Of course, you don't know what the dropdowns are, so, i'll tell you. 4 < 5 < 9, so √5 is between (3, 4, the square root of 3, the square root of 4) and (6, 9, the square root of 6, the square root of 9). this means that √5 is between (4 and 9, 2 and 3, 4 and 6, square root of 2 and square root of 3). so, √65 is between (6 x 2, 6 x 3, 6 x 4) and (6 x 3, 6 x 6, 6 x 9). you and me!

Part A

4 < 5 < 9 is given to us. Apply the square root to each term to end up with this inequality: sqrt(4) < sqrt(5) < sqrt(9)

So sqrt(5) is between sqrt(4) and sqrt(9)

Part B

Simplify those two mentioned square roots

sqrt(4) = sqrt(2^2) = 2

sqrt(9) = sqrt(3^2) = 3

Therefore, sqrt(5) is also between 2 and 3

We can see this through using a calculator: sqrt(5) = 2.23607 approximately

Part C

We can now say:

2 < sqrt(5) < 3

Multiply all three sides by 6

6*2 < 6*sqrt(5) < 6*3

So the expression 6*sqrt(5) is between 6 x 2 and 6 x 3

Sure enough, a calculator confirms this

6*sqrt(5) = 13.416408

since 6*2 = 12 and 6*3 = 18. We see that 13.416 is between 12 and 18.

the correct option is 2.

step-by-step explanation:

according to the given information triangle abc is a right angle triangle with right angle at a. segment ab is 5 and segment ac is 7. point d is on segment bc and angles adb and adc are right angles.

it is given that triangles abd, cad, and cba are similar.

two triangles are similar if their corresponding sides are proportional.

in triangle cba, using pythagoras theorem

                      )

triangle abd and cba are similar,

                            (2)

triangle cad and cba are similar,

                      )

using (1), (2) and (3), we get

hence proved.

therefore option 2 is correct.

b. hoped i'm right lol

step-by-step explanation: