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1 answer:
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Assume the first even integer is x.
The next even integer will be 2 digits after this digit. So the next even integer will be x+2.
The reciprocals of these two even integers can be written as
and 
respectively.
The sum of their reciprocals is 7/24. So we can set up the equation as:
Taking LCM on left hand side:
Cross Multiplying the denominators:
Using the quadratic formula to solve the above equation:
Since, the value of x can only be an integer, we discard the fractional value and keep x=6
So the first even integer is 6 and the next even integer is 8. The sum of reciprocals of 6 and 8 is 7/24
The next even integer will be 2 digits after this digit. So the next even integer will be x+2.
The reciprocals of these two even integers can be written as
The sum of their reciprocals is 7/24. So we can set up the equation as:
Taking LCM on left hand side:
Cross Multiplying the denominators:
Using the quadratic formula to solve the above equation:
Since, the value of x can only be an integer, we discard the fractional value and keep x=6
So the first even integer is 6 and the next even integer is 8. The sum of reciprocals of 6 and 8 is 7/24
Answer:
m∠HMO=102°
Step-by-step explanation:
we know that
In a Rhombus the diagonals bisect the angles and opposite angles are equal
In this problem
Angles HMO and HTO are opposite angles
m∠HMO=m∠HTO
m∠HTM=(1/2)m∠HMO ----> because the diagonals bisect the angles and opposite angles are congruent
substitute the values
solve for x
<em>Find the measure of angle HMO</em>
m∠HMO=(12x-6)°
substitute the value of x
m∠HMO=(12(9)-6)=102°
see the attached figure to better understand the problem
