A)
The question tells us that
y + z = 180
And
y=3x+20
z=x
So we put them in the first formula:
y + z = 180
(3x + 20) + x = 180
Add and get x to one side:
4x + 20 = 180
4x + 20 - 20 = 180-20
4x = 160
Divide both sides by 4
x = 40
B)
Put x back in to equation to get size of each angle:
Y =3x +20
Y=3(40)+20
Y=120+20
Y=140
Z=x
Z=40
Verify: y+z=180
140+40=180
180=180
Answer:
Step-by-step explanation:
Since it is a regular hexagon, the length of its sides are equal. And same as the distance across its flats.
So that;
NR ≅ OP (property of a regular polygon)
PM ≅ RM (half of the distance across flats of a polygon)
NM ≅ OM (half of the distance across flats of a polygon)
<NMR ≅ <PMO (vertically opposite angles)
<NRM ≅ <OPM (alternate angle property)
<RNM ≅ <POM (alternate angle property)
This therefore proves that: ΔNRM = ΔOPM
Answer:
Rate of change = -1
Step-by-step explanation:
Given:
f(x) = -½(x + 2)² + 5
Required:
Average rate of change from x = -3 to x = 1
Solution:
Rate of change = 
Where,
a = -3,
f(a) = f(-3) = -½(-3 + 2)² + 5 = -½(-1)² + 5 = 4.5
b = 1,
f(b) = f(1) = -½(1 + 2)² + 5 = -½(9) + 5 = 0.5
Plug in the values into the formula:
Rate of change = 
Rate of change = 
Rate of change = -1
