sin\alpha}{\cos\alpha}\).

Step2: Substitute the given values

Given \(\sin\alpha = \frac{5}{13}\) and \(\tan\alpha=\frac{5}{12}\), substituting into \(\tan\alpha=\frac{\sin\alpha}{\cos\alpha}\) gives \(\frac{5}{12}=\frac{\frac{5}{13}}{\cos\alpha}\).

Step3: Solve for \(\cos\alpha\)

Cross - multiply: \(5\cos\alpha=\frac{5\times12}{13}\). Then divide both sides by \(5\): \(\cos\alpha=\frac{12}{13}\).

Step1: Multiply the first equation by \(2\)

Multiply \(2x - y=7\) by \(2\) to get \(4x-2y = 14\).

Step2: Add the two equations

Add \(4x-2y = 14\) and \(-4x + 2y=2\). \((4x-4x)+(-2y + 2y)=14 + 2\), which simplifies to \(0=16\).

Answer:

A. \(\frac{12}{13}\)

Question 14