Answer:
15
Step-by-step explanation:
1 is neither prime nor composite
2 is the smallest prime
3 is the next smallest prime
5 is the next smallest
but 2,3,5 do not make a triangle
The third side must be smaller than the sum of the other two
2+3 <5 not equal to
7 is the next prime
3,5,7 are the three sides of the triangle
P = 3+5+7
P = 15
Answer:
x = 8.69
Step-by-step explanation:
we know that the perimeter of the dodecagon is 54, so each edge will be 54/12
54/12 = 4.5 cm
if we draw the lines to remove 6 vertices and form a hexagon, 6 triangles with 2 sides of 4.5 cm are formed.
we know that the angle of each vertex is 150 ° because it is a dodecagon
if we apply the law of cosines we can take the other side of the triangle, since we only need 2 side and the opposite angle to the side we want to know
a would be our x
b = 4.5
c = 4.5
A = 150°
a^2 = b^2 + c^2 - 2bc * cos (A)
x^2 = 4.5^2 + 4.5^2 - 2 * 4.5 * 4.5 * cos (150)
x^2 = 20.25 + 20.25 - 40.50 * -0.866
x^2 = 40.50 + 35.07
x = √ 75.57
x = 8.69
921,444 rounded to the nearest hundred thousand is 900,000. Hope I helped. =)
5^23 - 5^21 = 5^(21+2) - 5^21
5^23 - 5^21 = 5^21*5^2 - 5^21*1
5^23 - 5^21 = 5^21*(5^2 - 1)
5^23 - 5^21 = 5^21*(25 - 1)
5^23 - 5^21 = 5^21*24
5^23 - 5^21 = 24*5^21
5^23 - 5^21 = 24*k
The original number is in the form 24k where k = 5^21, so this proves that the original number is a multiple of 24
