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3 years ago

Please help me on this math problem

Mathematics

1 answer:

Fed [463]3 years ago

7 0

We know the first term is 16, because f(1) = 16. Next, we can use the recursive rule provided. f(3)=1/2*f(3-1). This gives us f(3)=1/2*f(2). We know f(2) is 8. We know have f(3)=1/2*8. This is 4.

The answer is 16, 4.

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Under a certain transformation T, AA'BC' is the image of AABC. The perimeter of AA'B'C' is twice the perimeter of ABC. What kind

Anika [276]

The dimensions of the image are twice the dimensions of the preimage,

which indicates that the transformation is a dilation.

The transformation T is; a dilation transformation with a scale factor of 2, D₂

Reasons:

The transformation applied to ΔABC = T

The image of ΔABC following the transformation, T = ΔA'B'C'

The perimeter of ΔA'B'C' = Twice the perimeter of ΔABC

Therefore, we have;

A'B' + B'C' + A'C' = 2 × (AB + BC + AC)

Which gives

A'B' + B'C' + A'C' = 2·AB + 2·BC + 2·AC

By similar triangles, we have the ratio of corresponding sides as follows;

$\displaystyle \frac{AB}{A'B'} = \frac{BC}{B'C'} = \mathbf{ \frac{AC}{A'C'}}$

Which gives;

$\displaystyle \frac{AB}{A'B'} = \frac{AB}{2 \cdot AB} = \frac{1}{2}$

A'B' = 2·AB

Therefore;

Triangle ΔA'B'C' is twice the dimension of triangle ΔABC, and T is a dilation transformation with a scale factor of 2, D₂

Learn more about dilation transformation here:

brainly.com/question/2458912

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2 years ago