Mrs. Arnold asked her 30 Geometry students who owned a pet. 16 students own a dog, 12 students have a cat and 6 students did not
have a cat or a dog. Thomas wrote the information in a Venn diagram but made an error. Explain where the error occurred.
2 answers:
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Given:
The two functions are:
To find:
The type of transformation from f(x) to g(x) in the problem above and including its distance moved.
Solution:
The transformation is defined as
.... (i)
Where, a is horizontal shift and b is vertical shift.
- If a>0, then the graph shifts a units left.
- If a<0, then the graph shifts a units right.
- If b>0, then the graph shifts b units up.
- If b<0, then the graph shifts b units down.
We have,
The function g(x) can be written as
...(ii)
On comparing (i) and (ii), we get
Therefore, the type of transformation is translation and the graph of f(x) shifts 2 units up to get the graph of g(x).
Answer:
CD ≈ 26.0 cm
Step-by-step explanation:
using the sine ratio in right triangle ABD
sin35° = =
=
( multiply both sides by BD )
BD × sin35° = 12 ( divide both sides by sin35° )
BD = ≈ 20.92 cm
using the sine rule in Δ BCD
=
, that is
=
( cross- multiply )
CD × sin52° = 20.92 × sin102° ( divide both sides by sin52° )
CD = ≈ 26.0 cm ( to 3 significant figures )