Each of the interior angles of a regular polygon is 140°. How many sides has the polygon?
9
9
7
5
Correct answer is A
Each interior angle = \(\frac{(n - 2)180}{n}\)
140 = \(\frac{(n - 2)180}{n}\)
Cross multiply:
140n = 180n - 360
40n = 360
n = 9 sides ( A Nonagon)
Find the length of a side of a rhombus whose diagonals are 6cm and 8cm
8cm
5cm
4cm
3cm
Correct answer is B
The diagonal of a rhombus is a line segment that joins any two non-adjacent vertices.
A rhombus has two diagonals that bisect each other at right angles.
i.e this splits 6cm into 3cm each AND 8cm to 4cm
Using Hyp\(^2\) = adj\(^2\) + opp\(^2\)
Hyp\(^2\) = 3\(^2\) + 4\(^2\)
Hyp\(^2\) = 25
Hyp = 5
∴ Length (L) is 5cm because a rhombus is a quadrilateral with 4 equal lengths
The angle of a sector of a circle, radius 10.5cm, is 48°, Calculate the perimeter of the sector
8.8cm
25.4cm
25.6cm
29.8cm
Correct answer is D
Length of Arc AB = \(\frac{\theta}{360}\) 2\(\pi\)r
= \(\frac{48}{360}\) x 2\(\frac{22}{7}\) x \(\frac{21}{2}\)
= \(\frac{4 \times 22 \times \times 3}{30}\) \(\frac{88}{10}\) = 8.8cm
Perimeter = 8.8 + 2r
= 8.8 + 2(10.5)
= 8.8 + 21
= 29.8cm
P(-6, 1) and Q(6, 6) are the two ends of the diameter of a given circle. Calculate the radius.
6.5 units
13.0 units
3.5 units
7.0 units
Correct answer is A
PQ\(^2\) = (x2 - x1)\(^2\) + (y2 - y1)\(^2\)
= 12\(^2\) + 5\(^2\)
= 144 + 25
= 169
PQ = √169 = 13
But PQ = diameter = 2r, r = PQ/2 = 6.5 units
N60 000.00
N54 000.00
N48 000.00
N42 000.00
Correct answer is B
use "T" to represent the total profit. The first receives \(\frac{1}{3}\) T
remaining, 1 - \(\frac{1}{3}\)
= \(\frac{2}{3}\)T
The seconds receives the remaining, which is \(\frac{2}{3}\) also
\(\frac{2}{3}\) x \(\frac{2}{3}\) x \(\frac{4}{9}\)
The third receives the left over, which is \(\frac{2}{3}\)T - \(\frac{4}{9}\)T = (\(\frac{6 - 4}{9}\))T
= \(\frac{2}{9}\)T
The third receives \(\frac{2}{9}\)T which is equivalent to N12000
If \(\frac{2}{9}\)T = N12, 000
T = \(\frac{12 000}{\frac{2}{9}}\)
= N54, 000