Hello,
1) draw [AB]
2) draw mes (BAB')=78° (|AB|=|AB'| (distance))
draw the circle center B' passant by A.
3)C=middle [BB']
4) draw the half circle with [BB'] as diameter.
5) Intesection of cercle =>D
explain: any right triangle is inscribed in a semicircle
Rem: 78+90=168 and 360-168=192
We use the identity sin (A - B) = sin A cos B - cos B sin A
so the above = sin (11pi/12 - pi/6) = sin 3pi/4 = 1 / sqrt2 answer
1.53
2.115
3.122
4.106
5.49
6.110
left to right
9. ¹/₃(x + 6) = 8
¹/₃(x) + ¹/₃(6) = 8
¹/₃x + 2 = 8
<u> - 2 - 2</u>
3 · ¹/₃x = 6 · 3
x = 18
15. ¹/₅(x + 10) = 6
¹/₅(x) + ¹/₅(10) = 6
¹/₅x + 2 = 6
<u> - 2 - 2</u>
5 · ¹/₅x = 4 · 5
x = 20
20. ¹/₈(24x + 32) = 10
¹/₈(24x) + ¹/₈(32) = 10
3x + 4 = 10
<u> - 4 - 4</u>
<u>3x</u> = <u>6</u>
3 3
x = 2
32. 5 - ¹/₂(x - 6) = 4
5 - ¹/₂(x) - ¹/₂(-6) = 4
5 - ¹/₂x + 3 = 4
5 + 3 - ¹/₂x = 4
8 - ¹/₂x = 4
<u>- 8 - 8</u>
-2 · (-¹/₂x) = -4 · (-2)
x = 8
33. ²/₃(3x - 6) = 3
²/₃(3x) - ²/₃(6) = 3
2x - 4 = 3
<u> + 4 + 4</u>
<u>2x</u> = <u>7</u>
2 2
x = 3¹/₂
If you divide negative by positive it will be negative.
If you divide positive by negative it will be negative.
If you divide 2 negatives you get a positive.
I hope this helps :)