It takes Engineer Kweku three hours to drive to his brother’s house at an average speed of 50 miles per hour. If He takes the sa
1 answer:
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Given:
ΔABC ΔDEF
To find:
The length of median CP
Solution:
In ΔABC,
AP = 12, BP = 12 and PC = 3x - 12
In ΔDEF,
DQ = 16, QE = 16 and FQ = 2x + 8
If two triangles are similar, then their median is proportional to the corresponding sides.
Do cross multiplication.
Add 192 on both sides.
Subtract 24x from both sides.
Divide by 24 on both sides.
⇒ 12 = x
Substitute x = 12 in CP.
CP = 3(12) - 12
= 36 - 12
= 24
The length of median CP is 24.
ANSWER
(3, 11) and (−3, −7)
EXPLANATION
The given system of equations are:
and
or
We equate the two equations to obtain,
We rewrite in standard quadratic form to obtain,
This simplifies to
We solve for x to obtain,
When
When x=-3,
Therefore the solution for the system is (3, 11) and (−3, −7).
(3, 11) and (−3, −7)
EXPLANATION
The given system of equations are:
and
or
We equate the two equations to obtain,
We rewrite in standard quadratic form to obtain,
This simplifies to
We solve for x to obtain,
When
When x=-3,
Therefore the solution for the system is (3, 11) and (−3, −7).