What is the following difference 11 sqrt 45 - 4 sqrt 5

29*sqrt(5)

Step-by-step explanation:

Start with sqrt (45). You must reduce it to it's prime factors.

45: 9 * 5            9 is not prime so reduce it.

45: 3 * 3 * 5  

When you write √45, you should replace it with √(3*3*5)

The rule is

Rule: when you have a pair of equal prime factors under a root sign, you can take one out and throw one away.

Rule 2: If there are an odd number of equal primes one of them will be left underneath the root sign.

√45 = 3√5

11sqrt(45) - 4 sqrt(5)              Substitute for 45

11*3*sqrt(5) - 4sqrt(5)            Take out sqrt(5) using the distributive property.

(11*3 - 4)*sqrt(5)                      Combine 11 * 3  

(33- 4) * sqrt(5)                       Do the subtraction

29 * sqrt(5)                             Answer

option 1 is correct.

step-by-step explanation:

y varies inversely with x and constant of variation is 4

the equation will be:

y = k/x

where k =4 so,

y = 4/x

if we put values of x of option 1 in the above equation and find values of y

y = 4/-2 => y =-2

y = 4/-1 => y = -4

y = 4/1 => y = 4

y = 4/2 => y =2

so, all the values of x and y are correct.

if we put values of x given in other options and find value of y we cannot find whole table satisfying the equation.

hence option 1 is correct.

hiking down a winding trail.

step-by-step explanation: