Answer:
HJ
Step-by-step explanation:
For a line to be perpendicular to another line, you must find the negative reciprocal.
The negative reciprocal of 1/2 is -2.
The only line with a slope of -2 is line HJ because it goes down 2 for every 1 to the right.
Answer:
is -65
Step-by-step explanation:
Answer: Longest distance she could measure is 70 mm
Step-by-step explanation:
To find the longest distance from one side to other across the center we have to find the diameter of the lampshade.
As it is given that the distance around the lampshade is 219.8 mm which is equal to the circumference of the lampshade.
Circumference of the lampshade is 
πD, where D is the diameter of the lampshade
where the value of π=3.14
Divide both sides by 3.14 we get
on solving we get
For (2), start with the base case. When n = 2, we have
(n + 1)! = (2 + 1)! = 3! = 6
2ⁿ = 2² = 4
6 > 4, so the case of n = 2 is true.
Now assume the inequality holds for n = k, so that
(k + 1)! > 2ᵏ
Under this hypothesis, we want to show the inequality holds for n = k + 1. By definition of factorial, we have
((k + 1) + 1)! = (k + 2)! = (k + 2) (k + 1)!
Then by our hypothesis,
(k + 2) (k + 1)! > (k + 2) 2ᵏ = k•2ᵏ + 2ᵏ⁺¹
and k•2ᵏ ≥ 2•2² = 8, so
k•2ᵏ + 2ᵏ⁺¹ ≥ 8 + 2ᵏ⁺¹ > 2ᵏ⁺¹
which proves the claim.
Unfortunately, I can't help you with (3). Sorry!
It's true......................................
