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)
Answer 16 (b)
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)
(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
Answer 18 (a).
(b).
(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)
