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Answer:
a) C x +x +x +3x +3x = 18
b) x = 2
c) 2 cm, 6 cm
Step-by-step explanation:
a) The sum of the lengths of the sides is equal to the length of the perimeter. The appropriate equation is ...
x +x +x +3x +3x = 18
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b) Simplifying, the equation becomes ...
9x = 18
x = 2 . . . . . divide by 9
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c) The shorter sides are x = 2 cm.
The longer sides are 3x = 6 cm.
Answer:
Cylinder
(with radius of 4 units and height of 4 units)
Step-by-step explanation:
First, determine the shape of the 2D figure.
Point B is above point A, and point C is above point D.
Point A and B, and points C and D are on the same horizontal line.
Points A and B both have an x-value of zero.
Points C and D both have an x-value of 4.
Therefore, the width of the shape is 4 units
Points A and D have an y-value of zero.
Points B and C have an y-values of 4.
Therefore, the height of the shape is 4 units.
Therefore, the shape of the 2d figure is a square with side length of 4 unit. (See first attached image).
If the square is rotated above the y-axis, it creates a cylinder with a radius of 4 units and a height of 4 units. (See second attached image).
The shortest side is 130 feet, the longest side is 260 feet and the greatest possible area is 33800 square feet
<h3>What dimensions would guarantee that the garden has the greatest possible area?</h3>
The given parameter is
Perimeter, P = 520 feet
Represent the shorter side with x and the longer side with y
One side of the garden is bordered by a river:
So the perimeter is:
P = 2x + y
Substitute P = 520
2x + y = 520
Make y the subject
y = 520 - 2x
The area is
A = xy
Substitute y = 520 - 2x in A = xy
A = x(520 - 2x)
Expand
A = 520x - 2x^2
Differentiate
A' = 520 - 4x
Set to 0
520 - 4x = 0
Rewrite as:
4x= 520
Divide by 4
x= 130
Substitute x= 130 in y = 520 - 2x
y = 520 - 2 *130
Evaluate
y = 260
The area is then calculated as:
A = xy
This gives
A = 130 * 260
Evaluate
A = 33800
Hence, the shortest side is 130 feet, the longest side is 260 feet and the greatest possible area is 33800 square feet
Read more about area at:
brainly.com/question/24487155
#SPJ1
Answer:
The probability of getting heads on the toss of a coin is 0.5. If we consider all possible outcomes of the toss of two coins as shown, there is only one outcome of the four in which both coins have come up heads, so the probability of getting heads on both coins is 0.25. The second useful rule is the Sum Rule.
Okay so to represent juice we are going to use X, and to represent water we are going to use Y.
We also know that the first two starting equations are:
6x + y = 135
4x + 2y = 110
We can re-arrange the first equation so that it equals y (for now), so it is going to end up looking like this:
y = -6x +135
Now you can take that equation and plug into either one of the starting two equations. I chose the second equation. We just substitute what y equals in for y in the equation, so we have:
4x + 2(135 - 6x) = 110
Now solve
4x + 270 -12x = 110
-8x + 270 = 110
Subtract 270 from both sides
-8x = -160
Now divide by -8 on both sides
x = 20
We can now confirm that juice costs $20
Now lets plug that into the equation where we solved for y, to get the actual value of y.
y = 135 - 6(20)
y = 135 - 120
y = 15
The price of water costs $15
From this we can conclude that the cost of juice is $20 and the price of water is $15
