If (-3)-5=1/x what is the value of x
1 answer:
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Answer
Find out the value of AM.
To prove
As given
In ABC,
centroid D is on median AM.
AD = x + 5 and DM = 3x – 5.
By using the centroid property
The centroid divides each median in a ratio of 2:1.
Thus D divide the median AM in a ratio of 2:1.
Therefore
(AD) = 2DM
(x + 5) = 6x – 10
5x = 15
x = 3
Now
AM = 3+ 5
= 8 unit
DM = 3 × 3- 5
= 4 unit
AM = AD + DM
= 8 + 4
AM = 12 unit
Therefore the AM is 12 unit.
Answer:
Price of the adult ticket is $13
Price of the child ticket is $3
Step-by-step explanation:
Lets x be the adult ticket and y be the child ticket.
Given:
School sold 14 adult tickets and 14 child tickets for a total of $224, so the first equation is.
-------------(1)
And the school took in $44 on the second day by selling 2 adult tickets and 6 child tickets, so the second equation is.
---------------(2)
We find the price of an adult ticket and the price of a child ticket by solving above system of equation.
Now, equation 2 multiplied by 7.
---------(3)
Now, equation 1 subtracted by equation 3.
-______________
14x is cancelled in both equations, so we get the equation.
y = 3
Now, we substitute y = 3 in equation 2.
x = 13
Therefore, the price of the adult ticket is $13 and the price of the child ticket is $3.
Answer:
If the midpoints of any two sides of a triangle are joined by a segment, then that segment is parallel to the third side and half its length.
Step-by-step explanation:
We know the following equalities by the midpoint construction:
AD = DC and AE = EB. We can use the reflexive property of equality for angle A to obtain a SAS similarity of triangles DAE and CAB. Now that the two triangles are congruent, we have m<ADE = m<ACB. By the converse of the Corresponding Angles Theorem, we have DE || CB.
Now we need to show that DE = ½ CB.
Claim: Quadrilateral CBEF is a parallelogram. If we can show FC=EB, we can conclude that CBEF is a parallelogram.
*(side): We have m<FCD = m<EAD by the Alternate Interior Angles Theorem
*(angle): We have AD = DC (from above – definition of midpoint)
*(side): We have m<FDC = m<ADE by the Vertical Angles Theorem.
**We now have Triangle FDC is congruent to Triangle EDA by the SAS Congruence Theorem.
Therefore, FC = AE --> FC = EB. If a pair of opposite sides of a quadrilateral are both congruent and parallel, then the quadrilateral is parallelogram (previous theorem). Therefore FE = CB. Also, the above triangle congruence gives us FD = DE.
Write: FE = FD + DE --> FE = 2DE --> DE = ½ FE
Since FE = CB, we can substitute: DE = ½ CB.
Therefore the Midsegment is half of the measure of the third side.
Conclusion: If the midpoints of any two sides of a triangle are joined by a segment, then that segment is parallel to the third side and half its length.
