9514 1404 393
Answer:
- arc BC = 60°
- m∠ADC = 60°
- m∠AEB = 105°
- m∠ADP = 45°
- m∠P = 60°
Step-by-step explanation:
The sum of arcs of a circle is 360°. The given conditions tell us arc BC ≅ arc AB, so the four arcs of the circle have ratios ...
CB : BA : AD : DC = 2 : 2 : 3 : 5
The sum of ratio units is 2+2+3+5 = 12, so each one stands for 360°/12 = 30°. Then the arc lengths are ...
arc BC = arc BA = 60° . . . . 2 ratio units each
arc AD = 90° . . . . . . . . . . . . 3 ratio units
arc DC = 150° . . . . . . . . . . . .5 ratio units
The inscribed angles are half the measure of the intercepted arcs:
∠ADC = (1/2) arc AC = 1/2(120°) = 60°
∠ADP = 1/2 arc AD = 1/2(90°) = 45°
The angles at E are half the sum of the measures of the intercepted arcs.
∠AEB = (arc AB + arc CD)/2 = (60° +150°)/2 = 105°
Angle P is half the difference of the intercepted arcs.
∠P = (arc BD -arc AD)/2 = (210° -90°)/2 = 120°/2 = 60°
__
In summary, ...
arc BC = 60°
m∠ADC = 60°
m∠AEB = 105°
m∠ADP = 45°
m∠P = 60°
Answer:
4 square root 2
Step-by-step explanation:
the pythagorian theorem will look like this: 2^2+b^2=6^2
simpify: 4+b^2=36
get b by itself by subtracting four from each side: b^2=32
take the square root of 32 and simplify: 4sqrt2
Substitution:
2x + (6(1/2x - 6)) = 19
2x + 3x - 36 = 19
5x - 36 = 19
+ 36
5x = 55
÷ 5
x = 11
y = (1/2 × 11) - 6
y = 5.5 - 6
y = -0.5
Elimination:
y = 1/2x - 6
- y
0 = 1/2x - 6 - y
+ 6
1/2x - y = 6
3x - 6y = 36
2x + 6y = 19
(add)
5x = 55
÷ 5
x = 11
y = (1/2 × 11) - 6
y = 5.5 - 6
y = -0.5
I hope this helps! Let me know if you need me to explain why I did some things :)
Answer: (a)
Step-by-step explanation:
the last step is
clear x
X=15.9/6.36
the answer is 5/2 or 2.50
