A dilation is a transformation
, with center O and a scale factor of k that is not zero, that maps O to itself and any other point P to P'.
The center O is a fixed point, P' is the image of P, points O, P and P' are on the same line.
In a dilation of
, the scale factor,
is mapping the original figure to the image in such a way that the
distances from O to the vertices of the image are half the distances
from O to the original figure. Also the size of the image is half the
size of the original figure.
Therefore, <span>If
is a dilation of △ABC, the truth about the image △A'B'C'</span> are:
<span>AB is parallel to A'B'.
The distance from A' to the origin is half the distance from A to the origin.</span>
Answer:
C
Step-by-step explanation:
Obviously this a log function. What you have to know about the parent graph of a log function is that it goes through the origin (0, 0). Ours appears to go through -1, so it has moved 1 unit to the left, and our appears to have moved up 3 units. The parent graph for the log function in standard form is
f(x) = log(x - h) + k.
where h indicates the side to side movement, and k represents the up and down movement. In our standard form, we fit in -1 as follows: (x - (-1)), which of course is equivalent to (x + 1). Because our function has moved up 3 units, our k is a positive 3. So the translation of the parent graph to what we see is
g(x) = log(x + 1) + 3, choice C
Answer: width = 5 units
Step-by-step explanation:
Let L represent the length of the rectangle.
The width of a rectangle is the length minus 2 units. It means that the width of the rectangle is (L - 2) units.
The formula for determining the area of a rectangle is expressed as
Area = length × width
The area of the rectangle is 35 units. It means that
L(L - 2) = 35
L² - 2L = 35
L² - 2L - 35 = 0
L² + 5L - 7L - 35 = 0
L(L + 5) - 7(L + 5) = 0
L - 7 = 0 or L + 5 = 0
L = 7 or L = - 5
Since the length cannot be negative, then
L = 7 units
Width = 7 - 2 = 5 units
Answer: The answer is going to be
120 x 65%/3
