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>
Answer:
G. 105.
Step-by-step explanation:
Percentage of cars with 3 or more people
= 15 + 7 + 3
= 25%,
25% of 420
= 0.25 * 420
= 105.
Answer:
D. 93°, 29°, 58°
Step-by-step explanation:
In a triangle we can only have 3 Interior angles.
The sum of the Interior angles in a triangle = 180°
Adding up the given Interior angles in the above question:
A. 15°, 48°, 27°
= 15° + 48° + 27°
= 90°
90° ≠ 180°
Option A is wrong
B. 56°, 45°, 46°
= 56 ° + 45° + 46°
= 147°
147° ≠ 180°
Option B is wrong
C. 42°, 84°, 64°
= 42° + 84° + 64°
= 190°
= 190° ≠ 180°
Option C is wrong.
D. 93°, 29°, 58°
93° + 29° + 58°
= 180°
180° = 180°
Option D is the correct Option.
Therefore, the set of angle measures that could be the interior angles of a triangle is Option D. 93°, 29°, 58°
Answer:
Step-by-step explanation:
I’m not sure u didn’t even add numbers
