Solutions Algebra

Algebra Exercise  :  Q.1 to Q.6 ,  Q.5 and Q.7  ,   Q.8 to Q.14  , Q.15 to Q.18  ,  Q.19 to Q. 21

Answer 15

Suppose cost to charter the aircraft by 40 people = $ ‘m’ per person

The total cost will be = 40 x m

If 36 people charter the plane then the cost increased by $ 12 per person

  The total cost for 36 person will be = 36 ( m + 12 )

So, Total Cost = 40 m = 36 ( m + 12)

Equation will be like this ;

40 m = 36 ( m + 12)……………………Equation 1

40 m = 36 m + 432

40 m – 36 m = 432

4 m  = 432

m = 432/4

m = 108

      Hence cost per person to charter the plane  will be = $ 108

The fixed total cost will be = 40 x m

= 40 x 108

=  4320

                        The fixed total cost = $ 4320

                                                                                                                                                  

Answer 16 

(a)

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Answer 16 (b)

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Answer 17  – Refer the figure from the book

(a).  Co-ordinates of Q will be   :  As Q is on the negative side of origin that means coorinate of x has to be a negative number  , and Q is on the x-axis ,  means y = 0 , that is why the coordinates of  Point Q will be  ( -2, 0 )

(b).   Length of PQ  ;  PQ is the vertical length parallel to y -axis .Point P is  at 6 units away from point Q , So length of PQ = 6.

            Similarly we can find the length of QR = 2 + 5  = 7

          As the triangle PQR  is a right angle triangle , so we apply Pythagorean Theorem

                      PR is hypotenuse and PQ and QR are side arms

                        Length of  PR² =  PQ² + QR²

                                                      =    6²  + 7²

                                                                   =  36 +  49

                                                                    =  85

                                                           PR  = √85

(c).   Perimeter of Δ PQR     =  PQ + QR  +  PR

=   6  +  7  + √85

                  Perimeter of Δ PQR     =   13 + √ 85

(d).   Area of   Δ PQR    =   ½   x  base  x height

=   ½   x  7  x 6

             Area of   Δ PQR   =21

(e).

(i)

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(ii)  y-intercept  is the y-coordinate of point on the line segment PR , when x = 0

y =  mx + b ,  where m = slope and  b = y-intercept

Put any one  of the coordinate of a point , here we take coordinates of

point R( 5,0)  i.e. x = 5 and y =0

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Answer 18 (a).

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(b). 

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(c)  Slope ; m = 3 , y = 1 , x =-2

y = mx + b

1  =  3 x (-2) + b

1 = -6  + b

b = 1 + 6

b = 7

     y-intercept ‘b’ = 7

(d)  

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