Someone help me with this algebra question please 100% correct only

An equivalent expression with a rational denominator is...

Whitepunk [10]

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.

4 0

3 years ago

F(x)=(x−6) 2 −12.25 What are the zeros of the function? What is the vertex of the parabola?

ollegr [7]

Answer: Zeroes: 2.5 and 9.5 Vertex: (6, 12.25)

Step-by-step explanation:

:) Done on khan

7 0

1 year ago

Write an equation for each translation of y lxl 5.5 units right

ahrayia [7]

Answer:

1. 3.5 units up

2. 3/4 units down.

3. down 3 units

4. up 2 units, right 1

5. up 4 units, right 3

6. down 4 units, left 2

Step-by-step explanation:

4 0

3 years ago

If m<9=97 and m<12=114, find each measure.

seropon [69]

Answer:

a. 97

b. 83

c.66

d. 114

e.83

f. 97

g. 114

h.66

i. 83

j. 66

k.83

l.97

m. 114

n. 66

6 0

3 years ago

What is the area of a parallelogram whose bases are 9

Nady [450]

 Base=9cm

height=3 cm

Area of parallelogram=b*h

 =9*3

 =27cm^2.

Hope this will help u...:)

6 0

3 years ago