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2 years ago

Which unit rate corresponds to the proportional relationship shown in the graph?

Mathematics

1 answer:

Y_Kistochka [10]2 years ago

6 0

To move from the point (0,0) to the point (6,9) we move up 9 units and right 6 units.

Slope = rise/run
Slope = change in y / change in x
Slope = 9 / 6
Slope = 3/2

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One month Tammy rented 2 movies and 6 video games for a total of $ 42 . The next month she rented 5 movies and 3 video games for

EastWind [94]

Answer:

The rental cost of one movie is $2.25 and the rental cost of one video game is $6.25

Step-by-step explanation:

Let the rental cost of 1 movie be m.

Let the rental cost of 1 video game be v.

One month, Tammy rented 2 movies and 6 video games for a total of $42. This means that:

2m + 6v = 42 ________ (1)

The next month she rented 5 movies and 3 video games for a total of $30. This means that:

5m + 3v = 30 _________(2)

We now have two simultaneous equations:

2m + 6v = 42 ________ (1)

5m + 3v = 30 _________(2)

Multiply (2) by 2, and we have:

2m + 6v = 42 __________ (1)

10m + 6v = 60 _________ (3)

Subtract (1) from (3):

10m + 6v = 60

- 2m + 6v = 42

8m = 18

=> m = 18 / 8

m = $2.25

Put the value of m back in (1):

2(2.25) + 6v = 42

4.5 + 6v = 42

=> 6v = 42 - 4.5 = 37.5

v = 37.5 / 6

v = $6.25

Therefore, the rental cost of one movie is $2.25 and the rental cost of one video game is $6.25

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3 years ago

Finding Derivatives Implicity In Exercise, find dy/dx implicity. x2 - 3 ln y + y2 = 10

Veseljchak [2.6K]

Answer:

$\frac{dy}{dx}=-\frac{2xy}{2y^2-3}$

Step-by-step explanation:

We are given that

$x^2-3lny+y^2=0$

Differentiate w.r.t x

$2x-\frac{3}{y}\frac{dy}{dx}+2y\frac{dy}{dx}=0$

By using formula

$\frac{dx^n}{dx}=nx^{n-1}$

$\frac{d(lnx)}{dx}=\frac{1}{x}$

$\frac{dy^n}{dx}=ny^{n-1}\frac{dy}{dx}$

$\frac{dy}{dx}(-\frac{3}{y}+2y)+2x=0$

$\frac{dy}{dx}(-\frac{3}{y}+2y)=-2x$

$\frac{dy}{dx}=-\frac{2x}{-\frac{3}{y}+2y}$

$\frac{dy}{dx}=-\frac{2xy}{2y^2-3}$

Hence, the derivative of function

$\frac{dy}{dx}=-\frac{2xy}{2y^2-3}$

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3 years ago