Answer:
Given:
and
.
Prove: 
Since
, By the definition of perpendicular lines angles 1, 2, 3 and 4 are 90 degree. similarly
, it means angles 5, 6, 7 and 8 are 90 degree.
We can say that,
,
,
and 
From figure it is noticed that the angle 1 and 5 are corresponding angles.
If two parallel lines are intersected by a transversal, then the corresponding angles are equal.
Since corresponding angles are congruent, therefore the line must be parallel to each other.
Hence proved that
.
Considering balloon to be an spherical object
Volume of sphere =
, where r is the radius of sphere.
After 19 minutes ,If radius of balloon changes from r to R, the Volume changes from V to V'.
V'=
,
As given,rate at which the air leaked out of the balloon (in liters of air per minute) was half of the rate at which Vavilen inflated the balloon.
Also,
Now, again the radius changes from R to r.So, Volume changes from V' to Back to V.
Time taken by the balloon to deflate = 38 minutes
But there is no relation between time and volume of Balloon.
So, we can't predict at which rate balloon is deflating or inflating.Apart from the statement given in Question:
Answer:
Step-by-step explanation:
m and n are parallel and cut by a transversal
<u>Finding x</u>
- 8x + 12 + 2x + 18 = 180 (consecutive interior angles sum up to 180°)
- 10x + 30 = 180
- 10x = 150
- x = 15
<u>Finding y</u>
- 8x + 12 = 3y - 18 (vertical angles are equal)
- 8(15) + 12 = 3y - 18
- 132 = 3y - 18
- 150 = 3y
- y = 50
Answer:
72-b=p
Step-by-step explanation:
You start with 72, then take away the people bringing their own supplies (b), and that equals the number of people that will have supplies provided for them (p).
72-b=p
Let the number be a
6a - 20 = 3a + 4
Group like terms
6a - 3a = 20 + 4
3a = 24
divide through by 3
a = 8
Therefore the number is 8