Simplify \(3\sqrt{12} + 10\sqrt{3} - \frac{6}{\sqrt{3}}\)
10\(\sqrt{3}\)
18\(\sqrt{3}\)
14\(\sqrt{3}\)
7\(\sqrt{3}\)
Correct answer is C
\(3\sqrt{12} + 10\sqrt{3} - \frac{6}{\sqrt{3}}\)
= \(3\sqrt{4\times3} + 10\sqrt{3} - \frac{6}{\sqrt{3}}\)
= \(6\sqrt{3} + 10\sqrt{3} - \frac{6}{\sqrt{3}}\)
treating like a fraction, then
= \(\frac{18 + 30 - 6}{\sqrt{3}}\)
= \(\frac{42}{\sqrt{3}}\)
rationalizing
= \(14\sqrt{3}\)
\(58^0\)
\(64^0\)
\(48^0\)
\(76^0\)
Correct answer is D
Reflex ∠MOR = 2 × 124° = 248° (angle at the centre is twice the angle at the circumference)
∠MOR = 360° - 248° = 112° (sum of angle at a point is 360°)
∠OMN = 360° - (124°+ 48° + 112°) (sum of angles in a quadrilateral is 360°)
= 360° - 284°
∴ ∠OMN = 76°
One-third of the sum of two numbers is 12, twice their difference is 12. Find the numbers.
22 and 14
20 and 16
21 and 15
23 and 13
Correct answer is C
Let the two numbers be x and y
\(\frac{1}{3}( x + y) = 12\)
then x + y = 36 ..........i
2( x - y) = 12
x - y = 6 ............ii
add equations i and ii
2x = 42
x = 21, put x = 21 into equation i
x + y = 36
21 + y = 36
y = 36 - 21 = 15
therefore the numbers are 21 and 15
147.78m
104.05m
161.87m
192.91m
Correct answer is B
From the diagram above; Tan\(\theta = \frac{opp}{adj}\)
tan50° = \(\frac{124}{d}\)
d = \(\frac{124}{tan50}\)
therefore, d = 104.05m
Mr Manu is 4 times as old as his son, Adu. 7 years ago the sum of their ages was 76. How old is Adu?
22years
12years
18years
15 years
Correct answer is C
Let Mr Manu be x years old and Adu be y years old.
But Mr Manu is four times as old as Adu then, x = 4y.
7 years ago, the sum of their ages was 76.
( x - 7) + ( y - 7) = 76
x + y - 14 = 76
x + y = 76 + 14 = 90
But x = 4y
Therefore, 4y + y = 90
5y = 90
y = \(\frac{90}{5}\)
y = 18
Therefore Adu is 18 years old.
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