Answer:
Step-by-step explanation:
1)
First we add what we know for y into the second equation.
5x - 4(x +2)= -3
From there, we simplify it
5x-4x-8= -3
x-8=-3
Now we get the x on its own
x=5
and now we add x=5 into the first equation that we had and simplify to find y
y=5+2
y=7
So the answer is x=5, y=7 or (5,7)
2)
For this one we do the same thing as with 1.
Add what we know for y (bottom equation) to the top equation
3x-8(x-8)=24
Now we simplify
3x-8x+64=24
-5x+64=24
And now solve for X
-5x=-40
x=8
And then substitute x=8 to find y
y=8=8
y=0
So the answer is x=8, y=0 or (8,0)
Potential Energy of an object of 5kg which is 6 meters in height is 294 Joules.
Step-by-step explanation:
We are given:
Mass = m = 5 kg
Height = h= 6 meters
Potential Energy = ?
The formula used to find Potential Energy is:

where m is mass, g is gravitational field and h is height
Putting the given values of mass and height, and g=9.8 m/s^2

So, Potential Energy of an object of 5kg which is 6 meters in height is 294 Joules.
Keywords: Potential Energy
Learn more about Potential Energy at:
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Answer:
A: 5
B: 6
C: 3x^2 - 2x
D: 8
E: 22
Step-by-step explanation:
A: (-1)^2 + 4 = 5
B: (-4)^2 +4 = 16
2 x (-3) -4 = -10,
16-10=6
C: 3(x^2 + 4) = 3x^2 + 12
3x^2 + 12 -2x -4, simplify
3x^2 - 2x
D: g(3) = 2*3 -4 = 2
f(2) = 2^2 +4 = 8
E: f(3) = 3^2 + 4 = 13
g(13) = 2*13 - 4 = 22
So there are 12 inches in a foot. What to do:
1) divide 200 by 12 which is roughly 16.6666 repeating
2) now we know that the average car length is at least 16 feet, but less than 17
3) What I do now, is I take 12 and multiply it by 16
12 x 16 = 192
4) 200-192 = 8
5) 16 feet and 8 inches is the answer
Answer:
The length and width of the plot that will maximize the area of the rectangular plot are 54 ft and 27 ft respectively.
Step-by-step explanation:
Given that,
The length of fencing of the rectangular plot is = 108 ft.
Let the longer side of the rectangular plot be x which is also the side along the river side and the width of the rectangular plot be y.
Since the fence along the river does not need.
So the total perimeter of the rectangle is =2(x+y) -x
=2x+2y-y
=x+2y
So,
x+2y =108
⇒x=108 -2y
Then the area of the rectangle plot is A = xy
A=xy
⇒A= (108-2y)y
⇒ A = 108y-2y²
A = 108y-2y²
Differentiating with respect to x
A'= 108 -4y
Again differentiating with respect to x
A''= -4
For maximum or minimum, A'=0
108 -4y=0
⇒4y=108

⇒y=27.

Since at y= 27, A''<0
So, at y=27 ft , the area of the rectangular plot maximum.
Then x= (108-2.27)
=54 ft.
The length and width of the plot that will maximize the area of the rectangular plot are 54 ft and 27 ft respectively.