Ashley is the oldest of four siblings whose ages are consecutive even integers. If the sum of their ages is 100, find Ashley's a
1 answer:
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Answer:
Width = 6.5 inches
Length = 10.5 inches
Step-by-step explanation:
Let
"l" be length of rectangle
and
"w" be width of rectangle
Since length of rectangle is 4 inches MORE THAN WIDTH, we can write:
l = 4 + w
The perimeter is sum of all sides, so
Perimeter = l + l + w + w = 2l + 2w
The perimeter is 34, so we can write:
2l + 2w = 34
Putting 1st equation in 2nd, we get equation in "w" and solve for this first:
Width is 6.5 in
Now, l = 4 + w, so
l = 4 + 6.5 = 10.5
Length is 10.5 in
Answer:
Options 2, 4 and 6 are True.
Step-by-step explanation:
Triangle MNO is dilated by a scale factor of centered at M(0, 6).
Rule to be followed to dilate the vertices of the given triangle,
(x, y) → (kx, ky)
Here, k = scale factor
By this rule vertices of the new triangle M'N'O' will be,
M(0, 6) → M'(0, 6) [Coordinates of M' will remain same as M because center of dilation is point M]
N(-4, -4) → N'(-6, -6)
O(6, -2) → O'(9, -3)
Option 1
M'N' is shorter than MN
Distance between M and N =
= 10.77
Distance between M' and N' =
= 13.42
Therefore M'N' > MN
Therefore, Option A is False.
Option 2
ON is shorter than O'N'
True.
Option 3
OM is longer than O'M'
False
Option 4
ON is parallel to O'N'
Since OM and MN are dilated with the same scale factor, O'N' will be parallel to ON.
True.
Option 5
OM is parallel than O'M'
Since, O'M' is the dilated form of OM,
Therefore, all the points (O, M and M') will be in a straight line.
False
Option 6
M'N' coincide with MN
True.
Therefore, Options 2, 4 and 6 are True.