Alice walks along a road which can be modeled by the equation y=6x, where (0,0) represents her starting point. When she reaches a certain point A, she turns right, so that she is traveling perpendicular to the original road, until she stops at the point (333,0). What was the point A where Alice turned?

9514 1404 393

  (9, 54)

Step-by-step explanation:

The first road has a slope of 6 on its graph. So, the perpendicular road will have a slope of -1/6, the negative reciprocal of the slope of the original road. Translating that from y=-1/6x the the right by 333 units, the equation of the second road is ...

  y = -1/6(x -333)

The point where Alice turned is the point of intersection of these two equations:

Substituting for y, we have ...

  6x = -1/6(x -333)

  36x = -x +333 . . . . . multiply by 6, eliminate parentheses

  37x = 333 . . . . . . . .  add x

  x = 9 . . . . . . .  divide by 37

So, the point where Alice turned is ...

  (x, y) = (9, 6·9)

  (x, y) = (9, 54)

the correct functions are

h(x) = 3x + 2  

g(x) = 2^x

step-by-step explanation:

i proceed to calculate the different values ​​of k (x)

case 1)  k(x) = g(x) ∘ h(x)

g(x) ∘ h(x)=g(h(x))

k(x) = [2]^[3x + > is the option  4. k(x) = 2^(3x + 2 )

case 2)  k(x) = g(x) + h(x)

k(x) = [2^x]+[3x + 2]=2^x+3x+> is the option  1.) k(x) = 2^x + 3x + 2

case 3)k(x) = h(x) ÷ g(x)

k(x) =  [3x + 2]/[2^x]=3x/(2^x)+2/(2^x)=3x*(2^-x)+2^(1-x)

is the option  3.)   k(x) = (3x)2^(-x) + 2^(-x + 1 )

case 4)k(x) = g(x) - h(x)

k(x) =  [2^x]-[3x + 2]=2^x-3x-> is the option  2.) k(x) = 2^x - 3x - 2 

case 5)  k(x) = g(x) × h(x)

k(x) = [2^x]*[3x + > is the option  5.) k(x) = 2^x(3x + 2)

case 6)k(x) = h(x) ∘ g(x)

h(x) ∘ g(x)=h(g(x))

k(x)=3*[2^x]+> is the option  6. k(x) = 3(2^x) +2

required rate of return = 0.166 = 16.6%

step-by-step explanation:

under the capital asset pricing model (capm), the required or expected rate of return for a particular security or asset is given using the formula:

required rate of return = risk-free rate + beta*(market risk premium)

we are given that;

risk-free rate = 4% = 0.04

beta = 1.4

market risk premium = 9% = 0.09

we simply plug these values into the above formula;

required rate of return = 0.04 + 1.4*(0.09)

required rate of return = 0.04 + 0.126

required rate of return = 0.166 = 16.6%