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alina1380 [7]
3 years ago
11

Suppose the function f(x) = 0.035x represents the number of U.S. dollars equivalent to x Russian rubles, and the function g(x) =

90x represents the number of Japanese yen equivalent to x U.S. dollars. Write a composite function that represents the number of Japanese yen equivalent to x Russian rubles. Show your work.
Mathematics
1 answer:
const2013 [10]3 years ago
4 0

Answer:

g(f(x)) = 3.15x

Step-by-step explanation:

To find the number of Japanese yen equivalent to x russian rubles, we need to put one function into another.

If we take f(x) and put in into g(x), we will get Japanese yen in terms of rubles. Thus,

g(f(x)) = 90 (0.035x)

g(f(x)) = 3.15x

THis is the composite function which represents the number of Japanese yen equivalent to x Russian Rubles.

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Part 1: Identify the vertex, focus, and directrix of each. Then sketch the graph.
Lina20 [59]

Answer:  \bold{1.\quad \text{Vertex}:(4,-1)\qquad \text{Focus}:\bigg(4,-\dfrac{9}{8}\bigg)\qquad \text{Directrix}:y=-\dfrac{7}{8}}

                \bold{2.\quad \text{Vertex}:(2,1)\qquad \text{Focus}:\bigg(\dfrac{9}{4},1\bigg)\qquad \text{Directrix}:y=\dfrac{7}{4}}            

<u>Step-by-step explanation:</u>

The vertex form of a parabola is y = a(x - h)² + k  or  x = a(y - k)² + h

  • (h, k) is the vertex
  • p is the distance from the vertex to the focus
  • -p is the distance from the vertex to the directrix

    \bullet\quad a=\dfrac{1}{4p}

1) y = -2(x - 4)² - 1     →      a = -2   (h, k) = (4, -1)

a=\dfrac{1}{4p}\quad \rightarrow \quad -2=\dfrac{1}{4p}\quad \rightarrow \quad p=-\dfrac{1}{8}\\\\\text{Focus = Vertex + p}\\\\.\qquad = \dfrac{-8}{8}+\dfrac{-1}{8}\\\\.\qquad =-\dfrac{9}{8}\qquad \rightarrow \qquad \text{Focus}=\bigg(4,-\dfrac{9}{8}\bigg)\\\\\\\text{Directrix: y=Vertex - p}\\\\.\qquad \qquad y=\dfrac{-8}{8}-\dfrac{-1}{8}\\\\.\qquad \qquad y=-\dfrac{7}{8}

*******************************************************************************************

2) x = (y - 1)² + 2     →      a = 1   (h, k) = (2, 1)

a=\dfrac{1}{4p}\quad \rightarrow \quad 1=\dfrac{1}{4p}\quad \rightarrow \quad p=-\dfrac{1}{4}\\\\\text{Focus = Vertex + p}\\\\.\qquad = \dfrac{8}{4}+\dfrac{1}{4}\\\\.\qquad =\dfrac{9}{4}\qquad \rightarrow \qquad \text{Focus}=\bigg(\dfrac{9}{4},1\bigg)\\\\\\\text{Directrix: x=Vertex - p}\\\\.\qquad \qquad x=\dfrac{8}{4}-\dfrac{1}{4}\\\\.\qquad \qquad x=\dfrac{7}{4}

6 0
3 years ago
How long does it take for a car traveling at a speed of 50.0 miles per hour to travel 300 feet?
beks73 [17]
We know, Time = distance / speed
t = 0.0568182 / 50  [ 300 Feet = 0.0568182 miles ]
t = 0.001136 * 3600 s
t = 4.09 sec

In short, Your Answer would be 4.09 Seconds

Hope this helps!
3 0
3 years ago
Write the equation 2x-3y=6 in the slope-intercept form
Snowcat [4.5K]
Y= 2/3x-2

-3y= -2x+6
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3 years ago
Question 2 (5 points) Saved
ratelena [41]

Answer:

(1, -1/2)

Step-by-step explanation:

7x - 2y = 8

5x + 2y = 4

I would use elimination to get rid of y

Add the two equations together

7x - 2y = 8

5x + 2y = 4

-------------------------

12x = 12

Divide each side by 12

x =1

Now find y

5x+2y = 4

5*1 +2y =4

Subtract 5 from each side

5+2y -5 = 4-5

2y = -1

Divide by 2

2y/2 =-1/2

y = -1/2

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The doctor prescribed Mrs.Larson 5 milliliters of medicine each day for 3 days.How many milliliters of medicine will she take al
aleksandr82 [10.1K]

Answer: 15

Step-by-step explanation: so you take the 5 ( or 3 it doesn’t matter In multiplication) and just add the 5 3 times. So 5+5+5 which is 15

5 0
3 years ago
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