2,76
5. Rationalize the denominator of the following: 2 root 6 divided by root 2 + root 3

6 √2 -4 √3

Step-by-step explanation:

Here, we want to rationalize the denominator of the following surdic fraction;

2√6/(√2 + √3)

To rationalize this, we have to multiply the numerator and the denominator by the conjugate of the denominator

The conjugate of the denominator is √2 - √3

So, we have the rationalization as follows;

2 √6(√2-√3)/(√2 + √3)(√2-√3)

Thus, we have

(4√3-6 √2)/(-1)

= 6 √2 -4 √3

see explanation

step-by-step explanation:

since the sequence is geometric there is a common ratio r between consecutive terms, that is

r = 4 ÷ - 2 = - 2

r = - 8 ÷ 4 = - 2

r = 16 ÷ 8 = - 2

the next term - 13 must be incorrect as it should be - 32 for the sequence to be geometric.

the first 4 terms are therefore geometric with common ratio r = - 2

x > 1.3

step by step:

8.5−0.9x> 9.8−1.9x

step 1: simplify both sides of the inequality.

−0.9x+8.5> −1.9x+9.8

step 2: add 1.9x to both sides.

−0.9x+8.5+1.9x> −1.9x+9.8+1.9x

1x+8.5> 9.8

step 3: subtract 8.5 from both sides.

1x+8.5−8.5> 9.8−8.5

1x> 1.3

step 4: divide both sides by 1.

1x/1 > 1.3/1