5. You have correctly shown the decimal equivalents of the numbers in selection C. Those are in order. The decimal equivalents for selection D would be
... -1.33, -2.00, -1.00, -0.08, -0.07
The first of these is greater than the second of these, so this list is not in order. The correct choice is D.
6. √169 = 13, the only rational number in the lot. The correct choice is C.
8. All the numbers except the ones with radicals are rational numbers, so the appropriate choice is the one that lists the radicals only: G.
9. You have correctly plotted the points. When you connect them to make a geometric figure, you get a triangle that is 6 units high and 6 units wide. Its area will be half that of a square that is 6×6, so is 18 square units.
_____
The formula for the area of a triangle is
... A = (1/2)bh
where b is the base length of the triangle (6 units), and h is the height (6 units). Filling in the numbers you have, this is
... A = (1/2)·6·6 = 18 . . . . square units.
When you have a plot like this on a graph, it is usually pretty easy to see that the triangle area is half the area of a rectangle (or square) with the same height and width.
Cost per meter(C) = $60/m
Length of rectangular field(L) = 50m
L = 2W
-> W = L/2
-> W = 50/2
-> Width of rectangular field = 25m
Cost of one field length(l) = L x C
-> l = 50 x 60
-> l = $3000
Two of the lengths of the field = 2 x l
-> 2 x $3000
-> $6000
Cost of one field width(w) = W x C
-> w = 25 x 60
-> w = $1500
Two of the widths of the field = 2 x w
-> 2 x $1500
-> $3000
Cost of fencing entire field = $6000+$3000
Hence, total field cost = $9000
Exponent rule : a^-b = 1 / a^b
52^-5 =
1 / 52^5 =
1 / (52 * 52 * 52 * 52 * 52)
