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2 Questions I need help with please.

Hi I'm new here. :smile:

Could someone please explain how to do the following two questions. Thanks.

1.Express the recurring decimal 0.427272727.... as a fraction.

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2. The diagram below shows the graph of equation y = x² + px +q

a.Find p and q.
b.Work out the coordinates of A.

Thanks. :smile:

Reply 1

steve2005

drunknmunky

Hi I'm new here. :smile:

Could someone please explain how to do the following two questions. Thanks.

1.Express the recurring decimal 0.427272727.... as a fraction.

:smile:

Let x = 0.427272 (1)
Then 100x = 42.72727 (2)
(2)-(1)
99x= 42.7 - 0.4
99x=42.3
990x=423
x=423/990

Reply 2

steve2005

drunknmunky

2. The diagram below shows the graph of equation y = x² + px +q

a.Find p and q.
b.Work out the coordinates of A.

Thanks. :smile:

-5 = (-3)²-3p+q
-5-9 =-3p + q
-14 = -3p +q
q=3p -14

0= 4 +2p +q
q= -4 -2 p
3p -14 = -4 - 2p
5p = 10
p =2
q=6-14 = -8

y= x² + 2x -8
y=(x +4 )(x - 2)
x= -4 or 2

Co-ordinates of A = ( -4, 0)

Reply 3

Mr. Pink

1. top and bottom are divisble by 9 (47/110)

2. a) just substitute the points given.

ie 0 = 2^2 + 2p + q and (-3)^2 + -3p + q = -5

and you have simultaneous equations:

2p + q = -4
-3p + q = -14

q = -8, p = 2

so y = x^2 + 2x - 8

(btw in x^2 the "^" means to the "power of" so in this case x to the power of 2)

b)First of all we make the observation that the y co-ordinate of B is 0
thus, by substituting this into the original equation,

0 = x^2 + 2x - 8

factorize the equation:

(x + 4)(x - 2) = 0

thus x+4 must equal zero or x-2 must equal zero

so, x=-4 or x=2,

the A co-ordinate has x = 2, so B must have x co-ordinate -4, thus B(-4,0)