1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
forsale [732]
3 years ago
11

An equivalent expression with a rational denominator is...

Mathematics
1 answer:
Whitepunk [10]3 years ago
4 0

Given the expression,

(8x-56x^2)/(\sqrt{14x-2})

We will have to rationalize the denominator first. To rationalize the denominator we have to multiply the numerator and denominator both by the square root part of the denominator.

[(8x-56x^2)(\sqrt{14x-2})]/[(\sqrt{14x-2})(\sqrt{14x-2})]

If we have (\sqrt{a})(\sqrt{a}), we will get \sqrt{a^2} by multiplying them. And \sqrt{a^2} = a.

So here in the problem, we will get,

[(8x-56x^2)(\sqrt{14x-2})]/(14x-2)

Now in the numerator we have (8x-56x^2). We can check 8x is common there. we will take out -8x from it, we will get,

-8x(-1+7x)

-8x(7x-1)

And in the denominator we have 14x-2. We can check 2 is common there. If we take out 2 from it we will get,

2(7x-1)

So we can write the expression as

[(-8x)(7x-1)(\sqrt{14x-2})]/[2(7x-1)]

(7x-1) is common to the numerator and denominator both, if we cancel it we will get,

(-8x)(\sqrt{14x-2})/2

We can divide -8 by the denominator, as -8 os divisible by 2. By dividing them we will get,

(-4x)(\sqrt{14x-2})

(-4x)(14x-2)^(1/2)

So we have got the required answer here.

The correct option is the last one.

You might be interested in
‼️can anyone help me with the question that says "meaning of slope" PLEASE, I NEED THIS FOR TOMORROW❗
miv72 [106K]

Answer: Slope is the measure of the steepness of a line. It can be calculated with the equation rise/run or change in y/change in x.

Step-by-step explanation:

3 0
2 years ago
Can someone help? i cannot get this question right
Blizzard [7]

Answer:

  see below

Step-by-step explanation:

The function f(x) is the absolute value function scaled vertically and shifted up. Neither of those transformations affects the interval on which it is increasing. The absolute value function increases for x > 0. (It is neither increasing nor decreasing at x=0.)

__

The function g(x) is a parabola that opens downward. Consequently, it is increasing for all values of x to the left of its vertex (or line of symmetry). That line of symmetry can be found as ...

  x = -b/(2a) = -(8)/(2·(-1)) = 4

So g(x) is increasing from -∞ to 4, but at x=4 is neither increasing nor decreasing.

__

Then the interval on which both functions are increasing is ...

  {x > 0} ∩ {x < 4} = {0 < x < 4}

This will be graphed as a line between 0 and 4 with open circles at each end.

_____

The second attachment shows the two functions so you can see where their slopes are positive.

5 0
3 years ago
Bella has 6.3 kg of berries. she packs 0.35 kg of berries in each containers. then sells each container for $2.99. how much mone
katovenus [111]

Answer:

$53.82

Step-by-step explanation:

6.3 / 0.35=18

$2.99 x 18= $53.82

hope this halps :)

8 0
3 years ago
HELP URGENT What is the total surface area of the triangular prism in square centimeters?
77julia77 [94]

Answer:

..................................................

Step-by-step explanation:

6 0
2 years ago
Write a verbal sentence to represent 5x+7=18
Romashka-Z-Leto [24]
Five times x plus seven equals eighteen 
7 0
3 years ago
Read 2 more answers
Other questions:
  • There's 754 students going to a field trip. There are only 23 buses. If only 4 students can ride each bus, how many buses will y
    8·1 answer
  • Factor the expression x^2-16x+63
    12·1 answer
  • You are given a circle of radius 12. What is the segment area of an arc that is 90 degrees?
    8·1 answer
  • Part of the psychological explanation for drug abuse has been a presumed __________, a psychological vulnerability resulting fro
    12·1 answer
  • Which of the functions have period pi?
    15·1 answer
  • A muffin recipe calls for 4 cups of sugar and yelled 36 muffins is Amelia only wants to make 2for muffins how much sugar will sh
    15·1 answer
  • the legs of a right triangle are 10 centimeters and 24 centimeters long. what is the length of the hypotenuse?
    15·2 answers
  • The PE teacher is making area for field day activities each activity will be located in a rectangular area each activity will us
    9·1 answer
  • Cathy attended a birthday party where the guests took their shoes off to jump in a bouncy castle. She made this graph to compare
    11·2 answers
  • Solve the inequity for x and identify the graph of its solution.|x+2|&lt;2
    15·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!