Question

Pls answer question 12,13,14,15,16,17 urgent answer fast

Answer 1

Answer:

Step-by-step explanation:

12. We can consider two triangles by putting a common line in between. So the sum of three angles = 180 degree.

 We have x + 108 = 180

               x = 180 - 108

              x = 72 degree

  Again x + 112 = 180

         x = 68 degree

 Adding both we get 72 + 68 = 140.

So angle x = 140 degree

13. Given PRT = 40, TSQ = 75 and RPT = 95 degrees

We know that angle RPT + PRT + PTR = 180

                                 95 + 40 + PTR = 180

                            So PTR = 180 - 135 = 45 degree

 But PTR = STQ (because alternate interior angles)

 So STQ = 45 degree

     Now TSQ + SQT + STQ = 180

             75 + SQT + 45 = 180

                SQT = 180 - 120

                SQT = 60 degree

14. 1) It lies in second quadrant

    2) It lies in third quadrant  

I quadrant is all positive, II quadrant is x is -ve and y is +ve, III quadrant is all negative and IV quadrant is x is +ve and y is -ve.

15. Find the LCM of 5 and 4 we get 20

1/5 x 4/4 = 4 /20 and 1/4 x 5/5 = 5/20 so denominator is same.

 we want 3 rational numbers so

4 /20 x 4/4 = 16/80 and 5/20 x 4/4 = 20 /80. hence we can keep rational numbers as 17 /80, 18/80 and 19/80.

16.  Given to rationalize: 6 / 3 + √2

            6 / 3 + √2 x 3 - √2 / 3 - √2

           6 (3 - √2) / 9 - 2

         6 / 7 (3 - √2)

17. Given : 27 x^3 + y ^3 + z^3 - 9 xyz

             We can write the equation as (3x)^3 + y^3 + z^3 - 3 x 3 x y z

This is in the form of a ^3 + b ^3 + c ^3 - 3 a b c

This as we know is given by (a + b + c)(a^2 + b^2 + c^2 - ab - bc - ca). Now

a = 3x, b = y c = z, Substituting the values in the formula we get

(3x + y + z)(9x^2 + y^2 + z^2 - 3xy - yz - 3xz)