Answer:
-5x-1
Step-by-step explanation:
Answer:
Option C.
Step-by-step explanation:
Given information: In triangle ABC, ST║AC, SB=10 ft, BT=9 ft and CT=2.7 ft.
Triangle proportionality theorem: If a line segment parallel to a side of a triangle then the line segments divides the remaining sides proportionally.
Using triangle proportionality theorem we get
On cross multiplication we get
Divide both sides by 9.
The length of SA is 3ft.
Therefore, the correct option is C.
Answer:
B: 72
Step-by-step explanation:
Split the shape into separate rectangles! It will make the problem much easier. You can split it so that you will have a 12 x 3 rectangle and a 6 x 6 rectangle because you subtract 3 from 9 and subtract 6 from 12.
12 x 3 = 36
6 x 6 = 36
36 + 36 = 72
Let me know if you're still confused!
Proving a relation for all natural numbers involves proving it for n = 1 and showing that it holds for n + 1 if it is assumed that it is true for any n.
The relation 2+4+6+...+2n = n^2+n has to be proved.
If n = 1, the right hand side is equal to 2*1 = 2 and the left hand side is equal to 1^1 + 1 = 1 + 1 = 2
Assume that the relation holds for any value of n.
2 + 4 + 6 + ... + 2n + 2(n+1) = n^2 + n + 2(n + 1)
= n^2 + n + 2n + 2
= n^2 + 2n + 1 + n + 1
= (n + 1)^2 + (n + 1)
This shows that the given relation is true for n = 1 and if it is assumed to be true for n it is also true for n + 1.
<span>By mathematical induction the relation is true for any value of n.</span>
