Which of the following is true of the location of an angle, Theta, whose tangent value is - sqrt3/3?
Theta has a 30-degree reference angle and is located in Quadrant II or IV
Theta has a 30-degree reference angle and is located in Quadrant II or III
Theta has a 60-degree reference angle and is located in Quadrant II or IV
Theta has a 60-degree reference angle and is located in Quadrant II or III

Step-by-step explanation:

Keep in mind that the tangent function is negative in Quadrants II and IV.

Of the three possible answers, the 2nd is invalid because the tangent is positive in Q III.

If the reference angle were in Quadrant II and had the value 30° (second possible answer), then the opposite side would be +1, the adjacent side -√3 and the hypotenuse 2.  Based on this, the tangent of theta would be opp / adj, or +1 / (-√3)  or -√3/3.    This is correct.

x + y = 90 5x – 10y = 90 90 – 10y = 5x 90 + 10y = 5x

step-by-step explanation:

last month maria hiked the 5-mile mountain trail a number of times and she hiked the 10-mile canal trail several times. let x represent the number of times she hiked the 5-mile trail, and let y represent the number of times she hiked the 10-mile trail. if she hiked a total of 90 miles, which equation can be used to find the number of times maria hiked each trail? x + y = 90 5x – 10y = 90 90 – 10y = 5x 90 + 10y = 5x