It should open up because the a which is 4 is positive
Answer:
7.36 cm²
Step-by-step explanation:
What is the area of a triangle whose base measures 3.2 centimeters and whose height is 4.6 centimeters.
The formula for the area of a triangle is given as:
1/2 × Base × Height
Base = 3.2 cm
Height = 4.6 cm
Hence,
Area of the triangle = 1/2 × 3.2 × 4.6
= 7.36 cm²
Answer:
Step-by-step explanation:
Answer:
- vertical scaling by a factor of 1/3 (compression)
- reflection over the y-axis
- horizontal scaling by a factor of 3 (expansion)
- translation left 1 unit
- translation up 3 units
Step-by-step explanation:
These are the transformations of interest:
g(x) = k·f(x) . . . . . vertical scaling (expansion) by a factor of k
g(x) = f(x) +k . . . . vertical translation by k units (upward)
g(x) = f(x/k) . . . . . horizontal expansion by a factor of k. When k < 0, the function is also reflected over the y-axis
g(x) = f(x-k) . . . . . horizontal translation to the right by k units
__
Here, we have ...
g(x) = 1/3f(-1/3(x+1)) +3
The vertical and horizontal transformations can be applied in either order, since neither affects the other. If we work left-to-right through the expression for g(x), we can see these transformations have been applied:
- vertical scaling by a factor of 1/3 (compression) . . . 1/3f(x)
- reflection over the y-axis . . . 1/3f(-x)
- horizontal scaling by a factor of 3 (expansion) . . . 1/3f(-1/3x)
- translation left 1 unit . . . 1/3f(-1/3(x+1))
- translation up 3 units . . . 1/3f(-1/3(x+1)) +3
_____
<em>Additional comment</em>
The "working" is a matter of matching the form of g(x) to the forms of the different transformations. It is a pattern-matching problem.
The horizontal transformations could also be described as ...
- translation right 1/3 unit . . . f(x -1/3)
- reflection over y and expansion by a factor of 3 . . . f(-1/3x -1/3)
The initial translation in this scenario would be reflected to a translation left 1/3 unit, then the horizontal expansion would turn that into a translation left 1 unit, as described above. Order matters.
Answer:
Area = 15.36 ft
Step-by-step explanation:
First find the area of the dotted line triangle using the formula: base x height x 1/2, which would be 1.2ft x 12.8 x 1/2 = 7.68ft.
Next, add another triangle at the top, mirroring the shown triangle, of the parallelogram.
Then, find the area of the shape as though it were a rectangle. (base x height) - 2.4 x 12.8 = 30.72.
Next, multiply the area of the invisible triangle by 2, 7.68 x 2 = 15.36ft
and Finally, subtract the area of the rectangle shape of the the sum of the two invisible triangles, 30.72 - 15.36 = 15.36ft
The area of the parallelogram is 15.36 ft.