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3 years ago

Hexagon DEFGHI is translated on the coordinate plane below to create hexagon D'E'F'G'H'I':

Mathematics

2 answers:

SVETLANKA909090 [29]3 years ago

6 0

Answer:

(x, y)→(x − 8, y − 7)

Step-by-step explanation:

If we take the hexagon DEFGHI coordinates and apply the rule (x, y)→(x − 8, y − 7) we get:

D (2, 5) → (2 - 8, 5 - 7) = (-6, -2) which corresponds to point D'

E (5, 5) → (5 - 8, 5 - 7) = (-3, -2) which corresponds to point E'

F (6, 3) → (6 - 8, 3 - 7) = (-2, -4) which corresponds to point F'

G (5, 1) → (5 - 8, 1 - 7) = (-3, -6) which corresponds to point G'

H (2, 1) → (2 - 8, 1 - 7) = (-6, -6) which corresponds to point H'

I (1, 3) → (1 - 8, 3 - 7) = (-7, -4) which corresponds to point I'

valentina_108 [34]3 years ago

4 0

The first one is the correct answer

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If m (x) = StartFraction x + 5 Over x minus 1 EndFraction and n(x) = x – 3, which function has the same domain as (m circle n) (

Andrew [12]

Answer:

The function h (x) = StartFraction 11 Over x minus 4 EndFraction

has the domain of h (x) = ( - ∞, 4) U (4, ∞ ) which is same as the

domain of (m ∘ n)(x) = ( - ∞, 4) U (4, ∞ ).

Step-by-step explanation:

m (x) = StartFraction x + 5 Over x minus 1 and n(x) = x – 3

As m (x) could be written as:

$m(x) = \frac{x+5}{x-1}$

n(x) = x – 3

(m ∘ n)(x) = m(n(x)) = m(x – 3)

= $\frac{(x-3) + 5}{(x-3) - 1}$

= $\frac{x+2}{x-4}$

In order to find the domain of (m ∘ n)(x) = $\frac{x+2}{x-4}$ , we need to

make sure that denominator can not be zero,

So,

x - 4 = 0

x = 4

So, our domain can be anything except for 4.

Hence, Domain = D = ( - ∞, 4) U (4, ∞ )

Now, compare the domain of (m ∘ n)(x) i.e D = ( - ∞, 4) U (4, ∞ ) with all the options:

Option A: h (x) = x + 5 / 11

Option A has the Domain of h (x) = Set of all real numbers

So, Option A is false.

Option B: h (x) = 11 / x - 1

x - 1 = 0

x = 1

Option B has the domain of h (x) = ( - ∞, 1) U (1, ∞ )

So, Option B is false.

Option C: h (x) = 11 / x - 4

x - 4 = 0

x = 4

Domain C has the domain of h (x) = ( - ∞, 4) U (4, ∞ )

So, Option C is true.

Option D: h (x) = 11 / x - 3

x - 3 = 0

x = 3

Option D has the domain of h (x) = ( - ∞, 3) U (3, ∞ )

So, option D is also false.

Hence, only option C is true as the option C i.e. h (x) = StartFraction 11 Over x minus 4 EndFraction has the domain of h (x) = ( - ∞, 4) U (4, ∞ ) which is same as the domain of (m ∘ n)(x) = ( - ∞, 4) U (4, ∞ ).

keywords: Domain, composite function

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Answer:

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Step-by-step explanation:

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