Step-by-step explanation:
the third of 7 consecutive numbers is 12.
so, this looks like
..., ..., 12, ..., ..., ..., ...
that means the numbers have to be
10, 11, 12, 13, 14, 15, 16
the sum is then
16+10 + 15+11 + 14+12 + 13 = 3×26 + 13 = 91
Answer:
11
Step-by-step explanation:
Use cosine rule:
c²=b²+a²-2ba cosC
Right triangle = 90 degrees
cosine 90 degrees = 0
c²=28²+15²-2×28×15×0
c²=28²+15²
c=√1009
c=31.8 in
Answer:
x = 14
Step-by-step explanation:
Solve for x:
90 = -4 + 2 x + 3 (x + 8)
3 (x + 8) = 3 x + 24:
90 = 3 x + 24 + 2 x - 4
Grouping like terms, 3 x + 2 x - 4 + 24 = (2 x + 3 x) + (-4 + 24):
90 = (2 x + 3 x) + (-4 + 24)
2 x + 3 x = 5 x:
90 = 5 x + (-4 + 24)
24 - 4 = 20:
90 = 5 x + 20
90 = 5 x + 20 is equivalent to 5 x + 20 = 90:
5 x + 20 = 90
Subtract 20 from both sides:
5 x + (20 - 20) = 90 - 20
20 - 20 = 0:
5 x = 90 - 20
90 - 20 = 70:
5 x = 70
Divide both sides of 5 x = 70 by 5:
(5 x)/5 = 70/5
5/5 = 1:
x = 70/5
The gcd of 70 and 5 is 5, so 70/5 = (5×14)/(5×1) = 5/5×14 = 14:
Answer: x = 14
