Convert 5.764764764 … to a rational expression in the form of a over b, where b ≠ 0

Answers

Answer 1

Answer: I just learned a short time ago how to convert a repeating decimal to a fraction.

-- Take the repeating part of the decimal. In this one, it's '764' .

-- Make a fraction out of it by writing it over the same number of 9s.

   The fraction here is 764/999 .

-- Simplify it if possible and if you feel like it.

   764/999 can't be simplified. (I think.)

So the rational expressions for this decimal are

   (5 and 764/999)   or   5759/999   .

Answer 2

Answer:

Final answer:

To convert the repeating decimal 5.764764764... to a rational number, we first create a variable to represent the decimal, then manipulate it to remove the repeating part. The resulting rational expression is 5759/999.

Explanation:

Conversion of a Repeating Decimal to a Rational Number

Let's create a variable, X, to represent the repeating decimal 5.764764764....

X = 5.764764764...

Now, to get rid of the repeating section, we'll multiply X by 1,000 (since the repeating part is three digits). This gives us a new equation:

1,000X = 5764.764764...

We can subtract the original equation from this new one to get rid of the repeating decimal.

1,000X - X = 5764.764764... - 5.764764764...

This simplifies to 999X = 5759.

Finally, we divide both sides by the coefficient of X (999) to get:

X = 5759 / 999

Therefore, the rational expression for the repeating decimal 5.764764764... is 5759/999.

Learn more about Repeating Decimal to Rational Number here:

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I have spent quite long on this but not able to solve it. Pls help ! Thanks!

Answers

Answer:

Adriana= $960

Tania= $1080

Step-by-step explanation:

Please see the attached pictures for the full solution.

• Do note that you could also use 'x' or other variables to represent the amount of money either Adriana or Tania brought for shopping. A unit was used in this case since I used model method to represent the given situation.

Help help plz lol thanks

Answers

$(9)/(4):(3)/(16)=\ \ \ \ | multiply\ first\ fraction\ by\ inverse\ of\ the\ second\n\n(9)/(4)*(16)/(3)=(3*4)/(4)=3\n\nSolution\ is\ 3.$

$(9)/(4)/(3)/(16)=(9)/(4)\cdot(16)/(3)=3\cdot4=12$

-5X - 8y = 3
6x + 3y =3
Solve using elimination ?

Answers

Answer:

for the first one its x=30

for the second one its x=6

Step-by-step explanation:

its x=30 because at the end if you do the problem yourself, you would have to multiply 5×6 which is 30.

im not sure why its x=6 on that one i might be wrong but i did it but im also confused on it but i tried so yeah maybe it is.

Show how to solve 6/15=2/?

Answers

There are two way sof doing this question:
1st solution is :
6/15 = 2/5
because 6/15 is divisible by 3 and it is done by this form :
     3 X 2 = 6
       and
    3 X 5 = 15
2nd solution is:
6/15 = 2/?
here we suppose that the missing value is x:
6/15 = 2/x
you shift the denominators and then multiply them by the their numerators:
6 * x = 15 * 2
      6x = 30
now you divide 6 on both sides:
6x/6 = 30/6
     x = 5

6 / 15 = 2 / x

6x = 30

x = 30 / 6 = 5

Jalyn plans to sell Algebra Nation t-shirts as a fundraiser for a new scholarship initiative. The wholesale t-shirt company charges Jalyn $10.00 a shirt for 75 shirts or less. If the number of t-shirts purchased is between 76 and 150 shirts, the company will lower its price to $7.50 per shirt. If Jalyn purchases 150 or more shirts, the price will decrease to $6.00 per shirt. Which of the following statements are true? Select all that apply.

Answers

If each shirt costs $10 within the purchase of 1 to 75 shirts, the function will be: 10x (with x being the number of shirts, from 1 to 75). If each shirt costs $7.50 within the purchase of 76 to 150 shirts, the function will be: 7.5x (with x being between 76 and 150). Finally, if each shirt costs $6 within the purchase of 150 or more shirts, the function will be: 6x (with x being any number from 150 up).

Which function has an inverse function a) f(x)=|x-4|+1 (b) f(x)=25x^2+70x+49 (c) x^4 (d) x+3÷7

Answers

Answer:

$f(x)=(x+3)/(7)$ is $f^(-1)(x)=7x-3$

Step-by-step explanation:

Property of inverse function:

The function should be bijective function ( one-to-one and onto)

Option A) f(x)=|x-4|+1

It is absolute function. Not one-to-one function.

Domain: All real (-∞,∞)

Range: [1,∞)

False ( Inverse not possible )

Option B) $f(x)=25x^2+70x+49$

It is quadratic function. Not one-to-one function.

Domain: All real (-∞,∞)

Range: [0,∞)

False ( Inverse not possible )

Option C) $f(x)=x^4$

It is polynomial function with even degree. Not one-to-one function.

Domain: All real (-∞,∞)

Range: [0,∞)

False ( Inverse not possible )

Option D) $f(x)=(x+3)/(7)$

It is linear function. one-to-one and onto

Domain: All real (-∞,∞)

Range: All real (-∞,∞)

True ( Inverse possible )

Inverse of $f(x)=(x+3)/(7)$ is $f^(-1)(x)=7x-3$

Hence, The function inverse function $f(x)=(x+3)/(7)$ is $f^(-1)(x)=7x-3$

Answer: Hello there!

A function only can have an inverse if the function is injective and surjective (and continuous):

Then we need to see; if f(x1) = f(x2) = y, and x1 is different from x2, then f(x) has not an inverse:

a) f(x) = Ix - 4I + 1

for example, f(0) = I-4I + 1 = 5

and f(8) = I8 -4I + 1 = 4 + 1 = 5

then f(x) does not have an inverse

b) f(x) = 25x^2 + 70x + 49

This is a cuadratic function, wich is graphed as a arc going up or down, wich means that there are two values of x that give the same value for f(x), then this function has not inverse. (this will be the case for all even powers)

c) f(x) = x^4

Again, an even power. But let's probe it:

f(1) = 1^4 = 1

f(-1) = (-1)^4 = 1

f(x) does not have an inverse:

d) f(x) = x + 3/7

Ok, here we have a linear equation, wich means that is injective and surjective.

The inverse of this function can be g(x) = x - 3/7

proof:

f(g(x)) = f( x - 3/7) = (x - 3/7) + 3/7 = x

then f and g are inverses of each other.

(if in this case f(x) = (x + 3)/7 = x/7 + 3/7 is also a linear equation, so it is injective and surjective (and continuous), wich implies that has an inverse)

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