Let
x-----> the length of rectangle
y-----> the width of rectangle
we know that
perimeter of rectangle=2*[x+y]
perimeter of rectangle=82 m
82=2*[x+y]---> divide by 2 both sides---> 41=x+y--> y=41-x---> equation 1
Area of rectangle=x*y
substitute equation 1 in the area formula
Area=x*[41-x]----> 41x-x²
using a graph tool
see the attached figure
the vertex is the point (20.5,420.25)
that means
for x=20.5 m ( length of rectangle)
the area is 420.25 m²
y=420.25/20.5----> 20.5 m
the dimensions are
20.5 m x 20.5 m------> is a square
the answer part 1) <span>
the dimensions of the rectangular with Maximum area is a square with length side 20.5 meters</span>
Part 2)<span>b) Suppose 41 barriers each 2m long, are used instead. Can the same area be enclosed?
</span>divide the length side of the square by 2
so
20.5/2=10.25--------> 10 barriers
the dimensions are 10 barriers x 10 barriers
10 barriers=10*2---> 20 m
the area enclosed with barriers is =20*20----> 400 m²
400 m² < 420.25 m²
so
the answer Part 2) is
<span>the area enclosed by the barriers is less than the area enclosed by the rope
</span>
Part 3)<span>How much more area can be enclosed if the rope is used instead of the barriers
</span>
area using the rope=420.25 m²
area using the barriers=400 m²
420.25-400=20.25 m²
the answer part 3) is20.25 m²
Answer:
C
Step-by-step explanation:
If you add the first equation up you get 2z+6 by combining like terms
if you see A a is equal to 3z+6 so a doesn’t work
If you look at B b is equal to z+12 so b doesn’t work
finally C if you distibute it out you get 2(z)+2(3) which equal 2z+6 which works
C
Okay, as you know, adding a positive and a positive gives you a bigger positive number. e.g 21 + 19 = 40.
Subtracting a positive from a positive might give you a negative number or a smaller positive number. e.g 21 - 19 = 2 or 20 - 24 = -4. That's simple, we all learned this! :)
Adding two negatives (e.g -4 + -5) will always give you a negative number. To make it easier, just think of the numbers only (4, 5), add them together, and then just put a negative sign by the answer (e.g 4 + 5 = 9 so put - to make -9).
Subtracting two negatives can be a bit tricky! When we say, for example, -5 - -4, we must turn the negative number that was to the right of the minus ( -4) into a positive number! So now it becomes -5 +4 ! And then you get your answer. (which is -1).
Adding a positive to a negative can give you a positive or a negative answer. It just depends which number is "bigger". E.g -20 + 31. << 31 is the "bigger" number, and it is a positive, so we know that our answer will be positive. E.g -20 + 9. << 20 is the "bigger" number (even though it's a negative but forget about that) and it is negative, so we know that our answer will be negative.
Adding a negative to a positive can give you a negative or a positive answer. Like I said, it depends on which number is "bigger". e.g 20 + -9 . We can just remove the + sign and it now becomes 20 -9, which is easier to understand. 20 is the bigger number, and it is positive, so we get a positive answer. e.g 20 + -30 becomes 20 -30 and -30 is the "bigger" number and it is negative, so we'll get a negative answer.
Subtracting a negative from a positive does the thing I mentioned earlier: e.g 20 - -9. The -9 is right of the minus sign and becomes positive: 20 +9! :)
Subtracting a positive from a negative, like I said, depends on which number is "bigger". e.g -30 - 9 (we know 9 is positive even though we don't show the + sign). Now, to make it simple, just block out the - sign by the 30 so it becomes 30 - 9. You know what that answer is: 21. But because -30 is "bigger", and it is a negative number, the answer will be negative so it's -21. E.g -30 - 42 << Block out the - sign by the 30, and 42 is the "bigger" number, so the answer will be a positive. Just look at the difference between "bigger" number and the smaller number (without signs) . That'll give your answer. 42 - 30 = 12. 42 was the "bigger" number and a positive, and we looked at the difference. :)