Mathematics Questions and Answers

Total donation = 4 x 500 + 7 x 2000 + 20 x 1000 + 9 x 700 + 4 x 500 + 5 x 100 + 3 x 50 + 1 x 2 + 2 x 10 = 20000 + 14000 + 20000 + 6300 + 2000 + 500 + 150 + 2 + 20 = N62,972

m + n = 110\(^o\), (n + r) = 130\(^o\)

(m + n) = 120\(^o\)

then, r = 130\(^o\) - n

and;

m + (130^o - n) = 120\(^o\)

m - n = -10\(^o\)

2m + (n + r) = 110 + 120 = 230

2m + 130 = 230

2m = 230 - 130

m = \(\frac{100}{2}\) = 50\(^o\)

n = 110\(^o\) - 50\(^o\)

= 60\(^o\)

r = 130\(^o\) - 60\(^o\) = 70\(^o\)

Hence, the ratio m : n : r

= 50 : 60 : 70

= 5 : 6 : 7

In the diagram,

a = z (alternate angles)

b = 180\(^o\) - a (angles on a straight line)

b = 180\(^o\) - z

c = 180\(^o\) - x (angles on a straight line)

y = b + c (sum of oposite interior angles)

y = 180\(^o\) - z + 180\(^o\) - x

y = 360\(^o\) - z - x

x = 360\(^o\) - y - z

In the diagram, < WOZ = 180\(^o\) (angle on a straight line)

< WOX = < XOY = < YOZ

(|WX| = |XY| = |YZ|)

\(\frac{180^o}{3}\) = 60\(^o\)

= 60\(^o\)

M + m =2m (base angles of isosceles \(\bigtriangleup\), |OY| and |OZ| are radii)

< YOZ + 2m (base angles of a \(\bigtriangleup\))

60\(^o\) + 2m = 180\(^o\) (sum of a \(\bigtriangleup\))

60\(^o\) + 2m = 180\(^o\)

2m = 180\(^o\) - 60\(^o\)

2m = 120\(^o\)

m = \(\frac{120^o}{2}\)

= 60\(^o\)

x + 2 \(\geq\) 2x + 1

x - 2x \(\geq\) 1 - 2

-x \(\geq\) -1

\(\frac{-x}{-1}\) \(\geq\) \(\frac{-1}{-1}\)

x \(\leq\) 1