Triangle ABC is rotated 45° counterclockwise about vertex A to obtain triangle XYZ . If the m∠ABC is equal to 30°, what is the m∠XYZ?

15°

30°

45°

75°

Prove sin2a + cos2a - 1 / sin2a + cos2a + 1 = 1 - tana / 1 + cota

Pentagon abcde is dilated according to the rule do,3(x, y) to create the image pentagon a'b'c'd'e', which is shown on the graph. what are the coordinates of point a of the pre-image? a) (-1, 1)b) (-1, 2)c) (-9, 6)d) (-9, 18)

At wind speeds above 1000 centimeters per second (cm/sec), significant sand-moving events begin to occur. wind speeds below 1000 cm/sec deposit sand and wind speeds above 1000 cm/sec move sand to new locations. the cyclic nature of wind and moving sand determines the shape and location of large dunes. at a test site, the prevailing direction of the wind did not change noticeably. however, the velocity did change. fifty-nine wind speed readings gave an average velocity of x = 1075 cm/sec. based on long-term experience, σ can be assumed to be 245 cm/sec. (a) find a 95% confidence interval for the population mean wind speed at this site. (round your answers to the nearest whole number.) lower limit cm/sec upper limit cm/sec