What is the answer for this problem in the picture

The correct answer option is .

Step-by-step explanation:

We are given the following expression and we are to simplify it and determine whether which of the given expressions is equivalent to it, assuming and :

Breaking the terms to get:

The correct answer is third option

8x⁴yz⁴√2yz

Step-by-step explanation:

It is given that,

√128x⁸y³z⁹

To find the equivalent of √128x⁸y³z⁹

We have 128 = 2⁷

x⁸ = (x⁴)², y³ = y² * y and z⁹ = (z⁴)² * z

√128x⁸y³z⁹ = √(2⁷ * (x⁴)² * y²y * (z)⁴)²z)

  = 2³x⁴yz⁴√(2 * y * z)

 = 8x⁴yz⁴√2yz

Therefore the correct answer is third option

35-60 students are taking math.

we have three similar triangles, because each has a right angle and shares an angle.   let's write the angles in order: opposite to short leg, long leg, hypotenuse.

cab similar to bad similar to cbd

or as ratios,

ca: ab: cb = ba: ad: bd = cb: bd: cd

we also know

ac = ad + cd

(ad+cd): ab: cb = ba: ad: bd = cb: bd: cd

(ad+cd)/cb=cb/cd

we have cb=6, ad=5 and seek x=cd.

we reject the negative root and conclude x=4

answer: 4