Enny’s mother is 5 years older than twice Jenny's age. The sum of their ages is 62 years. This is represented by the equation x
2 answers:
Answer:
Jenny´s age is 19 and her mother is 43.
Step-by-step explanation:
1. Plug in the first value of the set:
41 is different from 62, so Jenny isn´t 12 years old.
2. Plug in the second value of the set:
50 is different from 62, so Jenny isn´t 15 years old.
3. Plug in the third value of the set:
59 is different from 62, so Jenny isn´t 18 years old.
4. Plug in the fourth value of the set:
Therefore Jenny´s 19 years old.
5. Calculate Jenny´s mother age:
As the sum of their ages is 62 ages, we have the following equation:
where
x=Jenny´s age
y=Jenny´s mother age
Replacing the Jenny´s age we have:
Solving for y:
Therefore Jenny's mother age is 43 years old.
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Answer:
<em>f(g(2))=7</em>
Step-by-step explanation:
<u>The Composite Function</u>
Given f(x) and g(x) as real functions, the composite function is defined as:
It can be found by substituting g into f.
The given functions are:
It's required to find f( g( 2 ) )
Find g(2):
Operating:
g(2)=1
Now find f(1):
Thus:
f( g( 2 ) )=7
This question is incomplete, the complete question is;
If n is a positive integer, how many 5-tuples of integers from 1 through n can be formed in which the elements of the 5-tuple are written in increasing order but are not necessarily distinct.
In other words, how many 5-tuples of integers ( h, i , j , m ), are there with n ≥ h ≥ i ≥ j ≥ k ≥ m ≥ 1 ?
Answer:
the number of 5-tuples of integers from 1 through n that can be formed is [ n( n+1 ) ( n+2 ) ( n+3 ) ( n+4 ) ] / 120
Step-by-step explanation:
Given the data in the question;
Any quintuple ( h, i , j , m ), with n ≥ h ≥ i ≥ j ≥ k ≥ m ≥ 1
this can be represented as a string of ( n-1 ) vertical bars and 5 crosses.
So the positions of the crosses will indicate which 5 integers from 1 to n are indicated in the n-tuple'
Hence, the number of such quintuple is the same as the number of strings of ( n-1 ) vertical bars and 5 crosses such as;
= [( n + 4 )! ] / [ 5!( n + 4 - 5 )! ]
= [( n + 4 )!] / [ 5!( n-1 )! ]
= [ n( n+1 ) ( n+2 ) ( n+3 ) ( n+4 ) ] / 120
Therefore, the number of 5-tuples of integers from 1 through n that can be formed is [ n( n+1 ) ( n+2 ) ( n+3 ) ( n+4 ) ] / 120