Answer: Choice D
Reason:
Whenever we have two lines cross to form an X shape, the vertical angles are always opposite one another. They do not have to be vertically stacked (as they can be side by side like angles 2 and 4 are). Vertical angles are always congruent.
Answer:
3.5
Step-by-step explanation:
These are similar triangles.
BC:AC = BD:AD
6:5 is the ratio.
Then, simply multiply:
4.2 x 5/6 = 3.5
So, x = 3.5!
The answer for the first one would be 4 just divide both 16 & 4.
The answer for the second one would be -7 just divide both 63 & -9.
The answer for the third one would be -36 just multiply both 12 and -3.
The answer for the fourth one would be -120 just multiply -10 and 12.
Answer:
311.41 degrees
Step-by-step explanation:
If 4 sin Ф = -3 and Ф is between 0 and 360 degrees, then we conclude that Ф must be either in Quadrant III or Quadrant IV (because the sine is negative).
Let's assume we're in Quadrant IV. Then sin Ф = opp / hyp = -3/4; that is, the opp side is negative and has length 3, and the hypo is positive 4.
According to the Pythagorean Theorem, (-3)^2 + x^2 = 4^2, or,
x^2 = 16 - 9 = 7.
Then x is either √7 or -√7.
To find the angle Ф, use the inverse sine function:
Ф = arcsin (-3/4). Using a calculator we get the angle -40.59 degrees, which corresponds to (360 degrees - 40.59 degrees), or 311.41 degrees. We can check this by finding the sine of 311.41 degrees; the result is -0.75, which matches "If 4sintheta = -3."
