Math Help Please?? Explain the answer too thank you?

Question

Rationalize the Denominator:- 
2 + square root 3 divided by 2 - square root 3

Use laws of Exponents:-
2a –2 divided by (2a) –3

Complex Numbers: 
Leave in a+bi form
3+2i divided by 3-2i

A saline solution is 20% salt. How many gallons of water must be added to dilute the mixture to 8 gals of a 15 % saline solution?

If sam can do a job in 4 days that lisa can do in 6 days and tom can do in 2 days. How long would the job take if sam, lisa and tom worked together?

Shy · Accepted Answer

Hi Princess

1.
(2 + √3) / (2 - √3)
= [(2 + √3)*(2 + √3)] / [(2 - √3)*(2 + √3)]
= (4 + 3 + 4√3) / (4 - 3)
= 7 + 4√3

2.
(2a)^-2 / (2a)^-3
= 2a^ (-2+3)
= 2a

3.
(3 + 2i) / (3 - 2i)
= (3 + 2i)(3 + 2i) / ((3 - 2i)(3 + 2i)
= (9 + 4i^2 + 12i) / (9 - 4i^2)
= (9 - 4 + 12i)/(9+4)
= (5/13) +(12/13)i

4.
quantity saline solution / Quantity water = (15 -0) / (20-15) = 15/5 = 3/1
So to 6 gallons of 20% solution add 2 gallons of water to get 8 gallons of 15% solution.

5.
Time taken by all three working together is 'T'
T/4 + T/6 + T/2 = 1
T ( 3 + 2 + 6) / 12 = 1
T=12/11 days = 1 + 1/11 days

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Math Help Please?? Explain the answer too thank you?

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