Answer: a
Step-by-step explanation:
How to solve it (example) ⬇️
The perimeter of a triangle is 34 inches. The middle side is twicw as long as the shortest side. The longest side is 2 inches less than three times the shortest side. What are the lengths of the three
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let the sides of triangles be a, b, & c ; where c is the shortest side, a is the longest side and b is the middle side .
given perimeter of triangle = 34 inches
i.e. a + b + c = 34
given middle side is twice long as shortest side i.e. b = 2 x c = 2c .......(1)
given longest side is 2 inches less than three times shortest side
i.e. a = 3x c - 2 = 3c -2 .......... (2)
substituting (1) & (2) in equation a + b + c = 34
we get, 3c-2 + 2c + c = 34
3c+ 2c+ c -2 =34
6c -2 = 34
6c = 34 + 2 = 36
c = 36/ 6 = 6
a= 3c - 2
= (3 x 6) - 2
= 18- 2 = 16.
b = 2c = 2 x 6 = 12
so three sides of the triangle are 16 inches, 12 inches & 6 inches
The first place and 15th place are already decided, so we have to find the number of
different ways that the <em>other</em> 13 students can line up, in the places from #2 to #14.
2nd place can be any one of 13 people. For each of those . . .
3rd place can be any one of 12 people. For each of those . . .
4th place can be any one of 11 people. For each of those . . .
.
.
.
13th place can be any one of 2 people. For each of those . . .
14th place has to be the one student who is left.
Total number of ways that 13 students can line up in places #2 through #14 is
(13 x 12 x 11 x 10 x 9 x 8 x 7 x 6 x 5 x 4 x 3 x 2 x 1)
That number is called "thirteen factorial". The number is <u>6,227,020,800</u> .
When you write it in math, you write it like this: 13!
Answer: $4.54
1.87+2.67=4.54
I hope this is good enough: