Answer:
Step-by-step explanation:
(-6 , 4) & (-1 , 2)
Slope = 
![= \frac{2-4}{-1-[-6]}\\\\= \frac{-2}{-1+6}\\\\= \frac{-2}{5}](https://tex.z-dn.net/?f=%3D%20%5Cfrac%7B2-4%7D%7B-1-%5B-6%5D%7D%5C%5C%5C%5C%3D%20%5Cfrac%7B-2%7D%7B-1%2B6%7D%5C%5C%5C%5C%3D%20%5Cfrac%7B-2%7D%7B5%7D)
m = -2/5 & (-6 , 4)
y -y1 = m(x -x1)
![y - 4 = \frac{-2}{5}(x - [-6])\\\\y - 4 = \frac{-2}{5}(x + 6)\\\\y - 4 = \frac{-2}{5}x + 6*\frac{-2}{5}\\\\y = \frac{-2}{5}x -\frac{12}{5}+4\\\\y=\frac{-2}{5}x-\frac{12}{5}+\frac{4*5}{1*5}\\\\y=\frac{-2}{5}x-\frac{12}{5}+\frac{20}{5}\\\\y=\frac{-2}{5}x+\frac{8}{5}](https://tex.z-dn.net/?f=y%20-%204%20%3D%20%5Cfrac%7B-2%7D%7B5%7D%28x%20-%20%5B-6%5D%29%5C%5C%5C%5Cy%20-%204%20%3D%20%5Cfrac%7B-2%7D%7B5%7D%28x%20%2B%206%29%5C%5C%5C%5Cy%20-%204%20%3D%20%5Cfrac%7B-2%7D%7B5%7Dx%20%2B%206%2A%5Cfrac%7B-2%7D%7B5%7D%5C%5C%5C%5Cy%20%3D%20%5Cfrac%7B-2%7D%7B5%7Dx%20-%5Cfrac%7B12%7D%7B5%7D%2B4%5C%5C%5C%5Cy%3D%5Cfrac%7B-2%7D%7B5%7Dx-%5Cfrac%7B12%7D%7B5%7D%2B%5Cfrac%7B4%2A5%7D%7B1%2A5%7D%5C%5C%5C%5Cy%3D%5Cfrac%7B-2%7D%7B5%7Dx-%5Cfrac%7B12%7D%7B5%7D%2B%5Cfrac%7B20%7D%7B5%7D%5C%5C%5C%5Cy%3D%5Cfrac%7B-2%7D%7B5%7Dx%2B%5Cfrac%7B8%7D%7B5%7D)
Since E is the midpoint, DE and EF are the same length.
Set the equation DE and EF equal to each other and solve for x.
2x + 4 = 3x - 1
x = 5
Then plug in 5 to find the length.
DE = 2(5) + 4 = 14
EF = 3(5) - 1 = 14
DF = DE + EF = 28
Answer:
a) $520
b) $580
c) Interest amount is same each year
Step-by-step explanation:
Given - Georgie put $500 in her savings account, earning interest at a rate of 4% each year. She did not make any more deposits or withdrawals.
To find - a) How much money was in the account after one year?
b) How much money was in the account after 4 years?
c) Was the amount of money earned in interest the same or different each year?
Proof -
Here given that,
Principal amount = $500
rate of interest = 4% = 4/100 = 0.04
Now,
a)
Amount = P [ 1 + RT ]
= 500 [ 1 + 0.04(1)]
= 500 [ 1 + 0.04] = 520
⇒Amount = $520
b)
Amount = P [ 1 + RT ]
= 500 [ 1 + 0.04(4)]
= 500 [ 1 + 0.16] = 580
⇒Amount = $580
c)
In 2nd year,
Amount = P [ 1 + RT ]
= 500 [ 1 + 0.04(2)]
= 500 [ 1 + 0.08] = 540
⇒Amount = $540
Now,
Interest in 1st year = 520 - 500 = 20
Interest in 2nd year = 540 - 520 = 20
So,
The interest amount is same each year
Time taken by a regular bus to reach its destination = 3 1/4 hours
= 13/4 hours
Time taken by the express bus to make the same trip = 2 1/2 hours
= 5/2 hours
Time that can be saved by taking the express bus = (13/4) - (5/2) hours
= (13 - 10)/4 hours
= 3/4 hours
So 3/4 hours can be saved by taking the express bus rather than the regular bus. The correct option among all the options given in the question is option "C". I hope the procedure is simple enough for you to understand.
