Applying the triangle proportionality theorem, the missing segment length is: 3.
<h3>What is the Triangle Proportionality Theorem?</h3>
The triangle proportionality theorem states that if a line that is parallel to a third side intersects the other two sides of a triangle, it divides them proportionally.
Let x represent the given segment length. Using the triangle proportionality theorem, we would have:
(12 - 2)/2 = 15/x
10/2 = 15/x
5 = 15/x
5x = 15
x = 15/5
x = 3
The missing segment length is: 3.
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(a) 
= 4n + 8
(b) row 13 has 60 seats
(a)
the sequence of seats is an arithmetic sequence whose n th term is
= 
+ (n - 1 )d
where is the first term and d the common difference
here the sequence is 12, 16, ....
with = 12 and d = 16 - 12 = 4, thus
= 12 + 4( n - 1 ) = 12 + 4n - 4 = 4n + 8
(b)
calculate the number of rows n when 60 seats
solve 4n + 8 = 60 ( subtract 8 from both sides )
4n = 52 ( divide both sides by 4 )
n = 13 ← number of rows
Answer:
n = 15
Step-by-step explanation:
For inputs of the value of n, the running time for the algorithm A is 100n^2 and that of B is 2^n.
If A is to run faster than B, 100n^2 must be smaller than 2^n.
Let's check from n = 1 to know the value of n that fits
n = 1
100(1)^2 > 2^1
100 > 2
n = 2
100(2)^2 > 2^2
400 > 4
n = 4
100(4)^2 > 2^4
1600 > 16
n = 8
100(8)^2 > 2^8
6400 > 2^8
n = 16
100(16)^2 < 2^16
25600 < 2^16
This implies that between n = 8 and 16, A starts to run faster than B
n = (8+16)/2 = 12
100(12)^2 > 2^12
14400 > 2^12
n = (12+16)/2 = 14
100(14)^2 > 2^14
19600 > 2^14
n = (14+16)/2
n = 15
100(15)^2 < 2^15
22500 < 2^15
At n= 15, A starts running faster than B
Answer:
The slope is 3/5.
Step-by-step explanation:
I am assuming you mean
10x + 6y = 84
6y = -10x + 84
y = -5/3 x + 14.
So the slope of this line is -5/3 and the slope of a line perpendicular to it is
-1 / -5/3 = 3/5.
Answer:
The statement is not reasonable.
Step-by-step explanation:
Josefina gave away 130% of her stamp collection.
We cannot give more than what we have.
lets understand it mathematically.
suppose i have x stamp.
according to question, i have to give 130% of my stamp collection
130% of x = 130/100 x = 1.3x
so, i have to given 1.3x stamp while i do have only x stamp which does not make any sense.
maximum i can give is x stamp.
x stamp in percentage of my total stamp collection which is also x will be
= x/x*100 = 100%
Thus, maximum one can give is 100% of what he has.
Thus, we can say that Josefina gave away 130% of her stamp collection is not reasonable.
