Answer:
76 degrees
Step-by-step explanation:
The total of the three angles in a triangle should equal 180 degrees. So to find the third angle, subtract the two given angles from 180
180 - 87 = 93
93 - 17 = 76
The third angle is 76 degrees because then all angles will add up to 180
Translation to the right by 12 units adds 12 to every x-coordinate. The new vertices are
... D'(5, 10), E'(7, 5), F'(4, 1)
It will be ∆D'E'F'.
When you put this into standard form for a parabola, your equation (after much sweating and bleeding from the eyeballs) found by completing the square is:
, which has a vertex at (-2.4, 7.6). To find the distance that the directrix is from the vertex (which is also the same distance the focus is from the vertex) we use the fact that
(you can omit the negative in front of it cuz distance will always be positive), and
. Since this is an upside down parabola, the focus is under the vertex ("inside" the parabola) while the directrix is above it. The directrix is a horizontal line. Because it is a horizontal line, it is 5/32 above the y-coordinate (or k) or the vertex. So we add 5/32 to the y-coordinate of the vertex to get 7.6+5/32 and that gives us a directrix of y = 7.76 rounded.
Answer:
True
Step-by-step explanation:
Vertical angles always come in pairs. They share a common vertex but they cannot share a side. Vertical angles are congruent, which means they have equal measures.
Answer:
B
Step-by-step explanation:
Because alternate interior angles are congruent in parallel lines, the angle next to the 25° in the right triangle is 85 - 25 = 60° which makes the other angle in the right triangle 180 - 90 - 60 = 30°. Since they form a straight angle, we can write x + 30 + 85 = 180 → x + 115 = 180 → x = 65°.