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Artist 52 [7]
3 years ago
6

If f(x) = 2x2 and g(x)= x2 + 2x, which expression represents f(g(x))?

Mathematics
1 answer:
andre [41]3 years ago
7 0

Answer:

f(g(x)) = 2(x^2 + 2x)^2

f(g(x)) = 2x^4 + 8x^3 + 8x^2

Step-by-step explanation:

Given;

f(x) = 2x^2

g(x) = x^2 + 2x

To derive the expression for f(g(x)), we will substitute x in f(x) with g(x).

f(g(x)) = 2(g(x))^2

f(g(x)) = 2(x^2 + 2x)^2

Expanding the equation;

f(g(x)) = 2(x^2 + 2x)(x^2 + 2x)

f(g(x)) = 2(x^4 + 2x^3 + 2x^3 + 4x^2)

f(g(x)) = 2(x^4 + 4x^3 + 4x^2)

f(g(x)) = 2x^4 + 8x^3 + 8x^2

Hope this helps...

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The equation g(x) in vertex form of a  quadratic function for the transformations  whose graph is a  translation 4 units left and 1 unit up of the  graph of f(x) is (x-4)² + 1

Given a  quadratic function for the transformations given  the function f(x) = x²

If the function g(x) of the graph is translated 4 units to the left, the equation becomes (x-4)² (note that we subtracted 4 from the x value

  • Translating the graph 1 unit up will give the final function g(x) as (x-4)² + 1 (We added 1 since it is an upward translation.)

Hence the equation g(x) in vertex form of a  quadratic function for the transformations  whose graph is a  translation 4 units left and 1 unit up of the  graph of f(x) is (x-4)² + 1

Learn more here: brainly.com/question/15381183

8 0
2 years ago
he Statue of Liberty is approximately 305 feet tall. If the angle of elevation of a ship to the top of the statue is 22.9 degree
Andru [333]

Answer:

is at a distance of 722 feet

Step-by-step explanation:

we have the angle that forms between the water and the imaginary line between the ship and the tip of the statue

we have the statue height that would be the opposite leg to our angle and we want to know the distance of the ship to the statue that would be the adjacent leg

we see that it has (angle, adjacent, opposite)

well to start we have to know the relationship between angles, legas and the hypotenuse

a: adjacent

o: opposite

h: hypotenuse

sin α = o/h

cos α= a/h

tan α = o/a

it's the tangent

tan α = o/a

we replace the values ​​and solve

tan α = o/a

tan 22.9 = 305/a

a = 305/tan22.9

a = 305/0.4224

a = 722

is at a distance of 722 feet

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