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nignag [31]
3 years ago
15

If fx = 3x over 5 +3 which of the following is the inverse

Mathematics
1 answer:
Alborosie3 years ago
3 0

Answer:

f^(-1)(x) = -3x/(3x-3)

Step-by-step explanation:

1) replace f(x) by y

● y = 3x/(5x+3)

2) exchange x and y

● y = 3x/(5x+3)

● x = 3y / (3y +3)

3) solve for y

● x = 3y / (3y +3)

● x (3y +3) = 3y

● 3xy + 3x = 3y

● 3xy - 3y = -3x

● y (3x - 3) = -3x

● y = -3x /(3x-3)

4) replace y with f^(-1)(x)

● y = -3x/(3x-3)

● f^(-1)(x) = -3x/(3x-3)

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Please answer this correctly
Contact [7]

Answer:

3 4, 5 0 6

Step-by-step explanation:

88,946 - 54,440 = 34,506

So missing number :

3 4, 5 0 6

8 0
3 years ago
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The areas of two similar rectangles are 180 ft.² and 320 ft.². What scale factor applied to the smaller rectangle will give the
grigory [225]
The ratio of areas is the square of the scale factor, so that factor is
  √(320/180) = 4/3
8 0
3 years ago
Find the length of line segmentAB which joins the following points.A(10, 14) and B(2,6)​
Helen [10]

Answer:

The equation of the line AB is  y - x -4 = 0

Step-by-step explanation:

The points are A (10,14) and B(2,6)

Now, slope of the line AB :  m = \frac{y_2 - y_1}{x_2 - x_1}

or, m = \frac{14 -6 }{10 - 2} = \frac{8}{8}  = 1

So, slope of the equation AB = 1

Now, by SLOPE INTERCEPT FORM:

The equation of line is given as :    y - y0 = m (x-x0)

So,the equation of line AB is  y - 6 = 1(x-2)

or, y - 6 -x + 2 = 0

or, y - x -4 = 0

Hence, the equation of the line AB is  y - x -4 = 0

5 0
2 years ago
Given the sequence 1/2 ; 4 ; 1/4 ; 7 ; 1/8 ; 10;.. calculate the sum of 50 terms
miv72 [106K]

<u>Hint </u><u>:</u><u>-</u>

  • Break the given sequence into two parts .
  • Notice the terms at gap of one term beginning from the first term .They are like \dfrac{1}{2},\dfrac{1}{4},\dfrac{1}{8} . Next term is obtained by multiplying half to the previous term .
  • Notice the terms beginning from 2nd term , 4,7,10,13 . Next term is obtained by adding 3 to the previous term .

<u>Solution</u><u> </u><u>:</u><u>-</u><u> </u>

We need to find out the sum of 50 terms of the given sequence . After splitting the given sequence ,

\implies S_1 = \dfrac{1}{2},\dfrac{1}{4},\dfrac{1}{8} .

We can see that this is in <u>Geometric</u><u> </u><u>Progression </u> where 1/2 is the common ratio . Calculating the sum of 25 terms , we have ,

\implies S_1 = a\dfrac{1-r^n}{1-r} \\\\\implies S_1 = \dfrac{1}{2}\left[ \dfrac{1-\bigg(\dfrac{1}{2}\bigg)^{25}}{1-\dfrac{1}{2}}\right]

Notice the term \dfrac{1}{2^{25}} will be too small , so we can neglect it and take its approximation as 0 .

\implies S_1\approx \cancel{ \dfrac{1}{2} } \left[ \dfrac{1-0}{\cancel{\dfrac{1}{2} }}\right]

\\\implies \boxed{ S_1 \approx 1 }

\rule{200}2

Now the second sequence is in Arithmetic Progression , with common difference = 3 .

\implies S_2=\dfrac{n}{2}[2a + (n-1)d]

Substitute ,

\implies S_2=\dfrac{25}{2}[2(4) + (25-1)3] =\boxed{ 908}

Hence sum = 908 + 1 = 909

7 0
3 years ago
A movie collector has 105 movie posters and 90 band posters if she sells 21 movie posters then how many band posters should she
kotykmax [81]

Hi there! :)

<u>Answer:</u>

In order to maintain the same ratio, she should sell 18 band posters.


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

<u>Initial ratio:</u>

Ratio is: 105 movie posters for 90 band posters = <u>105 : 90</u>


She sells 21 movie posters, which means that we are left with 105 movies minus the 21 she sold.

105 - 21 = 84 → She now has <u>84</u> movie posters.


In order to answer your question, you'll need to use the cross product method:

105 movie posters → 90 band posters

84 movie posters  → X

<u>(90 × 84)</u> ÷ 105 = X

<u>7,560 ÷ 105</u> = X

72 = X ⇒ Number of band posters she should have left to maintain the same ratio.

She has 90 band posters :

90 <u>- X</u> = 72

Add "X" to each side of the equation → 72 + X = 72 + X

90 = <u>72</u> + X

Subtract 72 from each side of the equation → 90 - 72 = 18

<u>18 = X</u>


There you go! I really hope this helped, if there's anything just let me know! :)

4 0
3 years ago
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