A rectangle has length xcm and width (x - 1)cm. If the perimeter is 16cm. Find the value of x
3\(\frac{1}{2}\)cm
4cm
4\(\frac{1}{2}\)cm
5cm
Correct answer is C
l = x; b = x - 1
perimeter = 2(l + b) = 16
l + b = \(\frac{16}{2}\) = 8
l + b = 8
x + x - 1 = 8
2x = 8 + 1
2x = 9
x = \(\frac{9}{2}\)cm
x = 4\(\frac{1}{2}\)
If sin 3y = cos 2y and 0o \(\leq\) 90o, find the value of y
18o
36o
54o
90o
Correct answer is A
sin 3y = cos 2y, but sin \(\theta\) = cos(90 - \(\theta\))
sin 3y = cos(90 - 3y)
cos(90 - 3y) = cos 2y
90 - 3y = 2y
5y = 90
y = \(\frac{90}{5}\)
y = 18o
Simplify 2\(\sqrt{3}\) - \(\frac{6}{\sqrt{3}} + \frac{3}{\sqrt{27}}\)
1
\(\frac{1}{3}\sqrt{3}\)
2\(\sqrt{3} - 5\frac{2}{3}\)
6\(\sqrt{3}\) - 17
Correct answer is B
2\(\sqrt{3}\) - \(\frac{6}{\sqrt{3}} + \frac{3}{\sqrt{27}}\)
= 2\(\sqrt{3} - \frac{6}{\sqrt{3}} + \frac{3}{\sqrt{9 \times 3}}\)
= 2\(\sqrt{3} - \frac{6}{\sqrt{3}} \times \frac{\sqrt{3}}{\sqrt{3}} + \frac{3}{3\sqrt{3}}\)
= 2\(\sqrt{3} = 6 \frac{\sqrt{3}}{3} + \frac{1}{\sqrt{3}} \times \frac{\sqrt{3}}{\sqrt{3}}\)
= 2\(\sqrt{3} - 2\sqrt{3} + \frac{\sqrt{3}}{3}\)
= \(\frac{\sqrt{3}}{3} = \frac{1}{3} \sqrt{3}\)
\(\frac{1}{5}\)
\(\frac{2}{5}\)
\(\frac{3}{5}\)
\(\frac{4}{5}\)
Correct answer is C
pr. (More than one pet)
= \(\frac{\text{No. of students with > 1 pet}}{\text{total no. of students}}\)
= \(\frac{5 + 10 + 3}{30}\)
= \(\frac{18}{30}\)
= \(\frac{3}{5}\)
Given that \(\frac{5^{n +3}}{25^{2n -3}}\) = 5º, find n
n = 1
n = 2
n = 3
n = 5
Correct answer is C
\(\frac{5^{n +3}}{25^{2n -2}}\) = 5o
\(\frac{5^{n + 3}}{5^{2(2n - 3)}}\) = 5o
n + 3 - 4n + 6 = 0
-3n + 9 = 0
-3n = -9
n = \(\frac{-9}{-3}\)
n = 3