Examine the word PROBABILITY, if a letter is picked at random, find probability that 13 was picked. The number picked did not in
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Answer:
see attached
Step-by-step explanation:
Dilation is the transformation that changes the size of something. When you choose ×110% on a copy machine, you are making all the dimensions in the copy equal to 1.1 times the dimensions of the original, for example. That is dilation by a factor of 1.1, or 110%.
Here, you're asked to dilate triangle ABC by a factor of 3. That means all of the dimensions on the dilated figure will be 3 times their length on the original.
The center of dilation is point P. That means all the distances from point P are multiplied by 3.
In the attached figure, a gray arrow has been drawn from point P to each of the points A, B, and C. Then two more arrows of the same length are drawn in the same direction. The total distance at the end of the 3 arrows is 3 times the original distance from point P. These are the points A', B', and C' you are asked to draw. Connecting these points gives the dilated triangle A'B'C'.
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You could think of point P (the center of dilation) as having coordinates (0, 0). Then points A, B, and C would have coordinates A(-4, 0), B(0, -3), and C(-4, -3). To dilate these points by a factor of 3, multiply each coordinate value by 3: A'(-12, 0), B'(0, -9), C'(-12, -9). You will see that these are the coordinates of the vertices of the dilated triangle.
Consider the exponential function
By definition, the domain of a function is the set of input argument values for which the function is real and defined.
Let we take then
then
then
If we chose larger values of x, we get larger function values.
For example, If we take
Thus if we choose smaller and smaller values of x. the f unction values will be smaller and smaller functions.
Thus the domain of the function is the set of all real numbers.
Thus the range is limited to the set of positive real numbers. That is,
If we choose larger values of x, we will get larger function values, as the function values will be larger powers of 2.
If we choose smaller and smaller x values, the function values will be smaller and smaller fractions.