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Kaylis [27]
3 years ago
6

Quadrilateral EFGH is on a coordinate plane. Segment FG is on the line 3x − y = −2, and segment EH is on the 3x − y = −6. Which

statement proves how segments FG and EH are related?
A) They have opposite reciprocals slopes of one third and −3 and are, therefore, perpendicular.

B) They have the same slope of negative one third and are, therefore, parallel.

C) They have opposite reciprocal slopes of negative one third and 3 and are, therefore, perpendicular.

D) They have the same slope of 3 and are, therefore, parallel.
Mathematics
1 answer:
TEA [102]3 years ago
6 0

Answer:

D) They have the same slope of 3 and are, therefore, parallel.

Step-by-step explanation:

Given:

Segment FG is on the line 3x − y = −2

Segment EH is on the line 3x − y = −6

Take equation of a line: y = mx + b

Where,

Slope = m

y-intercept = b

Segment FG : <em>3x - y = -2</em>

Solve for y:

y = 3x + 2

Thus, we have:

Slope = 3

y-intercept = 2

For segment EH: 3x - y = -6

Solve for y:

y = 3x + 6

Thus, we have:

Slope = 3

y-intercept = 6

Since both lines have the same slope of 3, they are parallel.

Option D

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The function composition exists an operation " ∘ " that brings two functions f and g, and has a function h = g ∘ f such that h(x) = g(f(x)).

Let the functions be f(x) = 4x² + 1 and g(x) = x² - 3

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<h3>What is composition function?</h3>

The function composition exists an operation " ∘ " that brings two functions f and g, and has a function h = g ∘ f such that h(x) = g(f(x)). In this operation, the function g exists used for the outcome of applying the function f to x.

Given:

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a) (f o g)(x) = f[g(x)]

f[g(x)] = 4(x² - 3)² + 1

substitute the value of g(x) in the above equation, and we get

    = 4(x⁴ - 24x + 9) + 1

simplifying the above equation

    = 4x⁴ - 96x + 36 + 1

    = 4x⁴ - 96x + 37

(f o g)(x) = 4x⁴ - 96x + 37

b) (g o f)(x) = g[f(x)]

substitute the value of g(x) in the above equation, and we get

g[f(x)] = (4x² + 1)²- 3

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simplifying the above equation

      = 16x⁴ + 8x² - 2

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Therefore, the correct answer is (f o g)(x) = 4x⁴ - 96x + 37 and

(g o f)(x) = 16x⁴ + 8x² - 2.

To learn more about the function refer to:

brainly.com/question/26709985

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