G(x) = 2 cos [2x (x+2π/3)] -5 With respect to the parent function F(x) = cos(x) What is the amplitude, period, phase shift, and vertical translation of the function G(x)?

The amplitude is 2

The period is π/x

The phase shift is -2π/3

The vertical translation is -5

Step-by-step explanation:

The equation of the given function is G(x) = 2·cos[2·x·(x + 2π/3)] - 5

Comparing with the general equation for the cosine function, y = d + a·cos(b·(x - c))

Where:

= The amplitude

2·π/b = The period

c = The phase shift

d = Vertical shift

Therefore, we have;

The amplitude = 2

The period = 2·π/(2·x) = π/x

The phase shift = -2π/3 (The sign is opposite to in sign to the sign following it in the parenthesis of the angle of rotation

-5 = The vertical translation of the function G(x)

rick has $1400 and sally has $1500

step-by-step explanation:

to find amount of money rick has after 10 years :

principal = $1000 , time = 10 years , rate = 4% annually

to find amount of money sally has after 10 years :

her friend gives to pay her $50 per year, therefore money she has after 10 years = 50 × 10 = $500

also, sally gets $1000 after 10 years,

therefore, total amount of money sally has after 10 years = 500 + 1000 = $1500

so, after 10 years : rick has $1400 and sally has $1500

answer: a video game has three difficulty levels: easy, medium, and expert. the game's scoring works in such a way that a player has to score a fixed number of points to advance to the next level, and then the scoring starts over. the total score needed to clear all three difficulty levels is 7,500. two times the number of points needed to clear the easy level is 500 more than the number of points needed to clear the medium level. twice the number of points needed to clear the medium difficulty level is 1,500 more than the number of points needed to clear the expert level. if x, y, and z represent the easy, medium, and expert levels, respectively, and a is the coefficient matrix of the system of equations modeling this situation, identify the inverse matrix, a-1, and the solution matrix, x, of the system of equations.

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