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Answer:
B) 102 units
Step-by-step explanation:
The diagonals of a parallelogram bisect each other. This means ...
BE = ED
3 -9x = -8x +14
-11 = x . . . . . . . . . . . . add 9x -14
BE = 3 -9x = 3 -9(-11) = 3 +99
BE = 102 units
Answer: choice C) x-y <= 2
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Explanation:
The two points (0,-2) and (2,0) are on the boundary line. The boundary line equation is y = x-2. We find this equation through the use of the slope formula to find that m = 1. The y intercept is -2 so b = -2. Therefore, y = mx+b turns into y = 1x+(-2) which simplifies to y = x-2
The equation y = x-2 can be arranged to get x-y = 2 (subtract y from both sides; add 2 to both sides)
So the answer is either x-y <= 2 OR it is x-y >= 2
The question is: which inequality has the test point (0,0) in it? We pick on the origin since 0 is the easiest number to work with.
Plug (x,y) = (0,0) into the equation for choice C
x-y <= 2
0-0 <= 2
0 <= 2
which is true. So choice C is the answer.
Choice D can be ruled out since...
x-y >= 2
0-0 >= 2
0 >= 2
which is false: 0 is not larger or equal to 2
Answer:
![\displaystyle [8, -2]](https://tex.z-dn.net/?f=%5Cdisplaystyle%20%5B8%2C%20-2%5D)
Step-by-step explanation:
2x - 18 = x - 10
−8 = −x
[Plug this back into both equations above to get the y-coordinate of −2]; 
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Answer:
B. $200,000
Step-by-step explanation:
Let x be the amount placed at 5.5%
3x is the amount placed at 5%
This leaves the rest for the 4.5 % 500000- x - 3x = 500000-4x
Assuming simple interest
I = PRT where I is interest, P is principle, rate is rate and t is time
Interest for the 5.5% for 1 year is
I = x * .055 * 1 = .055x
Interest for the 5.% for 1 year is
I = 3x * .05 * 1 = .15x
Interest for the 4.5% for 1 year is
I = 500000-4x * .045 * 1 = 22500 - 0.18 x
Add the interest together to get the income for 1 year
.055x+ .15x+22500 - 0.18 x=25,000
Combine like terms
0.025x+22500=25000
Subtract 22500
.025x =2500
Divide by .025
x =100000
short term notes is 100000
3*x = 300000 = government bonds
The rest is utility bonds 500000- 100000-300000 = 100000
We want how much more in government bond than utility bond
300000 -100000 = 200000
