(a)
In the diagram, BA is parallel to DE. Find the value of x.
(b) Illustrate graphically and shade the region in which inequalities \(y - 2x < 5 ; 2y + x \geq 4 ; y + 2x \leq 10\) are satisfied.
Verified Correct Answer: .
Step-by-Step Mathematical Solution
(a)
Draw RC produced to E parallel to DE.
\(\therefore < BCR = 52^\circ\) (alternate angles BA//RC)
also < RCD = 48^\circ (alternate angles RC//DE)
\(x^\circ = 360^\circ - (52^\circ + 48^\circ) = 360^\circ - 100^\circ = 260^\circ\) (angles at a point = 360^\circ)
(b) \(y - 2x < 5 ... (i)\)
\(2y + 2x \geq 4 \implies y + x \geq 2 ... (ii)\)
\(y + 2x \leq 10 ... (iii)\)
From (i), if \(y - 2x = 5\), when x = 0, y = 5, when x = 2, y = 9.
From (ii), if \(y + x = 2\). when x = 0, y = 2, when x = 3, y = -1
From (iii), if \(y + 2x = 10\), when x = 0, y = 10, when x = 2, y = 6.
Source: Myschool Past Questions Archive (Record #54572)