1) Which expression represents the area of the frame in square inches?

Mathematics

1 answer:

yawa3891 [41]3 years ago

3 0

12^2 - s^2 is area of the large square minus area of the smaller square. It's the only correct option.

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A parabola has a vertex at (4, 0) and passes through the point (6, 1). Which of the following is the equation of this parabola i

Doss [256]

Easy

y=a(x-h)^2+k
vertex is (h,k)
we know that vertex is (4,0)
input that point for (h,k)
y=a(x-4)^2+0
y=a(x-4)^2
passes thorugh the point (6,1)
input that point to find a
1=a(6-4)^2
1=a(2)^2
1=a(4)
divide both sides by 4
1/4=a

thefor the equation is
y=(1/4)(x-4)^2
or
y=(1/4)x^2-2x+4

7 0

3 years ago

Please show full solutions! WIll Mark Brainliest for the best answer. <br><br> SERIOUS ANSWERS ONLY

Ierofanga [76]

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.