How can finding the slopes of MN and AB help in proving that MN is the midsegment of triangle ABC?
2 answers:
Answer: The slopes of two parallel lines are equal.
Step-by-step explanation: Let and
be the slopes of lines AB and MN respectively. We know that if the slopes of two parallel lines are equal, then the lines must be parallel. Thus, if we get
, then AB is parallel to MN. Also, if we already have M and N as the mid-points of AC and BC, the with the help of slopes of AB and MN, we arrive at our proof that MN is the mid-segment of Triangle ABC. Please see the figure for details.
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A system of equations with infinitely many solutions is a system where the two equations are identical. The lines coincide. Anything that is equal to 
will work. You could try multiply the entire equation by some number, or moving terms around, or adding terms to both sides, or any combination of operations that you apply to the entire equation.
You could multiply the whole thing by 4.5 to get
. If you want, you could mix things up and write it in slope-intercept form: 
. The point is, anything that is equivalent to the original equation will give infinitely many solutions x and y. You can test this by plugging in values x and y and seeing the answers!
The attached graph shows that four different equations are really the same.
You could multiply the whole thing by 4.5 to get
The attached graph shows that four different equations are really the same.
Answer:
The principal amount was $23,393.45
Step-by-step explanation:
The total amount paid on a 35 year loan was $98,000 at the rate of interest 4.1%
We will calculate Principal amount by this formula
Where A = amount (98,000)
P = Principal amount (P)
r = rate of interest 4.1% (0.041)
n = number of compounding interest monthly (12)
t = time (35 years)
98,000 = P(4.189386)
= 4.189386P = 98,000
P =
P = 23,392.4494 ≈ $23,392.45
The principal amount was $23,393.45